Exercises in Algebra to Simple Equations Inclusive
"Exercises in Algebra to Simple Equations Inclusive" by William Allen Whitworth offers a comprehensive collection of algebraic problems designed to enhance understanding and proficiency. Originally published in 1875, this book provides a structured approach to learning algebra, focusing on fundamental concepts and equation-solving techniques. Designed as a resource for students and educators alike, this book offers a progressive set of exercises that build from basic principles to more complex applications. Its enduring relevance makes it a valuable addition to any mathematics library, offering insights into historical teaching methods and a solid foundation in algebra. Perfect for self-study or classroom use, this book remains a testament to the timeless principles of algebraic education. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Secrets of the Hidden Palace
The Great Pyramid is arguably the most recognized and celebratedstructure in the world. It has been an enduring source of wonder andintense examination and study for ages. Yet it still excites a deep senseof mystery and awe. However, it is bereft of writing or images, exceptfor some construction markings. Wrong!It has writing in it that carries some of the most significant meaningof the ages, in languages that are both universal and timeless, thelanguages of mathematics and geometry.The Pyramid's shape and size are written in this language and reflectthe fact that its inception is in the heavens north of it. Here the northecliptic and north celestial poles create triangles that determine thePyramid's shape and its dimensions exactly. But this is only a beginning, as these same measures were used to determine the dimensions of theEarth. Astonishing, but true.There are also a substantial number of geometric images or figures thatwere encoded into the walls of the King's Chamber, using rudimentaryastronomical techniques. These figures comprise triangles, rectangles, stars, and circles, many of which have meanings in their own right, but when viewed in combination with others tell a profound tale, thesame one told by Plato in Timaeus. It is the tale of god and creation, andboth are told in the language of geometry. And, not by coincidence, thefigures in the Pyramid also name the Egyptian god of creation, Ptah.
The Propositions of the Fifth Book of Euclid Proved Algebraically
"The Propositions of the Fifth Book of Euclid Proved Algebraically" offers a rigorous exploration of Euclidean geometry through the lens of algebraic methods. Authored by George Sturton Ward, this treatise provides alternative proofs for Euclid's propositions, enhancing the understanding of fundamental geometric principles. By bridging the gap between geometry and algebra, this work serves as a valuable resource for students and educators alike. Its enduring relevance lies in its ability to illuminate the interconnectedness of mathematical disciplines and offer fresh perspectives on classic geometric theorems. This book is essential for anyone seeking a deeper appreciation of both Euclidean geometry and the power of algebraic reasoning.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Secrets of the Hidden Palace
The Great Pyramid is arguably the most recognized and celebratedstructure in the world. It has been an enduring source of wonder andintense examination and study for ages. Yet it still excites a deep senseof mystery and awe. However, it is bereft of writing or images, exceptfor some construction markings. Wrong!It has writing in it that carries some of the most significant meaningof the ages, in languages that are both universal and timeless, thelanguages of mathematics and geometry.The Pyramid's shape and size are written in this language and reflectthe fact that its inception is in the heavens north of it. Here the northecliptic and north celestial poles create triangles that determine thePyramid's shape and its dimensions exactly. But this is only a beginning, as these same measures were used to determine the dimensions of theEarth. Astonishing, but true.There are also a substantial number of geometric images or figures thatwere encoded into the walls of the King's Chamber, using rudimentaryastronomical techniques. These figures comprise triangles, rectangles, stars, and circles, many of which have meanings in their own right, but when viewed in combination with others tell a profound tale, thesame one told by Plato in Timaeus. It is the tale of god and creation, andboth are told in the language of geometry. And, not by coincidence, thefigures in the Pyramid also name the Egyptian god of creation, Ptah.
