Foundations of Quantitative Finance, Book VI
Every finance professional wants and needs a competitive edge. A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it. Many are not-and that is the competitive edge these books offer the astute reader.
Introduction to General and Generalized Linear Models
Providing a flexible framework for data analysis and model building, this text focuses on the statistical methods and models that can help predict the expected value of an outcome, dependent, or response variable. It offers a sound introduction to general and generalized linear models using the popular and powerful likelihood techniques. The aut
Statistical Methods in Biology
Written in simple language with relevant examples, this illustrative introductory book presents best practices in experimental design and simple data analysis. Taking a practical and intuitive approach, it only uses mathematical formulae to formalize the methods where necessary and appropriate. The text features extended discussions of examples
Computational Mathematics
Computational Mathematics: Models, Methods, and Analysis with MATLAB(R) and MPI is a unique book covering the concepts and techniques at the core of computational science. The author delivers a hands-on introduction to nonlinear, 2D, and 3D models; nonrectangular domains; systems of partial differential equations; and large algebraic problems requiring high-performance computing. The book shows how to apply a model, select a numerical method, implement computer simulations, and assess the ensuing results.Providing a wealth of MATLAB, Fortran, and C++ code online for download, the Second Edition of this very popular text: Includes a new chapter with two sections on the finite element method, two sections on shallow water waves, and two sections on the driven cavity problem Introduces multiprocessor/multicore computers, parallel MATLAB, and message passing interface (MPI) in the chapter on high-performance computing Updates and adds code and documentation Computational Mathematics: Models, Methods, and Analysis with MATLAB(R) and MPI, Second Edition is an ideal textbook for an undergraduate course taught to mathematics, computer science, and engineering students. By using code in practical ways, students take their first steps toward more sophisticated numerical modeling.
Measure and Integral
This classic text provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then introducing a more general treatment based on abstract notions characterized by axioms and with less geometric content. Packed with new exercises and material, the long-awaited s
Introduction to Mathematical Logic
This bestselling, classic textbook continues to provide a complete one-semester introduction to mathematical logic. The sixth edition incorporates recent work on G繹del's second incompleteness theorem as well as an appendix on consistency proofs for first-order arithmetic. It also offers historical perspectives and many new exercises of varying d
Topological Vector Spaces
With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn-Banach theorem. This edition explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes an entirely new chapter on vector-valued Hahn-Banach theorems. It also considers different approaches to the Banach-Stone theorem as well as variations of the theorem.The book covers locally convex spaces; barreled, bornological, and webbed spaces; and reflexivity. It traces the development of various theorems from their earliest beginnings to present day, providing historical notes to place the results in context. The authors also chronicle the lives of key mathematicians, including Stefan Banach and Eduard Helly. Suitable for both beginners and experienced researchers, this book contains an abundance of examples, exercises of varying levels of difficulty with many hints, and an extensive bibliography and index.
Enveloping Algebras
No detailed description available for "Enveloping Algebras".
The Relay Race to Infinity
Why were most historically important mathematicians wealthy? Why were they often lawyers and many had pastors for fathers? Why were original results sometimes discovered by two mathematicians independently within a short time of each other? Why did the Italian Fibonacci, speak Arabic?It all began a couple of years ago, when one of the authors started to write short biographies of important historical mathematicians for the teaching journal Australian Primary Mathematics Classroom. It was felt that teachers generally knew very little about the way the subject developed or the people who developed it. And it was felt that historical knowledge would help them see how the subject progressed and enable them to fit in with the historical episodes that would be of interest to students.Clearly, the book that developed contains mathematics up to the 17th century, but we are keen to set the subject in those times, to try to give short biographies of the people involved, as well as provide a perspective of the events that led up to the times and led up to the mathematics. Importantly, it is shown that the maths enterprise was not undertaken by a small few, but worked like a relay race. One or a few might take up an idea and develop it, but it often gets only so far. Later, others would take up the idea, the baton, and the relay race to find results continues.
Linear Algebra
This book is a comprehensive guide to Linear Algebra and covers all the fundamental topics such as vector spaces, linear independence, basis, linear transformations, matrices, determinants, inner products, eigenvectors, bilinear forms, and canonical forms. It also introduces concepts such as fields, rings, group homomorphism, and binary operations early on, which gives students a solid foundation to understand the rest of the material. Unlike other books on Linear Algebra that are either too theory-oriented with fewer solved examples or too problem-oriented with less good quality theory, this book strikes a balance between the two. It provides easy-to-follow theorem proofs and a considerable number of worked examples with various levels of difficulty. The fundamentals of the subject are explained in a methodical and straightforward way. This book is aimed at undergraduate and graduate students of Mathematics and Engineering Mathematics who are studying Linear Algebra. It is also a useful resource for students preparing for exams in higher education competitions such as NET, GATE, lectureships, etc. The book includes some of the most recent and challenging questions from these exams.
