An Elementary Course in the Integral Calculus
"An Elementary Course in the Integral Calculus" by Daniel Alexander Murray offers a comprehensive introduction to the principles and applications of integral calculus. Originally published in 1898, this textbook provides a structured approach to understanding integration techniques, making it an invaluable resource for students and educators alike. The book covers a wide range of topics, from basic integration rules to more advanced methods, ensuring a solid foundation in the subject. Murray's clear and concise explanations, coupled with numerous examples and exercises, make this text accessible to learners of all levels. This historical edition remains relevant for its rigorous treatment of the subject matter and its contribution to the development of 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.
Geschichte der Mathematischen Wissenschaften. Erster-zweiter Teil
"Geschichte der Mathematischen Wissenschaften. Erster-zweiter Teil" by Heinrich Suter, originally published in 1875, is a comprehensive historical account of the mathematical sciences. This meticulously researched work provides invaluable insights into the development of mathematics through the ages. Suter's detailed narrative explores key figures, significant discoveries, and the evolution of mathematical thought. This historical text serves as a crucial resource for scholars, students, and anyone interested in the rich heritage of mathematical knowledge. The book captures the intellectual climate of the 19th century, offering a glimpse into the foundations upon which modern mathematics was built.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.
Complex functions and integral transforms - Part I
This comprehensive textbook explores the theory and applications of complex functions in mathematics. Beginning with the foundations of complex numbers (z = x + iy), the book develops the geometric interpretation of the complex plane where these numbers reside. The core chapters examine mappings of complex numbers, covering linear transformations, M繹bius transformations, and conformal mappings, with special emphasis on the Riemann mapping theorem that allows conformally mapping any simply connected domain onto the unit disk.The text progresses to analytic functions, characterized by the Cauchy-Riemann equations, setting the groundwork for complex integration. The integration chapters develop the theory methodically, explaining path integrals, Cauchy's Integral Theorem (showing that integrals of analytic functions around closed contours equal zero), and path independence properties. Particular attention is given to function complex integration, covering contour deformation techniques, branch cuts for multi-valued functions, and integration on unbounded domains including Jordan's lemma.
High-Accuracy Methods for Singular Perturbation Problems
This book presents efficient numerical strategies for solving singular perturbation problems, particularly focus on differential-difference equations involving small delay parameters. Singular perturbation problems in various fields of engineering and applied sciences such as fluid dynamics, elasticity, quantum mechanics, electrical networks, are known for their boundary layer behavior, which challenges conventional numerical methods. This book reviews the theoretical background and existing literature before introducing two high-accuracy techniques: a Fourth-Order Adaptive Cubic Spline Method and a Variable Mesh Scheme. These methods are rigorously analyzed for stability, convergence, accuracy and are validated through extensive numerical experimentation. The work is motivated by the limitations of classical techniques and addresses the growing demand for robust computational methods in fields such as fluid dynamics, quantum mechanics, and reaction- diffusion process.
2024-2025 Middle School Contest Materials
This book contains one year of mathleague.org middle school tests and answer keys: 6 qualifying-level test sets and one national-level test set. Each test set contains a Sprint, Target, Team, and Countdown test.
Structured Epistemic Truth Volume I
SEMT Volume I introduces the Structured Epistemic Model of Truth, a framework that unites logic, epistemology, and complexity theory to address core issues in bounded AI and knowledge verification. Drawing from G繹del, Turing, and modern AI debates, the book proposes a non-classical conception of truth suited to agents operating under cognitive and resource constraints. It redefines epistemic rigor for computationally limited reasoners.
Heat and Mass Transfer Analysis of Non-Newtonian Flow through Cylinder
The present trend follows the advanced technology in any part of life, also as the same cooling and heating is main concept in almost every industrial, engineering sector and so to enhance and reduce heat transfer rate there are several properties regarding heat transfer phenomena by nanoparticles. There is much development and necessity in the study of Nano-fluid flow over boundary layer through inclined cylinder. For that, we have numerous of active and passive technique that aids in enhancing the heat transfer characteristic of convectional fluids.