Exercises in Algebra to Simple Equations Inclusive
"Exercises in Algebra to Simple Equations Inclusive" by William Allen Whitworth offers a comprehensive collection of algebraic problems designed to enhance understanding and proficiency. Originally published in 1875, this book provides a structured approach to learning algebra, focusing on fundamental concepts and equation-solving techniques. Designed as a resource for students and educators alike, this book offers a progressive set of exercises that build from basic principles to more complex applications. Its enduring relevance makes it a valuable addition to any mathematics library, offering insights into historical teaching methods and a solid foundation in algebra. Perfect for self-study or classroom use, this book remains a testament to the timeless principles of algebraic education. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
![Key to Exercises in Euclid [Book 1-6 and Parts of Book 11,12]](https://cdn.kingstone.com.tw/english/images/product/3478/9781023913478m.webp?Q=d8b08 "Key to Exercises in Euclid [Book 1-6 and Parts of Book 11,12]")
Key to Exercises in Euclid [Book 1-6 and Parts of Book 11,12]
This book provides the solutions and answers to the exercises found in Isaac Todhunter's edition of Euclid's Elements. Covering Books 1-6 and parts of Books 11 and 12, this key is designed to assist students and educators in mastering Euclidean geometry. It offers step-by-step solutions and explanations, making it an invaluable resource for self-study or classroom use.Originally intended to complement the textbook, this key enhances understanding of geometric principles and cultivates problem-solving skills. "Key to Exercises in Euclid" is essential for anyone seeking a deeper engagement with classical geometry and its applications. It remains relevant for modern students and teachers alike due to the enduring importance of Euclidean geometry in mathematical education.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A New & Compleat Treatise of the Doctrine of Fractions, Vulgar & Decimal ...
"A New & Compleat Treatise of the Doctrine of Fractions, Vulgar & Decimal," by Samuel Cunn, first published in 1714, offers a comprehensive exploration of fractions, both vulgar (common) and decimal, as understood in the early 18th century. This treatise provides a detailed explanation of arithmetical principles and practices related to fractions, offering insights into the mathematical techniques employed during this period. In addition to its focus on fractions, the book includes an epitome of duodecimals-a system of calculation based on twelve-and an idea of measuring, showcasing practical applications of mathematical concepts in everyday life. This work is a valuable resource for those interested in the history of mathematics, early modern education, and the evolution of mathematical notation and methodology. Cunn's treatise reflects the intellectual curiosity and practical concerns of his time, making it a compelling read for historians, mathematicians, and anyone fascinated by the development of mathematical thought.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elements of Geometry
"Elements of Geometry, Volume 2" by Irving Fisher and Andrew Wheeler Phillips, is a comprehensive exploration of geometric principles, designed for students and educators alike. This volume builds upon fundamental concepts, offering a detailed treatment of advanced topics within Euclidean geometry. The book is structured to provide a clear and logical progression, making it an invaluable resource for both classroom instruction and self-study.With its rigorous approach and numerous examples, "Elements of Geometry" remains a relevant and essential text for anyone seeking a deep understanding of geometric theory and its applications. This edition preserves the original clarity and precision, ensuring its continued value for generations of learners.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
G?(c)om?(c)trie Analytique, Ou, Application De L’alg癡bre ?€ La G?(c)om?(c)trie
"G矇om矇trie Analytique, Ou, Application De L'alg癡bre ? La G矇om矇trie" by Jean-Guillaume Garnier, originally published in 1813, explores the application of algebra to geometry. This historical text provides insights into the development of analytic geometry and showcases the mathematical techniques of the early 19th century. Garnier's work offers a detailed exposition of the principles connecting algebraic equations with geometric forms, making it a valuable resource for understanding the foundations of modern mathematical analysis. This edition retains the original language and notation, preserving its historical authenticity and making it an essential addition to the libraries of mathematicians, historians of science, and anyone interested in the evolution of mathematical thought.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Practical Treatise On Arithmetic
"A Practical Treatise On Arithmetic" by George Leonard, originally published in 1839, offers a comprehensive system for understanding arithmetic principles. This treatise distinguishes itself by explaining each concept in a simple and accessible manner, making it ideal for students and educators alike. Beyond basic calculations, the book includes a detailed description of bookkeeping practices, providing practical applications for the arithmetic principles discussed. This combination of theoretical knowledge and practical skills makes it a valuable resource for anyone seeking a solid foundation in mathematics and financial record-keeping. Its historical context also provides insight into 19th-century educational methods.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Advanced Arithmetic
Advanced Arithmetic, by Charles William Morey, offers a comprehensive exploration of arithmetic principles designed for advanced students and educators. Published in 1917, this book provides a detailed study of fundamental arithmetic concepts, accompanied by numerous exercises and practical applications. Morey's work not only covers standard topics but also delves into advanced areas, making it an invaluable resource for those seeking a deeper understanding of mathematical reasoning. Its historical context provides insight into early 20th-century educational practices, offering a unique perspective on the teaching of arithmetic. This edition retains the original content, ensuring that readers can experience the material as it was initially intended. Whether used as a reference, a teaching aid, or a historical artifact, 'Advanced Arithmetic' remains a valuable contribution to the field of mathematics education.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Practice Exercises in Probability Distributions
This book presents a comprehensive collection of solved exercises in probability theory, intended for students, educators, and practitioners in the fields of mathematics, statistics, and related disciplines. The work covers both discrete and continuous probability distributions, exploring fundamental concepts such as random variables, expectation, variance, probability laws, conditional probability, independence, and the central limit theorem. Through a series of carefully structured problems accompanied by rigorous solutions, readers are introduced to classical distributions including binomial, geometric, Poisson, uniform, exponential, and normal distributions. Each chapter is designed to strengthen conceptual understanding and to develop analytical proficiency through application-driven scenarios such as quality control, random sampling, reliability modeling, and statistical inference. In addition to core topics, the book integrates advanced problem-solving strategies, approximation techniques (e.g., normal approximation to the binomial distribution), and real-world applications that bridge theoretical concepts with practical relevance.