The Relay Race to Infinity
Why were most historically important mathematicians wealthy? Why were they often lawyers and many had pastors for fathers? Why were original results sometimes discovered by two mathematicians independently within a short time of each other? Why did the Italian Fibonacci, speak Arabic?It all began a couple of years ago, when one of the authors started to write short biographies of important historical mathematicians for the teaching journal Australian Primary Mathematics Classroom. It was felt that teachers generally knew very little about the way the subject developed or the people who developed it. And it was felt that historical knowledge would help them see how the subject progressed and enable them to fit in with the historical episodes that would be of interest to students.Clearly, the book that developed contains mathematics up to the 17th century, but we are keen to set the subject in those times, to try to give short biographies of the people involved, as well as provide a perspective of the events that led up to the times and led up to the mathematics. Importantly, it is shown that the maths enterprise was not undertaken by a small few, but worked like a relay race. One or a few might take up an idea and develop it, but it often gets only so far. Later, others would take up the idea, the baton, and the relay race to find results continues.
Algebraic Topology
The aim of the textbook is two-fold: first to serve as an introductory graduate course in Algebraic Topology and then to provide an application-oriented presentation of some fundamental concepts in Algebraic Topology to the fixed point theory. A simple approach based on point-set Topology is used throughout to introduce many standard constructions of fundamental and homological groups of surfaces and topological spaces. The approach does not rely on Homological Algebra. The constructions of some spaces using the quotient spaces such as the join, the suspension, and the adjunction spaces are developed in the setting of Topology only. The computations of the fundamental and homological groups of many surfaces and topological spaces occupy large parts of the book (sphere, torus, projective space, Mobius band, Klein bottle, manifolds, adjunctions spaces). Borsuk's theory of retracts which is intimately related to the problem of the extendability of continuous functions is developed in details. This theory together with the homotopy theory, the lifting and covering maps may serve as additional course material for students involved in General Topology. The book comprises 280 detailed worked examples, 320 exercises (with hints or references), 80 illustrative figures, and more than 80 commutative diagrams to make it more oriented towards applications (maps between spheres, Borsuk-Ulam Theory, Fixed Point Theorems, ...) As applications, the book offers some existence results on the solvability of some nonlinear differential equations subject to initial or boundary conditions. The book is suitable for students primarily enrolled in Algebraic Topology, General Topology, Homological Algebra, Differential Topology, Differential Geometry, and Topological Geometry. It is also useful for advanced undergraduate students who aspire to grasp easily some new concepts in Algebraic Topology and Applications. The textbook is practical both as a teaching and research document for Bachelor, Master students, and first-year PhD students since it is accessible to any reader with a modest understanding of topological spaces. The book aspires to fill a gap in the existing literature by providing a research and teaching document which investigates both the theory and the applications of Algebraic Topology in an accessible way without missing the main results of the topics covered.
Computational mathematics in R Programming
Computational mathematics in R programming harnesses the power of R's extensive libraries and tools to tackle complex numerical analysis, statistical computations, and data visualization tasks. This versatile programming language is widely adopted in a range of scientific and engineering disciplines for executing matrix operations, optimization techniques, and solving differential equations. Whether applied in data science, physics, economics, or engineering, R provides a robust platform for performing sophisticated mathematical computations, enabling researchers and professionals to analyze data efficiently, model real-world systems, and gain deeper insights from their work. Its user-friendly interface, combined with powerful computational capabilities, makes it an invaluable resource for anyone engaged in computational mathematics.
A Stitch in Line
A Stitch in Line: Mathematics and One-Stitch Sashiko provides readers with instructions for creating hitomezashi items with minimum outlay. The reader is guided through the practical steps involved in creating each design, and then the mathematics which underpins it is explained in a friendly, accessible way. This is a fantastic book for anyone who is interested in recreational mathematics and/or fibre arts and can be a useful resource for teaching and learning mathematical concepts in a fun and engaging format.Features Numerous full-colour photographs of hitomezashi stitch patterns which have been mathematically designed Suitable for readers of all mathematical levels and backgrounds -- no prior knowledge is automatically assumed A compressed encoding for recording and designing hitomezashi patterns to be stitched or drawn Accessible explanations and explorations of mathematical concepts inherent in, or illustrated by, hitomezashi patterns
Invertibility and Asymptotics of Toeplitz Matrices
No detailed description available for "Invertibility and Asymptotics of Toeplitz Matrices".