Developing Queue Network Model with Bulk Arrival
This book explores the steady state analysis of bi-serial servers with bulk arrival. The book consists of two chapters. In the first chapter bi serial servers linked to a common sever has been analysed. The arriving unit enters into the system at bi-serial servers in batches of fixed size. Various queue characteristics have been obtained using generating function technique.The second chapter studies the network model with probabilistic batch arrival under geometrical distribution. The queue characteristics of the model has been analysed for two parameters under geometrical distribution. Numerical analysis is also done to check the validity of the model.
New Models of SUDOKU
The author of New Models of Sudoku, Nael Qutub, is a well-versed and experienced math teacher of various programmes at middle and high schools. He wanted the puzzles not only to entertain, but also to stimulate the thinking skills of puzzle-solvers while reinforcing simple math concepts by placing the right number in the right place while going around and across the 9x9 grid.The author offers a unique and enjoyable way to engage reasoning through a new style of Sudoku while avoiding stress. It is the kind of puzzle that contributes to memory improvement and mental clarity.New Models of Sudoku is an excellent tool for challenging and enhancing the mindset and logic of individuals. It takes Sudoku a step further, whereby the numbers used have a meaning. Incorporating mathematical elements will make the puzzle a rewarding experience for those who embrace changes and challenges.While most Sudoku puzzles have three levels, New Models of Sudoku, to the contrary, has six levels ranging from Beginner to Expert levels to accommodate all sorts of abilities and skills. Calculators are NOT needed. TRY TO SOLVE THE NEW MODELS!
Regularity for the 3D Navier-Stokes Equations with Damping
This book is concerned with the 3D Navier-Stokes equations with damping(DNS). We've obtained some important results such as the uniqueness of the weak solutions and the existence of the strong solutions while studying DNS for several years.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, I hope that the interested scientist will enjoy this book and derive great benefit from reading it just as I did while writing it.
Notes, Problems and Solutions in Differential Equations
This book is designed for senior undergraduate and graduate students pursuing courses in mathematics, physics, engineering and biology. The text begins with a study of ordinary differential equations. The concepts of first- and second-order equations are covered initially. It moves further to linear systems, series solutions, regular Sturm-Liouville theory, boundary value problems and qualitative theory. Thereafter, partial differential equations are explored. Topics such as first-order partial differential equations, classification of partial differential equations and Laplace and Poisson equations are also discussed in detail. The book concludes with heat equation, one-dimensional wave equation and wave equation in higher dimensions. It highlights the importance of analysis, linear algebra and geometry in the study of differential equations. It provides sufficient theoretical material at the beginning of each chapter, which will enable students to better understand the concepts and begin solving problems straightaway.
A mathematical analysis of the corruption dynamics model
This book presents a comprehensive mathematical analysis of a corruption dynamics model, integrating optimal control strategies to mitigate corruption in various systems. The research explores the underlying mechanisms of corruption, examining how it spreads and affects societal structures. By employing advanced mathematical techniques, the study develops a model that captures the dynamics of corruption and identifies effective control measures. The findings provide valuable insights for policymakers and researchers, offering a framework for understanding and addressing corruption through strategic interventions. This work contributes to the field of applied mathematics by demonstrating the practical application of mathematical modeling in social issues, making it a significant resource for scholars, practitioners, and students interested in the intersection of mathematics and social sciences.
Discrete Mathematics
This book has been carefully structured in accordance with the model syllabus prescribed by the University Grants Commission (UGC), India. It is ideally suited for undergraduate students pursuing B.Tech in Computer Science and Engineering or Mathematics, as well as postgraduate students enrolled in M.C.A. (Master of Computer Applications) or M.Sc. Mathematics programs.To make the book self-contained and accessible, it begins with foundational chapters on Mathematical Logic and Set Theory, which are essential components of the curriculum. Building upon these basics, the book introduces a wide array of key topics relevant to both Computer Science and Mathematics, including Combinatorics, Graph Theory, and Algebraic Structures such as Groups, Rings, and Boolean Algebra.In addition to traditional topics, the book includes important subjects like Finite State Machines (Theory of Computation) and Probability, making it a comprehensive guide for students navigating the intersection of mathematics and computer science.The content is presented in a simple, lucid, and student-friendly manner, with numerous examples and applications that demonstrate the practical relevance of abstract concepts, especially in the domain of Computer Science.To enhance its academic scope, the book also offers a final chapter on Fuzzy Set Theory-a modern extension of classical set theory-introducing students to contemporary topics in mathematical reasoning and logic. Overall, it is an excellent academic and reference resource.