A Practical Treatise On Arithmetic
"A Practical Treatise On Arithmetic" by George Leonard, originally published in 1839, offers a comprehensive system for understanding arithmetic principles. This treatise distinguishes itself by explaining each concept in a simple and accessible manner, making it ideal for students and educators alike. Beyond basic calculations, the book includes a detailed description of bookkeeping practices, providing practical applications for the arithmetic principles discussed. This combination of theoretical knowledge and practical skills makes it a valuable resource for anyone seeking a solid foundation in mathematics and financial record-keeping. Its historical context also provides insight into 19th-century educational methods.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Determinants of Project Success in Emergency Projects
This book investigates the critical success factors (CSFs) for Emergency Humanitarians projects in the Tigray region of Ethiopia for the period of the concurrent post conflict situation. A total of 46 respondents selected from various humanitarian non-governmental organizations participated in the study, yielding a response rate of 92%. The research employed a binary regression model to identify the significant determinants of project success. The findings reveal that project team experience and commitment, stakeholder management, proposal designing, monitoring and evaluation, implementation management, and communication management significantly influence project success, with p-values less than 0.05. These factors collectively account for an 89.1% project success ratio. Interestingly, project risk management, often considered a key aspect of project success, was not found to be a significant determinant in this context (p>0.05). The study underscores the meaningful achievements made by emergency humanitarian projects across all technical components and households exposed to more project activities. It concludes that effective management involvement, communication, team commitment.
Advanced Arithmetic
Advanced Arithmetic, by Charles William Morey, offers a comprehensive exploration of arithmetic principles designed for advanced students and educators. Published in 1917, this book provides a detailed study of fundamental arithmetic concepts, accompanied by numerous exercises and practical applications. Morey's work not only covers standard topics but also delves into advanced areas, making it an invaluable resource for those seeking a deeper understanding of mathematical reasoning. Its historical context provides insight into early 20th-century educational practices, offering a unique perspective on the teaching of arithmetic. This edition retains the original content, ensuring that readers can experience the material as it was initially intended. Whether used as a reference, a teaching aid, or a historical artifact, 'Advanced Arithmetic' remains a valuable contribution to the field of mathematics education.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Cambridge Mathematical Journal
The Cambridge Mathematical Journal, Volume 2, presents a fascinating snapshot of mathematical thought and inquiry in the mid-19th century. This volume showcases a collection of articles, problems, and solutions contributed by leading mathematicians and scholars of the time. It offers insights into the mathematical challenges and innovations that shaped the field during this period. Published in 1841, this journal reflects the intellectual climate of Cambridge University and the broader scientific community. It remains a valuable resource for historians of mathematics, researchers, and anyone interested in the development of mathematical ideas and techniques. Explore the historical roots of modern mathematics through this meticulously preserved volume.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A New & Compleat Treatise of the Doctrine of Fractions, Vulgar & Decimal ...
"A New & Compleat Treatise of the Doctrine of Fractions, Vulgar & Decimal," by Samuel Cunn, first published in 1714, offers a comprehensive exploration of fractions, both vulgar (common) and decimal, as understood in the early 18th century. This treatise provides a detailed explanation of arithmetical principles and practices related to fractions, offering insights into the mathematical techniques employed during this period. In addition to its focus on fractions, the book includes an epitome of duodecimals-a system of calculation based on twelve-and an idea of measuring, showcasing practical applications of mathematical concepts in everyday life. This work is a valuable resource for those interested in the history of mathematics, early modern education, and the evolution of mathematical notation and methodology. Cunn's treatise reflects the intellectual curiosity and practical concerns of his time, making it a compelling read for historians, mathematicians, and anyone fascinated by the development of mathematical thought.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Mathematical Modelling
Manual loading is one of the primary activities and consumes a good amount of time in the Coal mine. With formulation of the mathematical model, improvements in the present method of manual loading which can conserve human energy besides increasing the productivity and reducing the time required. Some of the variables used to formulate this model are (1) Environment of working area such as illumination, ambient temperature and air circulation facility around the manual loading coal mine work station, (2) Anthropometric data which include the ergonomic aspects and (3) Tools used by miner for manual loading operation which include geometric dimensions of tool, based on the data collected of these variables, a mathematical model is formulated.