Theory of Nonlinear Operators
No detailed description available for "Theory of Nonlinear Operators".
The (wrong) paths of tourism
This study deals with the socio-environmental issues related to the implementation and paving of the GO-239 road, called Estrada-parque Prefeito Divaldo Rinco, which links Alto Para穩so de Goi獺s to Colinas do Sul, in the Chapada dos Veadeiros, in Goi獺s. The road borders and also leads to the Chapada dos Veadeiros National Park (PNCV) and its route presents a scenic beauty typical of the region, showing the high-altitude Cerrado all around. The objectives are to describe the condition of the road and to show what people think about it. This is a qualitative, exploratory study that used direct observation of the road and interviews with residents and institutional agents (PNCV, Municipal Tourism Office) to capture their perceptions of the road's importance and issues surrounding its construction. It was concluded that the road still lacks the conditions that characterise it as a parkway, such as a management plan, but that it has great tourist potential due to the landscape that surrounds it.
Singularities and Low Dimensional Topology
The special semester 'Singularities and low dimensional topology' in the Spring of 2023 at the Erdős Center (Budapest) brought together algebraic geometers and topologists to discuss and explore the strong connection between surface singularities and topological properties of three- and four-dimensional manifolds. The semester featured a Winter School (with four lecture series) and several focused weeks. This volume contains the notes of the lecture series of the Winter School and some of the lecture notes from the focused weeks. Topics covered in this collection range from algebraic geometry of complex curves, lattice homology of curve and surface singularities to novel results in smooth four-dimensional topology and grid homology, and to Seiberg-Witten homotopy theory and 'spacification' of knot invariants. Some of these topics are already well-documented in the literature, and the lectures aim to provide a new perspective and fresh connections. Other topics are rather new and have been covered only in research papers. We hope that this volume will be useful not only for advanced graduate students and early-stage researchers, but also for the more experienced geometers and topologists who want to be informed about the latest developments in the field.
Geometric mathematics in the slab cistern
This work came about through research in the rural community of S穩tio Barra do Japi in the municipality of Japi-RN. It shows the step-by-step mathematics involved in building a cement slab cistern. However, the aim was to bring together the mathematical concepts involved in carrying out this work. The aim is for the community's math teacher to be able to integrate his lessons with the daily reality of these people, bringing the school closer to the daily lives of the community's residents.
Statistical Machine Learning for Engineering with Applications
Modeling and Simulation of Environmental Systems
This book presents an overview of modeling and simulation of environmental systems via diverse research problems and pertinent case studies, covering air pollution modeling, sustainable water resources modeling, IoT based applications in environmental systems, and future algorithms and conceptual frameworks in environmental systems.
A Stitch in Line
A Stitch in Line: Mathematics and One-Stitch Sashiko provides readers with instructions for creating hitomezashi items with minimum outlay. The reader is guided through the practical steps involved in creating each design, and then the mathematics which underpins it is explained in a friendly, accessible way. This is a fantastic book for anyone who is interested in recreational mathematics and/or fibre arts and can be a useful resource for teaching and learning mathematical concepts in a fun and engaging format.Features Numerous full-colour photographs of hitomezashi stitch patterns which have been mathematically designed Suitable for readers of all mathematical levels and backgrounds -- no prior knowledge is automatically assumed A compressed encoding for recording and designing hitomezashi patterns to be stitched or drawn Accessible explanations and explorations of mathematical concepts inherent in, or illustrated by, hitomezashi patterns
Mathematical Modelling
This book investigates human-machine systems through the use of case studies such as crankshaft maintenance, liner piston maintenance, and biodiesel blend performance.