Functional Differential Equations and Dynamic Equations on Time Scales
The Statistical Methods
This book acquaints the readers with the mathematical and statistical aspects extensively used in a variety of disciplines of social, biological and engineering sciences. The statistical models find tremendous applications through their use in facilitating economic evaluation and in a number of decision-making contexts. In the present era, the applications of statistical techniques to a variety of disciplines including economics, commerce, biology, chemistry and physics are of great importance and the present book meets the requirements of these researchers.
Mathematical Study of Epidemic Models
This book covers mathematical study of epidemic model and explores mathematical modeling techniques for infectious disease dynamics, focusing on stability, bifurcation analysis, stochastic influences, diffusion, and optimal control. It begins with an introductory overview of epidemiological concepts, historical modeling approaches, and methodologies. The subsequent chapters present the author's original contributions, analyzing various epidemic models under deterministic, delayed, stochastic, and controlled frameworks.
Intuitionistic Fuzzy Digital Spaces
This book is intended to define and analyse the geometrical and topological properties among the digital subsets of the digital images such as convexity, convex envelopes, continuity, connectedness and r-simplexes with the background of intuitionistic fuzzy logic. As an example automated detection of diabetic retinopathy using intuitionistic fuzzy digital convex envelope segmentation algorithm is propounded. As the co-extension of the above notions, some of the maps between the digital images such as continuous maps, connected maps, C-maps and enfolding maps are presented and investigated with intuitionistic fuzzy logic. Finally, intuitionistic fuzzy digital topology is framed up. Under this notion, CS - filtered spaces and Hausdorff CS - filtered spaces are instigated.
Nonlinear Convection in Earth’s Outer Core
I worked on linear and weakly non-linear theories on magneto convection in a rotating fluid with isotropic/anisotropic diffusivities using analytical methods. In linear stability analysis, we have determined the marginal stability curves at the onset of stationary and oscillatory convection using one-term Galerkin method. In weakly nonlinear analysis, a two dimensional non-linear amplitude equation near the onset of stationary and oscillatory convection has been derived. Conditions for the occurrence of secondary instabilities such as Eckhaus and Zigzag instabilities are studied. Also, stability regions of travelling waves and standing waves are studied.
Forced Convection Heat Transfer Inparallel Plate Channels Partially Fi
This book explains the hydrodynamic and thermal behavior of laminar Newtonian fluid flow in channels partially filled with porous material, symmetrically distributed at the walls. Using the Successive Accelerated Replacement (SAR) numerical scheme, the analysis explores the influence of porous fraction (γₚ), Darcy number (Da), Peclet number (Pe), and Brinkman number (Br) on flow and heat transfer. Results show that axial conduction significantly affects temperature profiles at low Pe (
Numerical Study of Multi Parameter Boundary Layer Problems
This book aims to present, analyze, and evaluate various straightforward and effective numerical methodologies for addressing two-parameter boundary layer problems, also referred to as singularly perturbed two-parameter boundary value problems, which exhibit dual boundary layer characteristics in their solutions. The book comprises five chapters. Chapter -1 delves into elucidating the definition and rationale behind singular perturbation problems, as well as singularly perturbed two parameters boundary value problems. A fourth order computational scheme with an exponential spline, a numerical scheme using an adaptive cubic spline function, a completely exponential fitted second order finite difference method, a completely exponential fitted modified upwind finite difference method for the solution of two parameters singularly perturbed two-point boundary value problems having dual layers are proposed in the remaining four chapters. These approaches may be applied to solve differential-difference equations with several parameters, as well as higher order order singular perturbation problems. The approaches proposed are efficient for doing computations with minimal computing effort.
