We have compiled the list of Best Reference Books on Calculus subject. These books are used by students of top universities, institutes and colleges. Here is the full list of best books on Calculus along with reviews.
Kindly note that we have put a lot of effort into researching the best books on Calculus subject and came out with a recommended list of best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on “Calculus” as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.
List of Calculus Books with author’s names, publishers, and an unbiased review as well as links to the Amazon website to directly purchase these books.
- Transform Calculus
- Differential Calculus and Vector Calculus
- Multivariable Calculus
- Integral Calculus
|1. “Calculus – Single and Multivariable” by Hughes-Hallett
“Calculus – Single and Multivariable” Book Review: The book aims at providing a fair introduction to calculus. It is an excellent blend of modeling and skills. The topics like library of functions, derivatives, definite integrals, antiderivatives, sequence and series, differential equations, vectors, functions of several variables, local and global extrema, parameterization and vector fields, line integrals, and flux integrals are discussed in detail. The mathematical concepts like differentiation, integration, and calculus of vector fields are used as tools in this piece of writing. To give book’s content visual support fundamental concepts are explained graphically, numerically, symbolically, and verbally.
|2. “Calculus” by James Stewart
“Calculus” Book Review: The book presents calculus from a technical point-of-view. The chapters of this book are well-written and feature topics like functions and limits, derivatives, integrals, inverse functions, polar coordinates, infinite sequence and series, vectors, partial derivatives, and vector calculus. Chapters highlighting applications of differentiation, applications of integration, and techniques of integration are included. Many applications of calculus like differential equations, parametric equations, multiple integrals, and second order differential equations are presented. The content of this book is comprehensive, precise, and illustrated with many real-world examples.
|3. “Calculus Vol. I” by T M Apostol
“Calculus Vol. I” Book Review: The book is an excellent blend of both theoretical as well as technical concepts of calculus. The chapters of this book begin with a thorough explanation of integration and then move to differentiation. The book aims at displaying the real link between integrals and derivatives. It reflects linear algebra as well as the mean-value theorems along with their applications. The featured theorems are illustrated with the help of their proofs, followed by geometric or intuitive discussion. Many exercises are included in this text for self-assessment and practices of the readers.
|4. “Calculus Vol. II” by T M Apostol
“Calculus Vol. II” Book Review: The book is written from both theoretical as well as technical point-of-view. It begins with a historical introduction of calculus. The chapters of this book present all the major topics related to linear analysis as well as nonlinear analysis. The final section of the book features some unique topics like set functions, elementary probability, calculus of probabilities, and numerical analysis. The theorems mentioned in this book are thoroughly explained along with their proofs and applications. Each chapter contains plenty of examples and exercises.
|5. “Calculus and Analytic Geometry” by G B Thomas and R L Finney|
| 6. “Multivariable Calculus” by James Stewart
“Multivariable Calculus” Book Review: The book aims in delivering deep knowledge of calculus and enables the readers to develop technical competence. The chapters of this book cover parametric equations, infinite sequence and series, vectors and geometry of space, vector functions, partial derivatives, multiple integrals, vector calculus, and second-order differential equations. It is a well-structured and reader-friendly piece of work featuring comprehensive, precise, and clear-cut content. The book helps its readers in brushing up their mathematical skills. It is a rich source of information and is supported by many relatable examples.
| 7. “Multivariable Calculus” by James Stewart
“Multivariable Calculus” Book Review: The book aims at presenting calculus from a technical perspective. The chapters of this book are straightforward, precise, and are enhanced with several real-world examples. The topics like parametric equations, infinite sequence and series, vectors and geometry of space, vector functions, partial derivatives, multiple integrals, vector calculus, and second-order differential equations are thoroughly explained. The applications and uses of featured topics and concepts are highlighted. Many exercises as well as solved and unsolved problems are included in this text. The book will be suitable for the individuals with a mathematical background as well as the students pursuing their career in the field of mathematics.
| 8. “Multivariable Calculus” by William L Briggs and Lyle Cochran
“Multivariable Calculus” Book Review: The book reflects the fundamental principles and key concepts of multivariable calculus in a reader-friendly manner. It provides a strong foundation of calculus, hence enabling the readers to deal with advanced concepts of multivariable calculus. It lays an emphasis on geometrical concepts for better explanation of the related topics. The chapters of this text are compact, creative, and efficient. The book is illustrated with several figures, questions, and exercises. The further scope and developments that are due in multivariable calculus are highlighted in this book.
| 9. “Multivariable Calculus” by C Henry Edwards and David E Penney
“Multivariable Calculus” Book Review: The book aims at presenting deep information on each and every aspect of calculus. The book presents thorough information on each and every aspect of calculus. The latest ideas and discoveries in the field of multivariable calculus are mentioned. The application of geometrical concepts and methods in calculus is reflected through this text. The book introduces calculator and computer technology and aims in presenting the major topics related to them. The book will be suitable for the undergraduate courses of calculus.
| 10. “Multivariable Calculus” by James Stewart
“Multivariable Calculus” Book Review: The book is a rich source of information featuring many aspects, examples, and applications of multivariable calculus. The initial chapters of this book describe parametric equations, polar coordinates, and infinite sequence and series in detail. The remaining chapters cover vectors and geometry of space, vector functions, partial derivatives, multiple integrals, vector calculus, and second-order differential equations. The topics of this book are illustrated from a technical view-point. Many problems and exercises are included for self-study and practice of the readers. The book will enable the readers in enhancing their mathematical as well as technical skills.