Everything Is Predictable
A "fascinating, witty, and perspective-shifting" (Oliver Burkeman, New York Times bestselling author) tour of Bayes's theorem and its global impact on modern life from the acclaimed science writer and author of The Rationalist's Guide to the Galaxy.At its simplest, Bayes's theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. But in Everything Is Predictable, Tom Chivers lays out how it affects every aspect of our lives. He explains why highly accurate screening tests can lead to false positives and how a failure to account for it in court has put innocent people in jail. A cornerstone of rational thought, many argue that Bayes's theorem is a description of almost everything. But who was the man who lent his name to this theorem? How did an 18th-century Presbyterian minister and amateur mathematician uncover a theorem that would affect fields as diverse as medicine, law, and artificial intelligence? "Witty, lively, and best of all, extremely nerdy" (Tim Harford, author of The Undercover Economist), Everything Is Predictable is an entertaining and accessible illustration of how a single compelling idea can have far reaching consequences.
Spline Approch for Solution of Fluid Flow Problems
The book on the numerical solution of Magnetohydrodynamic (MHD) fluid flow problems using the spline collocation method provides a comprehensive exploration of how spline functions can be applied to solve complex MHD equations. It covers the fundamentals of MHD, where fluid dynamics and electromagnetism intersect, and introduces spline collocation as an efficient numerical technique for approximating solutions. The book details the method's application in various MHD problems, emphasizing its accuracy and computational efficiency. Through examples and case studies, the text illustrates how the spline collocation method can effectively handle boundary layers, singularities, and other challenges typical in MHD fluid flow analysis.
Evolutionary Computation
Evolutionary computation offers powerful problem-solving methodologies inspired by models of natural genetics and evolutionary processes. Potential applications are wide-ranging and include problems related to combinatorial optimization, numerical optimization, multi-objective optimization, and others, as well as specific applications of these problems in diverse domains, such as engineering, design, medicine, robotics, science, etc. Techniques from evolutionary computation often lend themselves well to parallel and distributed implementations and are often more effective in dealing with challenging problem characteristics such as non-linearity and high dimensionality than alternative approaches. This Special Issue brings together recent advances in the theory and application of evolutionary computation.
A First Course on Orthogonal Polynomials
This book provides an introduction to orthogonal polynomials and special functions aimed at graduate students studying these topics for the first time. A large part of its content is essentially inspired by the works of Pascal Maroni on the so-called algebraic theory of orthogonal polynomials.
Math Mammoth Grade 8 Answer Keys, International Version
This book includes answers for the Math Mammoth Grade 8-A and 8-B student worktexts (international version), for all the chapter tests, the end-of-year test, and for the cumulative revisions.
Theory of Distributions
The Theory of Distributions, also known as the theory of generalized functions, is a mathematical analysis framework extending the classical notion of functions and derivatives. Introduced by Laurent Schwartz in the mid-20th century, this theory addresses limitations in traditional function analysis, particularly in handling functions that are not differentiable in the classical sense. Distributions generalize functions by defining them as continuous linear functional on a space of test functions, typically smooth and rapidly decreasing functions. This approach facilitates the rigorous treatment of objects like the Dirac delta function, which is pivotal in various applications across physics and engineering. Distributions are integral in solving differential equations, especially in contexts where classical solutions may not exist or be easily identifiable. They enable the extension of operations such as differentiation and convolution to a broader class of objects, thereby providing a robust toolkit for addressing problems in partial differential equations, signal processing, and quantum mechanics.
General Mathematical Theory Dynamic Global Politic Eco
William Jevons (1866 and 1871) established a ground-breaking milestone with 'A General Mathematical Theory of Political Economy' for economic analysis. Jevons' work was praised as the start of the mathematical method in the discipline of economics, which is inherently a subject involved with mathematics and quantities. This book focuses on the most fast-evolving and encompassing area in political economy -- the dynamic global political economy. Under the high level of globalization currently, intertemporal and cross-boundary interactive elements are present in political-economic encounters. Indeed, almost all studies in the political economy may fall into the study of dynamic global political economy. Since the world has changed significantly, new mathematics developed by the authors of this book is used to formulate a general mathematical theory for the dynamic global political economy nowadays. A distinctive feature of the current book is that it combines advanced mathematics, game-theoretic concepts, and economics to develop a general mathematical theory supporting the study of the dynamic global political economy.The book covers mathematical theory for different areas of the dynamic global political economy. In addition, it explicates the application of the mathematical theory in real-world scenarios, including (i) environmental degradation under an uncoordinated interaction scenario, (ii) global climate accords with collaboration and cooperation, (iii) trade network involving the Belt-Road Initiative (BRI) and Build Back Better World (B3W) Initiative, and (iv) random termination of international joint ventures.