The Formula for Growth
This book explores the integration of mathematics, data, and psychology as essential tools for driving sustainable business growth. It provides business leaders with strategies for optimizing operations, improving customer engagement, and scaling effectively across diverse markets. The book emphasizes the importance of using predictive analytics and data-driven decision-making to anticipate trends and enhance business performance, while also highlighting the role of psychological insights in fostering customer loyalty and understanding consumer behavior. With real-world case studies and practical frameworks, the book offers actionable strategies for building resilient, growth-oriented business models that can adapt to future challenges. By combining these three disciplines, businesses can create a holistic approach to growth that is both innovative and sustainable.
Analysis of Numerical Schemes to Singular Perturbation Problems
The primary goal of this book is to present, evaluate, and analyze efficient numerical methods for solving a specific class of singularly perturbed differential equations characterized by boundary and interior layer behaviors. Organized into six chapters, the book begins with a detailed overview of definitions, motivations, singular perturbation problems, differential-difference equations, boundary layers, and a comprehensive literature review. Subsequent chapters introduce advanced numerical methods, such as adaptive splines, numerical integration on specialized meshes, trigonometric splines, and fitted numerical schemes using the backward Euler method, to address interior layer problems, differential-difference equations, and singularly perturbed parabolic differential-difference equations. These studies underscore the significance of developing numerical techniques for singularly perturbed differential-difference equations. The research emphasizes creating simple, non-asymptotic, user-friendly, and efficient methods that are easily adaptable for computer implementation with minimal preparation.
Three Body Scattering Problem
This book introduces the classical three-body problem, highlighting its complexity, non-integrability, and relevance in celestial mechanics. Discusses types of three-body systems and basic solution approaches. Applies the restricted three-body model to analyze the Moon's motion under the gravitational influence of Earth and the Sun, including effects like orbital perturbations and tidal interactions. This book explores temporary interactions among three bodies, focusing on scattering, capture, and escape phenomena. Describes chaotic behavior and energy exchanges during close encounters. Analyzes how binaries interact with a third body, leading to outcomes like binary disruption, exchange, or tightening. Crucial in stellar dynamics and compact object interactions. Examines how giant molecular clouds gravitationally perturb Oort Cloud comets, triggering inward migration and potential comet showers in the solar system.
Mathematics of Machine Learning
Build a solid foundation in the core math behind machine learning algorithms with this comprehensive guide to linear algebra, calculus, and probability, explained through practical Python examplesPurchase of the print or Kindle book includes a free PDF eBookKey Features: - Master linear algebra, calculus, and probability theory for ML- Bridge the gap between theory and real-world applications- Learn Python implementations of core mathematical conceptsBook Description: Mathematics of Machine Learning provides a rigorous yet accessible introduction to the mathematical underpinnings of machine learning, designed for engineers, developers, and data scientists ready to elevate their technical expertise. With this book, you'll explore the core disciplines of linear algebra, calculus, and probability theory essential for mastering advanced machine learning concepts.PhD mathematician turned ML engineer Tivadar Danka-known for his intuitive teaching style that has attracted 100k+ followers-guides you through complex concepts with clarity, providing the structured guidance you need to deepen your theoretical knowledge and enhance your ability to solve complex machine learning problems. Balancing theory with application, this book offers clear explanations of mathematical constructs and their direct relevance to machine learning tasks. Through practical Python examples, you'll learn to implement and use these ideas in real-world scenarios, such as training machine learning models with gradient descent or working with vectors, matrices, and tensors.By the end of this book, you'll have gained the confidence to engage with advanced machine learning literature and tailor algorithms to meet specific project requirements.What You Will Learn: - Understand core concepts of linear algebra, including matrices, eigenvalues, and decompositions- Grasp fundamental principles of calculus, including differentiation and integration- Explore advanced topics in multivariable calculus for optimization in high dimensions- Master essential probability concepts like distributions, Bayes' theorem, and entropy- Bring mathematical ideas to life through Python-based implementationsWho this book is for: This book is for aspiring machine learning engineers, data scientists, software developers, and researchers who want to gain a deeper understanding of the mathematics that drives machine learning. A foundational understanding of algebra and Python, and basic familiarity with machine learning tools are recommended.Table of Contents- Vectors and vector spaces- The geometric structure of vector spaces- Linear algebra in practice spaces: measuring distances- Linear transformations- Matrices and equations- Eigenvalues and eigenvectors- Matrix factorizations- Matrices and graphs- Functions- Numbers, sequences, and series- Topology, limits, and continuity- Differentiation- Optimization- Integration- Multivariable functions- Derivatives and gradients- Optimization in multiple variables- What is probability?- Random variables and distributions- The expected value- The maximum likelihood estimation- It's just logic- The structure of mathematics- Basics of set theory- Complex numbers