G?(c)om?(c)trie Analytique, Ou, Application De L’alg癡bre ?€ La G?(c)om?(c)trie
"G矇om矇trie Analytique, Ou, Application De L'alg癡bre ? La G矇om矇trie" by Jean-Guillaume Garnier, originally published in 1813, explores the application of algebra to geometry. This historical text provides insights into the development of analytic geometry and showcases the mathematical techniques of the early 19th century. Garnier's work offers a detailed exposition of the principles connecting algebraic equations with geometric forms, making it a valuable resource for understanding the foundations of modern mathematical analysis. This edition retains the original language and notation, preserving its historical authenticity and making it an essential addition to the libraries of mathematicians, historians of science, and anyone interested in the evolution of mathematical thought.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Numerical Solutions of Heat and Mass Transfer in Different Geometries
This book focuses on research related to heat and mass transfer problems in various geometries with different physical parameters. Governing partial differential equations are converted into coupled ordinary differential equations and solved using numerical techniques supported by MATLAB. Chapter 1 introduces the topic, literature, basic concepts related to heat and mass transfer, boundary-layer theory and relevant equations. Chapter 2 investigates the MHD Darcy-Forchheimer Jeffrey nanofluid flow over a nonlinear radial stretching sheet with radiation and heat generation/absorption. Chapter 3 explores the numerical study of Carreau fluid over a porous vertical microchannel, entropy generation in heat transport. Chapter 4 analyzes thermally radiative buoyancy flow influenced by higher-order chemical reactions and microbial suspensions. Chapter 5 presents the radiative flow of magneto Casson fluid via a vertical microchannel, focusing on steady entropy generation fluid. Across chapters, PDEs are transformed into ODEs using similarity transformations, solving two-point BVPs. Results are graphically and tabularly presented, showcasing velocity, temperature, and concentration profiles.
Time Series Forecasting of Meteorological Parameters
This book focuses on the time series forecasting of critical meteorological parameters including temperature, rainfall, humidity, and wind. It explores classical statistical models such as ARIMA, Holt-Winters, and Exponential Smoothing, along with a novel enhancement-the Modified Sliding Window Algorithm. The objective is to improve prediction accuracy in meteorological datasets by applying adaptive techniques. Real-time weather data has been analyzed using these models, and a comparative study highlights the performance of each. This work is beneficial for researchers, meteorologists, and data scientists working in climate modeling and weather prediction.
Probability
This book serves as a tutorial guide, covering both MATLAB's fundamental functions and its applications in probability theory and statistical analysis. Designed for beginners and those seeking to deepen their understanding, this resource seamlessly integrates theoretical knowledge with practical applications.
The Chemotaxis-Navier Stokes Equations in Bounded Domain
When bacteria of the species Bacillus subtilis are suspended in water, it can be observed experimentally that spatial patterns may spontaneously emerge from initially almost homogeneous distributions of bacteria. A mathematical model for such processes was proposed in many literatures, where it is assumed that the essentially responsible mechanisms are a chemotactic movement of bacteria towards oxygen which they consume, a gravitational effect on the motion of the fluid by the heavier bacteria, and a convective transport of both cells and oxygen through the water. We've studied chemotaxis-Navier-Stokes systems for several years and obtained some important results. In the current edition, we synthesis and analysis these results as well as make our effort to give the proofs of them in detail and perfectly. However, in this process, we have benefited enormously. In conclusion, we hope that the interested scientist will enjoy this book and derive great benefit from reading it just as we did while writing it.
Spatiotemporal Population Modeling and Simulation Using MATLAB
Spatiotemporal population modeling uses mathematical and computational tools to analyze how populations change over time and space. MATLAB provides a flexible environment for simulating these dynamics through differential equations, agent-based models, and spatially explicit frameworks. Such models help study species distribution, migration, and interactions with environmental factors. Key components include spatial grids, time-stepping methods, and parameter estimation. Applications range from ecology and epidemiology to urban planning. MATLAB's built-in functions and toolboxes allow for visualization, numerical integration, and GIS data handling, making it ideal for modeling habitat fragmentation, dispersal, and population responses to environmental changes. This approach supports both deterministic and stochastic simulations, offering insights into complex biological systems.