Distribution Dependent Stochastic Differential Equations
Corresponding to the link of It繫's stochastic differential equations (SDEs) and linear parabolic equations, distribution dependent SDEs (DDSDEs) characterize nonlinear Fokker-Planck equations. This type of SDEs is named after McKean-Vlasov due to the pioneering work of H P McKean (1966), where an expectation dependent SDE is proposed to characterize nonlinear PDEs for Maxwellian gas. Moreover, by using the propagation of chaos for Kac particle systems, weak solutions of DDSDEs are constructed as weak limits of mean field particle systems when the number of particles goes to infinity, so that DDSDEs are also called mean-field SDEs. To restrict a DDSDE in a domain, we consider the reflection boundary by following the line of A V Skorohod (1961).This book provides a self-contained account on singular SDEs and DDSDEs with or without reflection. It covers well-posedness and regularities for singular stochastic differential equations; well-posedness for singular reflected SDEs; well-posedness of singular DDSDEs; Harnack inequalities and derivative formulas for singular DDSDEs; long time behaviors for DDSDEs; DDSDEs with reflecting boundary; and killed DDSDEs.
Math Mammoth Grade 8 Tests and Cumulative Revisions, International Version
Math Mammoth Grade 8 Tests and Cumulative Revisions (international version) contains the chapter tests, end-of-year test, and cumulative revision worksheets for Math Mammoth Grade 8 curriculum (international version). It does not contain answers; the answer key book may be purchased separately.
Math Mammoth Grade 8-B Worktext, International Version
Math Mammoth Grade 8-B Worktext (International Version) is the second student book for eighth grade mathematics, and part of the Math Mammoth Grade 8 complete curriculum.The book starts with chapter 5, graphing linear equations. Students study slope, and graph and write linear equations in slope-intercept and standard forms. They also learn about parallel and perpendicular lines.In chapter 6, students delve into square roots, cube roots, and irrational numbers and solve equations involving square and cube roots. The rest of the chapter is spent studying the Pythagorean Theorem and its applications.Next, in chapter 7, we focus on systems of linear equations. Students learn the three basic techniques for solving these and also solve a variety of problems that are solved with a pair of linear equations. The last chapter covers statistical topics: scatter plots and two-way tables.
Math Mammoth Grade 8-A Worktext, International Version
Math Mammoth Grade 8-A Worktext (International Version) is the first student book for eighth grade mathematics, and part of the Math Mammoth Grade 8 complete curriculum.This book starts with a study of exponent laws, using both numerical and algebraic expressions. The first chapter also covers scientific notation (both with large and small numbers), significant digits, and calculations with numbers given in scientific notations.In chapter 2, students learn about geometric transformations (translations, reflections, rotations, dilations), common angle relationships, and volume of prisms, cylinders, spheres, and cones. Next, in chapter 3, our focus is on linear equations.Students both review and learn more about solving linear equations, including equations whose solutions require the usage of the distributive property and equations where the variable is on both sides.Chapter 4 presents an introduction to functions. Students construct functions to model linear relationships, learn to use the rate of change and initial value of the function, and they describe functions qualitatively based on their graphs.
Mathematical Methods Applied in Artificial Intelligence and Multi-Agent Systems
Due to rapid developments in computing, communication, and sensing technology, multi-agent systems have become increasingly ubiquitous. Their applications include mobile sensor networks, autonomous vehicles, intelligent transportation systems, and smart grids. The complex unknown environment and inaccurate dynamics prose additional challenges for the modeling, control, and optimization of such systems. Therefore, data science and machine learning are providing opportunities to develop artificial intelligence-based methods and enable new control and optimization paradigms for multi-agent systems. The aim of this Special Issue is to bring together significant developments in the interface between machine learning, neurodynamics, and swarm intelligence.
46 Ways to Play Math
Math Games Enhance LearningMath games build mental flexibility and strategic reasoning in players of all ages. And even people who hated math in school can enjoy the friendly challenge of a game.These are NOT the typical memory-and-speed-based math games you've probably seen online, but true battles of wit and skill (plus a bit of luck). Even the preschool games can be fun for adults, too.Most of the games take only seconds to learn and less than 15 minutes to play, making them perfect ice-breakers for family gatherings, classroom warmups, or for launching a group game night.You'll love these strategic challenges for preschoolers to adult gamers. Easy to learn, quick to play! Who knew math could be so much fun?Includes six skill-level game chapters: Early Counting Games: 7 Ways to Play Math with Young LearnersCounting Games with Bigger Numbers: 7 Ways to Play Math with Primary StudentsEarly Mental Math: 6 Ways to Play Math with Primary StudentsIntermediate Mental Math: 6 Ways to Play Math in the Middle GradesAdvanced Mental Math: 6 Ways to Play Math with Older StudentsGraphing Games: 6 Ways to Play Math with Older StudentsPlus four bonus chapters for all ages: The Best Math Game Ever: Creative Math for All AgesCreative Nim: Make Your Own Math & Logic GamesThe Function Machine: A Card Game of Algebraic ThinkingNumber Neighborhoods: Two Math Games of Logical Deduction46 Ways To Play Math features instructions and math game pages in full-color, tips for the teacher, and plenty of room to record your game modification or house rules.Grab a deck of cards, a few dice, or markers and graph paper, and let's play some math!