Fundamentals of Ordinary Differential Equations
This textbook offers an introduction to ODEs that focuses on the qualitative behavior of differential equations rather than specialized methods for solving them. The book is organized around this approach with important topics, such as existence, uniqueness, qualitative behaviour, and stability, appearing in early chapters and explicit solution methods covered later. Proofs are included in an approachable manner, which are first motivated by describing the main ideas in a general sense before being written out in detail. A clear and accessible writing style is used, containing numerous examples and calculations throughout the text. Two appendices offer readers further material to explore, with the first using the orbits of the planets as an illustrative example and the second providing insightful historical notes. After reading this book, students will have a strong foundation for a course in PDEs or mathematical modeling. Fundamentals of Ordinary Differential Equations is suitable for an undergraduate course for students who have taken basic calculus and linear algebra courses, and who are able to read and write basic proofs. Because of its detailed approach, it is also conducive to self-study.
How to talk about Mathematics. Wie man 羹ber Mathematik spricht.
In this booklet, you find the language of describing and explaining mathematical concepts, symbols, and procedures in English and German. This booklet is intended to assist people who have to learn, to teach or to apply mathematics while using English or German as a foreign language. In diesem B羹chlein findet man die Sprache der Beschreibung und Erkl瓣rung mathematischer Begriffe, Symbole und Prozeduren. Dieses B羹chlein soll Leute unterst羹tzen, die Mathematik lernen, anwenden oder lehren m羹ssen, w瓣hrend sie Englisch oder Deutsch als Fremdsprache nutzen.
Varia Mesopotamica
The central theme of the 21 essays collected here and written between 1989 and 2019 is Ancient Mesopotamian Mathematics - its techniques and concepts, but also its historical dynamics and its influence on later Greek and Arabic (and thus to later European) mathematical reasoning. In addition, the first essay deals with historical dynamics in the field of language and argues that the Sumerian as a language originated from a creole language of the slaves of the late fourth millennium and only thereafter developed into the elaborate Sumerian language attested in the late 3rd Millennium BCE.
Dynamics and Stability of Continuous-Time Switched Linear Systems
An Introduction to String Diagrams for Computer Scientists
String diagrams are a powerful graphical language used to represent computational phenomena across diverse scientific fields, including computer science, physics, linguistics, amongst others. The appeal of string diagrams lies in their multi-faceted nature: they offer a simple, visual representation of complex scientific ideas, while also allowing rigorous mathematical treatment. Originating in category theory, string diagrams have since evolved into a versatile formalism, extending well beyond their abstract algebraic roots, and offering alternative entry points to their study. This text provides an accessible introduction to string diagrams from the perspective of computer science. Rather than starting from categorical concepts, the authors draw on intuitions from formal language theory, treating string diagrams as a syntax with its own semantics. They survey the basic theory, outline fundamental principles, and highlight modern applications of string diagrams in different fields. This title is also available as open access on Cambridge Core.
An Introduction to String Diagrams for Computer Scientists
String diagrams are a powerful graphical language used to represent computational phenomena across diverse scientific fields, including computer science, physics, linguistics, amongst others. The appeal of string diagrams lies in their multi-faceted nature: they offer a simple, visual representation of complex scientific ideas, while also allowing rigorous mathematical treatment. Originating in category theory, string diagrams have since evolved into a versatile formalism, extending well beyond their abstract algebraic roots, and offering alternative entry points to their study. This text provides an accessible introduction to string diagrams from the perspective of computer science. Rather than starting from categorical concepts, the authors draw on intuitions from formal language theory, treating string diagrams as a syntax with its own semantics. They survey the basic theory, outline fundamental principles, and highlight modern applications of string diagrams in different fields. This title is also available as open access on Cambridge Core.