Modern Statistical Computing and Data Analysis with RStudio and SAS
Modern Statistical Computing and Data Analysis with RStudio and SAS offers a practical, hands-on introduction to the essential tools and techniques used in modern data science. Blending statistical theory with real-world applications, this book guides readers through data manipulation, visualization, modeling, and interpretation using two of the most powerful platforms in the field RStudio and SAS. Ideal for students, researchers, and professionals, it emphasizes clarity, reproducibility, and the integration of computational thinking in statistical analysis.
Model Order Reduction Techniques in Control System Design
In modeling physical systems, the order of the system gives an idea of the measure of accuracy of the modeling of the system. The higher order system model will be more accurate in describing the physical system. But in several cases, the amount of information contained in a complex model may obfuscate simple, insightful behaviors, which can be better captured and explored by a model with a much lesser order. Thus, by approximating a higher order system to a suitable lower order system, a much better understanding of the system is reached. Hence, the process of Model Order Reduction involves studying the properties of a complex dynamic system in application for reducing its complexity, while preserving (to the maximum possible extent) its input - output behavior. Depending upon the practical application, certain specific properties of the higher order complex system have to be preserved in the reduced order model. The detailed comparative analysis of proposed model order reduction scenarios over the conventional reduction schemes has been presented in this book to validate the effectiveness of the proposed reduction schemes.
Advances in the Approximation for the Mathematical Constants
This book is the mathematical reference book which is helpful and accessible for not only professional mathematicians but also readers who have a little knowledge of mathematics.Mathematical constants have important applications in almost every field of engineering and science.In the study of mathematical constants, the remarkable trend is to find more accurate approximations and inequalities for them. Hence, many mathematicians and scientists have made great efforts in this subject of establishing more precise approximations for the mathematical constants and had lots of inspiring results. In this book, we extend our remarkable results and offer a more comprehensive overview.The book contains 3 chapters.Chapter 1 describes new sequences with continued fraction towards the Euler-Mascheroni constant and generalized Euler-Mascheroni constant, and summarizes several methods often employed to evolute the rate of convergence of our new sequences.Chapter 2 deals with our new classes of sequences converging to the Lugo's constant based on continued fraction, and summarizes several methods often employed to evolute the rate of convergence of our new sequences.
Nonmonotone Methods for Solving Multi-objective Optimization Problems
In recent years, the multi-objective optimization (vector optimization) problems has been actively studied and widely applied in many fields of science such as medicine, economics, finance, engineering, radio resource management, discrete optimization, variational inequality, computational biology, machine design and control, environmental science, agriculture, production and management activities, etc.In this book we propose a nonmonotone methods to solve the multi-objective optimization problem, which makes use of approximation to Hessian matrices of the objective functions by diagonal positive matrices in computing search direction.Finally, we proved the effectiveness of the proposed methods by numerical experiments.
Linear Algebra I with MATLAB
Linear Algebra is a fundamental branch of mathematics that plays a crucial role in numerous fields, including engineering, physics, computer science, and data science. This book, Linear Algebra I with MATLAB, aims to provide a clear and practical introduction to the subject, integrating mathematical theory with computational applications using MATLAB.The book is structured to cover essential topics such as matrices, determinants, systems of linear equations, vector spaces, and transformations. Each chapter presents theoretical concepts with rigorous mathematical proofs, followed by computational techniques that illustrate their implementation in MATLAB. Through examples, exercises, and MATLAB code snippets, readers will gain both theoretical understanding and practical problem-solving skills.This book is contains four chapters Matrices, Determinants, System of linear equations, Spatial vectors.
A time fractional reaction-diffusion equation
The reaction-diffusion equation is a differential equation that mathematically models problems in various fields of the national economy such as food, chemical, biotechnology, etc., but there are still many open questions.In this book, we introduce recent developments in nonlinear reaction-diffusion equationThe book is organized in three chapters and seven sections.In Chapter 1, the mathematical theory of the initial-boundary value problem of the reaction-diffusion equation and the previous results concerning the optimal control problem of the system described by the reaction-diffusion equation are summarized, the problems to be solved in the paper are presented, and some basic results are presented.Chapter 2 demonstrates the existence and uniqueness of weak solutions to the initial-boundary value problem of a time-fractional system of reaction-diffusion equations (fractional Selkov model).In Chapter 3, we show the existence of solutions to the optimal control problem of a system described by an initial-boundary value problem of a time fractional system of reaction-diffusion equations, and derive the optimality condition of this optimal control problem.