So You Think You Know III
The secret qualities of numbers revealing the keys to understanding ancient cryptic works. Numbers related to biology, chemistry and secrets of Fibonacci and Polynacci Single Digit Cycles. Golden Angles and the Great Pyramid are new discoveries together with a detailed study of long division Single Digit Properties and Magic Squares. An ancient method of calculating planetary distances is detailed.
Utility of Quaternions in Physics
Utility of Quaternions in Physics, a classical book, has been considered important throughout the human history, and so that this work is never forgotten we at Alpha Editions have made efforts in its preservation by republishing this book in a modern format for present and future generations. This whole book has been reformatted, retyped and designed. These books are not made of scanned copies of their original work and hence the text is clear and readable.
The Non-Uniform Riemann Approach to Stochastic Integration
This is the first book that presents the theory of stochastic integral using the generalized Riemann approach. Readers who are familiar with undergraduate calculus and want to have an easy access to the theory of stochastic integral will find most of this book pleasantly readable, especially the first four chapters. The references to the theory of classical stochastic integral and stochastic processes are also included for the convenience of readers who are familiar with the measure theoretic approach.
Didactic games
This book arose from the desire and need to make maths lessons more attractive, interesting and enjoyable for both teachers and students. We are using didactic games as a way of intervening in maths lessons to try to reduce or solve the difficulties that students have in this subject. Our intention is to contribute to a reflection on the teacher's didactic-pedagogical action in order to improve the teaching-learning process in Maths, bringing about more meaningful learning, suggesting games as a teaching strategy that will reduce the existing blockages between the student and this subject, as well as reporting on some classroom experiences.
Journal of Applied Logics. The IfCoLog Journal of Logics and their Applications. Volume 15, issue 5, October 2024. Special Issue
The Journal of Applied Logics- IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.
Problems and elegant solutions in mathematical analysis
This is a mathematical reference book for students, graduates and researchers who are interested in the challenging problems as the extreme of function, equation and series arising in the mathematical analysis. The book aims at encouraging those who were accustomed to standard calculation to be interested in solution of more challenging problems such as differential equation, integral equation and series. This research paper is the limit part of "challenging problems and elegant solution in mathematical analysis" to continuity of limit part, integral part and equation part. It can be widely used by students in mathematics and physics, and everyone who is interested in mathematical analysis. It is certain that this will be contributed to the students, the graduates and researchers who are going to mathematically analyze the physical situations arise in advanced science and technology.
Mathematical Logic
The book "Mathematical Logic" has been meticulously prepared to serve the students of the B.A./ B.Sc./ B.Com. third semester (As per NEP-2020 new syllabus) Mathematics skill enhancement course under Dibrugarh University. Mathematical logic is a fundamental course in undergraduate mathematics, providing essential tools and concepts that are foundational for further studies in the field. This book covers all the topics outlined in the syllabus.
Applications of partial differential equations in plasma physics I
Authors introduced advanced applications of partial differential equations in plasma physics using analytical methods based on Boltzmann-Maxwell equations. The book creates theoretical tools for predicting and controlling plasma behavior in many outstanding applications. In the study was introduced a new mathematical model for calculating the thermodynamic forces, kinetic coefficients, and flux variables as two new scientific achievements. Secondly, with reasonable accuracy, was determined the thermodynamic equilibrium time of electrons under an external force. Authors clarify the difference between an equilibrium velocity distribution function and a perturbed one. The book introduces the extended Gibbs equation, which predicts ratios between various contributions to the internal energy change for diamagnetic and paramagnetic plasmas. A standard laboratory argon plasma model is used to apply the results. It advances our understanding of plasma physics and holds immense potential for practical applications in aerospace engineering, plasma technology, and materials science. This book lays the groundwork for future innovations and technological advancements in plasma.