Mathematics for Data Science and Artificial Intelligence
This book provides a comprehensive foundation in the mathematical tools essential for modern data science and machine learning. It blends core subjects such as linear algebra, calculus, probability, statistics, optimization, and numerical methods with real-world applications. Readers explore matrix operations, eigenvalues, and dimensionality reduction techniques like PCA and t-SNE. Optimization is covered through gradient-based methods and regularization strategies. Probability theory, Bayes' theorem, and statistical inference form the basis for modeling uncertainty. Information theory concepts like entropy, cross-entropy, and KL divergence are applied to learning and feature selection. Efficient computational methods are introduced using Python/Numpy implementations. Advanced topics include graph theory for network analysis and stochastic models such as Markov chains and ARIMA for time series forecasting. This book bridges theory and practice, offering step-by-step problem-solving, coding exercises, and a deep understanding of the mathematical backbone driving AI and data science.
Polygraphs: From Rewriting to Higher Categories
This is the first book to revisit the theory of rewriting in the context of strict higher categories, through the unified approach provided by polygraphs, and put it in the context of homotopical algebra. The first half explores the theory of polygraphs in low dimensions and its applications to the computation of the coherence of algebraic structures. Illustrated with algorithmic computations on algebraic structures, the only prerequisite in this section is basic category theory. The theory is introduced step-by-step, with detailed proofs. The second half introduces and studies the general notion of n-polygraph, before addressing the homotopy theory of these polygraphs. It constructs the folk model structure on the category on strict higher categories and exhibits polygraphs as cofibrant objects. This allows the formulation of higher-dimensional generalizations of the coherence results developed in the first half. Graduate students and researchers in mathematics and computer science will find this work invaluable.
Elements Of Arithmetic
Unlock the timeless wisdom of numbers with "Elements of Arithmetic" by Augustus De Morgan, a masterpiece that has been out of print for decades and is now beautifully restored by Alpha Editions. This isn't just a reprint; it's a collector's item and a cultural treasure, meticulously revived for today's and future generations. Dive into the mind of one of history's greatest mathematical thinkers as De Morgan unravels the mysteries of arithmetic with clarity and elegance. This classic work offers a unique blend of rigorous logic and engaging narrative, making complex concepts accessible to all. Whether you're a casual reader or a devoted collector of classic literature, this edition promises to enrich your understanding and appreciation of mathematics. Experience the joy of discovery as you explore the foundational principles that have shaped modern arithmetic. With its timeless insights and enduring value, "Elements of Arithmetic" is more than a book it's a journey into the heart of mathematical beauty. Don't miss the chance to own this exquisite piece of literary history, lovingly restored for you to cherish and enjoy.
Essentials of Nonlinearity Bifurcation and Chaos Theory
"Essentials of Nonlinearity, Bifurcation, and Chaos Theory" provides a concise yet comprehensive overview of these fundamental concepts in dynamical systems theory. This book introduces readers to the principles of nonlinear dynamics, bifurcation theory, and chaos theory, exploring their applications across various scientific disciplines. Through clear explanations and illustrative examples, readers gain insight into the behavior of nonlinear systems, including their stability, bifurcation points, and chaotic dynamics. Whether you're a student, researcher, or practitioner in fields such as physics, engineering, biology, or economics, this book serves as an essential guide to understanding the intriguing phenomena of nonlinearity, bifurcation, and chaos and their implications for modeling and analysis in complex systems.
Introduction to Finite Elements in Engineering
"Introduction to Finite Elements in Engineering" provides a comprehensive introduction to the fundamentals of finite element analysis and its application in engineering problem-solving. Through collaboration with experts, this book covers topics such as mathematical foundations, element formulations, numerical techniques, software tools, and practical applications in structural, thermal, and fluid analysis. With theoretical explanations and practical examples, readers gain insights into understanding and applying FEA concepts in engineering practice. Bridging theory and application, this book empowers readers to leverage the power of computational simulation to innovate and advance engineering design and analysis.