Functional Phase Space Methods
This book focuses on functional phase space methods in quantum optics and provides a comprehensive introduction to the Wigner functional formalism. The book shows how this formalism can be used for analyzing and designing practical photonic quantum information systems. It also explains in detail the application of the Wigner functional formalism to parametric down-conversion, an important process in quantum optics.
Statistical Computing With Machine Learning
Statistical Computing with Machine Learning explores the powerful synergy between statistical analysis and machine learning techniques in addressing real-world medical challenges. With a strong focus on disease prediction and diagnosis, this book bridges foundational theory with cutting-edge applications, offering researchers, practitioners, and students a comprehensive guide to modern healthcare analytics.
Applied Cluster Analysis - Part I
This book is Part 1 of a series on cluster analysis, developed through a search to define its boundaries. While many existing sources mention topics covered here, this book offers new reflections, developments, and example applications that provide fresh insights into cluster analysis. Its primary goal is to introduce new perspectives while exploring various ideas and approaches. Topics include the goals and assumptions of cluster analysis, its importance and applications, and an overview of common clustering models along with their use, distance measures, and selection criteria. The book also covers popular methods for evaluating clustering quality and validating clusters, supported by multiple example applications.Additionally, it addresses common challenges in determining the number of clusters, with attention to both hierarchical and non-hierarchical methods. The book concludes with a discussion on typical cluster types found in datasets and offers guidance on how to classify them accurately.
Sampling Techniques
"Sampling Techniques: From Fundamentals to Advanced Applications" is a comprehensive guide that covers both classical and modern approaches to sampling. Aimed at master's level students and professionals, the book blends theory, real-world applications, and computational tools.It begins with core sampling concepts and classical methods like SRS, stratified, and cluster sampling, then advances to specialized topics including adaptive sampling, Bayesian methods, and model-assisted techniques. Each chapter includes theorems, proofs, examples, illustrations, exercises with solutions, and coding practices in R and Python.This book equips readers with the knowledge to design efficient surveys and analyze data in fields such as public health, business, environment, and policy research.
Performance Enhancement in Multiprocessing Systems
Parallel processing is an efficient form of information processing that emphasizes the concurrent manipulation of data elements belonging to one or more processes solving a single problem. It makes a tremendous impact on many areas of computer applications like computational simulations for scientific and engineering applications, commercial applications in data mining, transaction processing etc. It is one of the approaches known today, to make computation feasible. Heterogeneous systems create unlimited opportunities and challenges in the fields of parallel processing, design of algorithms, and partitioning and mapping of parallel tasks. In mapping of parallel tasks, scheduling plays an important role. In this book, three algorithms Task oriented Dynamic Scheduling Algorithm (TDSA), Dynamic Task Duplication based Scheduling Algorithm (DyDupSA) and Dynamic Ant Colony Optimization (DyACO) are proposed. TDSA algorithm use the concept of migration, DyDupSA applies duplication and migration and DyACO meta heuristic to minimize the makespan and to maximize the processor utilization. Among the proposed algorithms, DyACO algorithm outperforms the other algorithms.
A posteriori error estimates of FEM
Different real-life objects and technological processes are mathematical problems that need to be solved to achieve optimal control over the object described by elliptic differential equations. The technique of finite element method has become one of the main tools of numerical methods for solving differential equations today and has found wide application in the solution of the optimal control problem of systems described by differential equations.In this book, we describe the finite element method, error estimation method and detailed numerical simulation method to solve the optimal control problem of some semi-linear second order elliptic differential equations in two dimensions.In Chapter 1, finite element posteriori error estimation, convergence and numerical simulation for the source optimal control problem of semi-linear elliptic equations with nonlinear Robin boundary conditions are presented.In Chapter 2, we evaluate the finite element posteriori error and the priori error for the source optimal control problem of a semi-linear system of convection-diffusion equations with Dirichlet boundary conditions and describe the numerical simulations.