Modern Trigonometry
"Modern Trigonometry" provides a comprehensive overview of trigonometric principles, techniques, and applications in contemporary mathematics and scientific inquiry. Through collaboration with experts, this book covers topics such as trigonometric functions, identities, equations, vectors, complex numbers, Fourier analysis, and applications in fields such as physics, engineering, computer graphics, and signal processing. With theoretical foundations and practical applications, readers gain a thorough understanding of modern trigonometry. Bridging theory and application, this book empowers readers to appreciate the beauty and utility of trigonometric concepts in the modern age.
Introduction to Modern Algebra
It covers a range of topics related to the study of algebra, from the basics of set theory to advanced topics such as Galois Theory and representation theory. The book begins with an overview of modern algebra and its importance in various fields of mathematics and also covers the history and development of ring theory, including its applications in algebraic geometry and number theory.The book covers the basics of set theory, including the axioms of set theory and cardinality and introduces module theory, which is a generalization of vector spaces, and its applications in various fields of mathematics.The book discusses the applications of commutative algebra in algebraic geometry and algebraic number theory and also includes a discussion of current research topics in group theory.The book covers the history and development of Galois Theory and discusses the importance of representation theory in various fields of mathematics, including physics and geometry.It is suitable for undergraduate and graduate students as well as researchers in mathematics and related fields.
Handbook of Algebra and Algebraic Topology
Covering all aspects of Elementary Algebra, it will surely serve as the complete elementary textbook for studying different concepts.The subject is presented in its simplest, most essential form, but with many explanatory details, figures and examples.The content of the book is sequentially presented in the book for easy and comprehensive learning.This book forms a strong basis for students and teachers engaged in the field of mathematics especially algebra and algebraic topology.
AP Calculus Study Guide AP 微积分 AB/BC 指导用书
本书是一部系统全面的微积分教程，涵盖了从基础概念到高级应用的完整内容。书中包括了极限与连续性、微分及其基本性质、复合函数的微分、积分及其累积变化、微分方程和积分应用等主题。内容结构清晰，循序渐进，辅以大量的例题和解析，帮助学生理解并掌握微积分的核心概念及解题技巧，特别适用于准备AP微积分的学习者。这部书为学生提供了深入的理论知识和实用的数学工具，使其能更好地理解和应用微积分于实际问题中。This book is a systematic and comprehensive calculus tutorial that covers a complete range of content from basic concepts to advanced applications. The book includes topics such as limits and continuity, differentiation and its basic properties, differentiation of composite functions, integration and its cumulative change, differential equations, and applications of integration. With a clear content structure and a step-by-step approach, it is supplemented by a large number of examples and analyses to help students understand and master the core concepts of calculus and problem-solving techniques. It is especially suitable for learners preparing for AP Calculus. This book provides students with in-depth theoretical knowledge and practical mathematical tools, enabling them to better understand and apply calculus to practical problems.
The Geometry of Equilibrium
James Clerk Maxwell is one of the giants of scientific thought, and whilst his groundbreaking contributions to electromagnetism and statistical physics are well known, his profound insights into the theory of structures are appreciated less widely. Maxwell's approach was deeply geometrical, and this richly illustrated book reveals his astute perception of the remarkable dualities that exist between the form of a structure and the forces it can carry, with understandings that will surprise contemporary readers. Early chapters introduce the background in which Maxwell was working, followed by contributions by leading researchers describing the latest applications of these ideas. Subsequent chapters introduce the many subtopics that this work embraces. The book ends with Maxwell's original papers on structural mechanics, each annotated to highlight and explain the ideas therein. This is a wonderful resource for mathematicians, scientists, engineers, and designers to enter this rich and underexplored aspect of the genius of Maxwell.
A Little History of Mathematics
A lively, accessible history of mathematics throughout the ages and across the globe Mathematics is fundamental to our daily lives. Science, computing, economics--all aspects of modern life rely on some kind of maths. But how did our ancestors think about numbers? How did they use mathematics to explain and understand the world around them? Where do numbers even come from? In this Little History, Snezana Lawrence traces the fascinating history of mathematics, from the Egyptians and Babylonians to Renaissance masters and enigma codebreakers. Like literature, music, or philosophy, mathematics has a rich history of breakthroughs, creativity and experimentation. And its story is a global one. We see Chinese Mathematical Art from 200 BCE, the invention of algebra in Baghdad's House of Wisdom, and sangaku geometrical theorems at Japanese shrines. Lawrence goes beyond the familiar names of Newton and Pascal, exploring the prominent role women have played in the history of maths, including Emmy Noether and Maryam Mirzakhani.