Mosquito Ecology in The Urban Area
The study investigates mosquito ecology in Rajkot City, Gujarat, India, focusing on species diversity, breeding habitats, and adult resting preferences in an urban setting. A total of nine mosquito species across four genera were identified through larval and adult sampling conducted between January 2006 and December 2007. Breeding habitats included domestic water containers, drains, and natural water bodies, with species-specific preferences observed. Seasonal variation in larval and adult densities showed peak populations during monsoon and post-monsoon months, influenced by rainfall, temperature, and humidity. High densities of Culex quinquefasciatus and Anopheles stephensi indicate a substantial vector risk. The study highlights the importance of environmental management, community awareness, and integrated vector control strategies for effective mosquito control in urban areas like Rajkot. 'Prevention is better than a cure'.
Numerical Methods for Fractional Partial Differential Equations
In this book, we describe the definition and the properties of fractional derivative and fractional integral and the approximation methods of fractional derivative and give the solutions of some time-fractional diffusion equations by the difference method.The main aspects of the analysis of difference equations are stability, convergence and error estimations.The essential difference from the other books is that for some fractional diffusion equations with nonlocal boundary conditions as well as ones with classical boundary conditions, stability and error estimates of the difference equations in uniform and graded grids, respectively, are given and computational examples are given to show the validity of the theory.
Numerical and Algorithmic Approaches for Solvable Integrals
This third volume of the Numerical and Algorithmic Approaches to Integrals series focuses on error analysis, precision, and comparison of major numerical integration methods applied to analytically solvable integrals. Combining theoretical rigor with practical Python implementation, the book offers a systematic study of absolute and relative errors, algorithm design, and guided, corrected exercises. Each method follows a consistent structure: theoretical foundations, precision estimation, algorithm development, and hands-on application. Designed for students in the sciences, as well as researchers and engineers, this volume helps consolidate numerical analysis skills through an autonomous, progressive, and comparative reading experience. It serves as a valuable resource for mastering the reliability of numerical methods in academic and professional settings that demand both precision and analytical depth.
Advanced Numerical and Algorithmic Approaches for Irresolvable Integrals
This fourth volume, Advanced Numerical and Algorithmic Approaches for Irreducible Integrals, is intended for students, researchers, and engineers dealing with integrals that cannot be solved analytically. Through a rigorous framework, it presents error bounds, estimates of maximum achievable precision, and methods for determining the optimal number of intervals required. Each numerical technique is illustrated with an algorithm, a Python implementation, and exercises grounded in diverse application domains such as biology, finance, and telecommunications. By combining mathematical theory, computational tools, and real-world case studies, the book offers a clear methodological framework for assessing and mastering the precision of numerical methods. This volume completes a four-part series dedicated to both analytical and numerical integration, delivering a structured, comprehensive, and practically oriented vision of integral calculus in the sciences and engineering.
Evolutionary Dynamic Equations
The book discusses the stability, observability, and controllability of nonlinear systems of PDEs (such as Wave, Heat, Euler-Bernoulli beam, Petrovsky, Kirchhoff, equations, and more). Methods based on the theory of classical weak functions analysis and movements in Sobolev spaces are used to analyze nonlinear systems of evolutionary partial differential equations. With the unifying theme of evolutionary dynamic equations, both linear and nonlinear, in more complex environments with different approaches, the book presents a multidisciplinary blend of topics, spanning the fields of PDEs applied to various models coming from theoretical physics, biology, engineering, and natural sciences.This comprehensive book is prepared for a diverse audience interested in applied mathematics. With its broad applicability, this book aims to foster interdisciplinary collaboration and facilitate a deeper understanding of complex phenomenon concepts, practically in electromagnetic waves, the acoustic model for seismic waves, waves in blood vessels, wind drag on space, the linear shallow water equations, sound waves in liquids and gases, non-elastic effects in the string.
Nonlinear Analysis and Computational Techniques
The book focuses on the theory of fixed points, which is a foundation for many branches of pure and applied mathematics. Fixed point theorems have been studied in various function spaces. The book contains modern results on these theorems, investigated in generalized spaces such as S-metric spaces, convex metric spaces, and bipolar metric spaces, with applications in medical imaging. The nonlinear analysis presented in the book is valuable for modeling and solving real-world problems. It includes work on specific nonlinear operators and nonlinear fractional integral equations in Banach spaces. Relevant studies are also included on statistical convergence, inventory model modeling, computational techniques for Sentiment Analysis on Twitter Data, and Blood Management applications. The book is intended for young researchers interested in nonlinear analysis, fixed-point theory, and computational techniques.
Applied Analysis (3rd Ed)
This book is to be a new edition of Applied Analysis. Several fundamental materials of applied and theoretical sciences are added, which are needed by the current society, as well as recent developments in pure and applied mathematics. New materials in the basic level are the mathematical modelling using ODEs in applied sciences, elements in Riemann geometry in accordance with tensor analysis used in continuum mechanics, combining engineering and modern mathematics, detailed description of optimization, and real analysis used in the recent study of PDEs. Those in the advance level are the integration of ODEs, inverse Strum Liouville problems, interface vanishing of the Maxwell system, method of gradient inequality, diffusion geometry, mathematical oncology. Several descriptions on the analysis of Smoluchowski-Poisson equation in two space dimension are corrected and extended, to ensure quantized blowup mechanism of this model, particularly, the residual vanishing both in blowup solution in finite time with possible collision of sub-collapses and blowup solutions in infinite time without it.
Point-Set Topology with Topics
This textbook can be used as introduction to a general topology course at undergraduate and graduate level courses. However, many parts of this book present topological concepts that apply directly to functional analysis, which will be of interest to scholars working in those fields.In Part I, readers are eased into the main subject matter of general topology, being presented with summaries of normed vector spaces and metric spaces. Parts II to VI form the core material contained in most Basic General Topology courses. After having worked through the most fundamental concepts of topology, the reader will be exposed to brief introductions to more specialized or advanced topics of pointset topology. These are presented in Part VII in the form of a sequence of chapters, many of which can be read or studied independently or in short sequences of two or three chapters, provided that the student has mastered the previous sections.Chapters related to the more basic ideas of general topology are followed by a collection of 'concept review' questions, the answers to which are found in the main body of the text. These questions highlight the main concepts presented in that chapter, as well as ideas that are often overlooked when first encountered, which will help to test the students' understanding. The efforts required in answering correctly such questions will provide the student with the ability to solve more complex problems in the exercises collected at the end of each section.
Solutions of the Cambridge Problems for ... 1840, 1841
"Solutions of the Cambridge Problems for ... 1840, 1841" offers a comprehensive guide to solving mathematical problems presented to students at Cambridge University. Compiled by John Adams Coombe, this volume provides detailed solutions to the questions posed during the 1840 and 1841 examinations. It serves as an invaluable resource for students preparing for similar rigorous assessments.This book not only aids in mastering mathematical concepts but also provides insights into the educational standards and methods prevalent in 19th-century Cambridge. Its enduring value lies in its capacity to illustrate problem-solving techniques and deepen understanding of mathematical principles, making it a relevant historical artifact for educators and mathematics enthusiasts alike.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Solutions of the Cambridge Problems for ... 1840, 1841
"Solutions of the Cambridge Problems for ... 1840, 1841" offers a comprehensive guide to solving mathematical problems presented to students at Cambridge University. Compiled by John Adams Coombe, this volume provides detailed solutions to the questions posed during the 1840 and 1841 examinations. It serves as an invaluable resource for students preparing for similar rigorous assessments.This book not only aids in mastering mathematical concepts but also provides insights into the educational standards and methods prevalent in 19th-century Cambridge. Its enduring value lies in its capacity to illustrate problem-solving techniques and deepen understanding of mathematical principles, making it a relevant historical artifact for educators and mathematics enthusiasts alike.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Cambridge Mathematical Journal
The Cambridge Mathematical Journal, Volume 2, presents a fascinating snapshot of mathematical thought and inquiry in the mid-19th century. This volume showcases a collection of articles, problems, and solutions contributed by leading mathematicians and scholars of the time. It offers insights into the mathematical challenges and innovations that shaped the field during this period. Published in 1841, this journal reflects the intellectual climate of Cambridge University and the broader scientific community. It remains a valuable resource for historians of mathematics, researchers, and anyone interested in the development of mathematical ideas and techniques. Explore the historical roots of modern mathematics through this meticulously preserved volume.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elements of Geometry
"Elements of Geometry, Volume 2" by Irving Fisher and Andrew Wheeler Phillips, is a comprehensive exploration of geometric principles, designed for students and educators alike. This volume builds upon fundamental concepts, offering a detailed treatment of advanced topics within Euclidean geometry. The book is structured to provide a clear and logical progression, making it an invaluable resource for both classroom instruction and self-study.With its rigorous approach and numerous examples, "Elements of Geometry" remains a relevant and essential text for anyone seeking a deep understanding of geometric theory and its applications. This edition preserves the original clarity and precision, ensuring its continued value for generations of learners.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