Mathematica
A fascinating look into how the transformative joys of mathematical experience are available to everyone, not just specialists Math has a reputation for being inaccessible. People think that it requires a special gift or that comprehension is a matter of genes. Yet the greatest mathematicians throughout history, from Ren矇 Descartes to Alexander Grothendieck, have insisted that this is not the case. Like Albert Einstein, who famously claimed to have "no special talent," they said that they had accomplished what they did using ordinary human doubts, weaknesses, curiosity, and imagination. David Bessis guides us on an illuminating path toward deeper mathematical comprehension, reconnecting us with the mental plasticity we experienced as children. With simple, concrete examples, Bessis shows how mathematical comprehension is integral to the great learning milestones of life, such as learning to see, to speak, to walk, and to eat with a spoon. Focusing on the deeply human roots of mathematics, Bessis dispels the myths of mathematical genius. He offers an engaging initiation into the experience of math not as a series of discouragingly incomprehensible logic problems but as a physical activity akin to yoga, meditation, or a martial art. This perspective will change the way you think not only about math but also about intelligence, intuition, and everything that goes on inside your head.
HESI Math Workbook
Over 200 HESI A2(R) practice questions, prepared by a dedicated team of exam experts, with detailed answer key, Math shortcuts, tips and tricks, tutorials and multiple choice strategies! You have arrived!Here is everything you need to pass the HESI(R) Math! We have helped thousands of students and we can help you!Complete HESI Math workbook, prepared by exam experts, with over 200 questions. Basic MathSolving Word ProblemsSolve Algebra EquationsMetric ConversionData InterpretationWhy Us?The Complete Test Preparation Team has been publishing high quality study materials since 2005, with a catalogue of over 145 titles, in English, French and Chinese, as well as ESL curriculum for all levels.You have come to the right place.If you want to spend your valuable study time where it will help you the most - we've got you covered today and tomorrow.You can pass the HESI with a great score! Here is how! You already know that Practice Makes Perfect! The more questions you see, and the more you practice - the better your HESI score! HESI A2(R) Math practice questions, easy-to-read tutorials explaining everything in plain language, exam tips and tricks, math shortcuts, and multiple choice strategies! Everything you need, complied by a dedicated team of experts with everything you need all in one place! Please note that HESI(R) is a registered trademark of the Health Education Systems Inc., which was not involved in the production of, and does not endorse, this product. Practice Really Does Make Perfect! The more questions you see, the more likely you are to pass the test. And between our study guide and practice tests, you'll have over 200 practice questions that cover every category. Our practice test questions have been developed by our dedicated team of experts. All the material in the study guide, including every practice question, are designed to engage your critical thinking skills needed to pass the test! Heard it all before? Maybe you have heard this kind of thing before, and don't feel you need it. Maybe you are not sure if you are going to buy this book. Remember though, it only a few percentage points divide the PASS from the FAIL students! Even if our test tips increase your score by a few percentage points, isn't that worth it?
Carleman Estimates in Mean Field Games
This book provides a comprehensive exploration of Mean Field Games (MFG) theory, a mathematical framework for modeling the collective behavior of rational agents in complex systems. MFG theory can govern a range of societal phenomena, including finance, sociology, machine learning, and economics. The focus is on the system of two coupled nonlinear parabolic partial differential equations (PDEs) that define the Mean Field Games System. The book covers key theoretical topics such as solution stability and uniqueness, with a particular emphasis on Carleman estimates, which are used to estimate solution errors based on noise in the input data. It also introduces the theory of Ill-Posed and Inverse Problems within MFG theory. Both theoretical and numerical aspects of forward and inverse problems are explored through Carleman estimates, offering a rigorous foundation for researchers and practitioners in applied mathematics and related fields. This book offers a rigorous approach to Carleman estimates, a key element of Mean Field Games theory, making it an essential resource for researchers, graduate students, and professionals looking to apply this powerful framework to complex, real-world systems.