|11. “Calculus and Analytic Geometry” by G B Thomas
“Calculus and Analytic Geometry” Book Review: The book introduces derivatives and their applications along with integration, its methods, and applications of definite integrals. This is followed by extensive coverage of transcendental and hyperbolic functions, sequences and infinite series, power series, partial derivatives, multiple integrals and differential equations. Subsequent chapters deal with plane analytic geometry, polar coordinates, vectors, vector functions and their derivatives, and vector analysis. Illustrations, examples and solved exercises are also included. This book is designed for undergraduate students and teachers.
|12. “100 Instructive Calculus-based Physics Examples: Electricity and Magnetism: Volume 2 (Calculus-based Physics Problems with Solutions)” by Chris McMullen
“100 Instructive Calculus-based Physics Examples: Electricity and Magnetism: Volume 2 (Calculus-based Physics Problems with Solutions)” Book Review: This book covers electricity and magnetism, including electric field, gauss’s law, electric potential, capacitance, resistance, Kirchhoff’s rules, and the law of Biot-Savart. It has 100 examples with step by step solutions and explanations. It also includes tables of equations, symbols and units. It provides a variety of examples for how to solve fundamental physics problems.
|13. “Schaum’s Outline of Advanced Calculus, Third Edition (Schaum’s Outlines)” by Robert Wrede
“Schaum’s Outline of Advanced Calculus, Third Edition (Schaum’s Outlines)” Book Review: This Schaum’s Outline provides 1,370 fully solved problems, Complete review of all course fundamentals,Clear, concise explanations of all Advanced Calculus concepts. Topics include: Numbers; Sequences; Functions, Limits, and Continuity; Derivatives; Integrals; Partial Derivatives; Vectors; Applications of Partial Derivatives; Multiple Integrals; Line Integrals, Surface Integrals, and Integral Theorems; Infinite Series; Improper Integrals; Fourier Series; Fourier Integrals; Gamma and Beta Functions; and Functions of a Complex Variable.
2. Transform Calculus
|1. “Distributions in the Physical and Engineering Sciences: Distributional and Fractal Calculus, Integral Transforms and Wavelets” by Alexander I Saichev and Wojbor A Woyczynski
“Distributions in the Physical and Engineering Sciences: Distributional and Fractal Calculus, Integral Transforms and Wavelets: 1 (Applied and Numerical Harmonic Analysis)” Book Review: Conveyances in the Physical and Engineering Sciences is an exhaustive work on logical strategies for taking care of science and designing issues. It is composed from the bringing together perspective of appropriation hypothesis and advanced with numerous cutting edge themes which are significant for professionals and analysts. The objective of the books is to give the peruser, subject matter expert and non-trained professional, usable and current numerical instruments in their exploration and investigation. This new content is proposed for graduate understudies and analysts in applied math, actual sciences and designing. The cautious clarifications, available composing style, and numerous representations/models likewise make it reasonable for use as a self-study reference by anybody looking for more prominent agreement and capability in critical thinking strategies introduced. The book is ideal for an overall logical and designing crowd, yet it is numerically exact.
|2. “Schaum’s Outline of Laplace Transforms (Schaum’s Outlines of Theory and Problems)” by Murray R Spiegel
“Schaum’s Outline of Laplace Transforms (Schaum’s Outlines of Theory and Problems)” Book Review: In excess of 40 million understudies have believed Schaum’s to assist them with succeeding the homeroom and on tests. Schaum’s is the way to quicker learning and higher evaluations in each subject. Each Outline presents all the fundamental course data in a simple to-follow, theme by-point design. You likewise get many models, tackle issues, and practice activities to test your abilities.
|3. “Fourier Transforms (Dover Books on Mathematics)” by Ian Naismith Sneddon
“Fourier Transforms (Dover Books on Mathematics)” Book Review: The reason for this book is to introduce the hypothesis of Fourier changes and related subjects in a structure appropriate for the utilization of understudies and examination laborers intrigued by the limit esteem issues of material science and designing. The focal point of the book is on applications, instead of on the actual hypothesis; hence, the initial three sections are dedicated to an overall treatment of the basics, yet no endeavor is made to introduce the establishment in their most broad structure. All things being equal, the primary hypotheses are set up for a specific class of capacities which is adequately wide to accept the majority of those which happen in issues in applied math. The last seven sections cover the employment of the hypothesis in taking care of limits and beginning worth issues in designing and material science. To make the book open to students starting the investigation of hypothetical physical science, no specific information on physical science is expected, anyway a decent establishment in cutting edge analytics is essential. Every section starts with a conversation of the actual essentials and the deduction of the fundamental conditions. Additionally, the creator has made careful arrangements to incorporate, in the sections on fundamental hypothesis, not just the regular properties of the Fourier changes, yet additionally those of the Mellin, Laplace, and Hankel changes. Limited changes, double vital conditions, the Wiener-Hopf methodology, and the properties of the Dirac delta work are additionally thought to be in some detail. The actual issues remembered for the content were deliberately picked for their significance and pertinence to the subject being talked about.
| 4. “Complex Variables and the Laplace Transform for Engineers (Dover Books on Electrical Engineering)” by Wilbur R LePage
“Complex Variables and the Laplace Transform for Engineers (Dover Books on Electrical Engineering” Book Review: Mechanical and Applied Mathematics Specialists regularly don’t have the opportunity to enroll in a class to study complex variable hypothesis as students, yet is perhaps the most significant and valuable parts of arithmetic, with numerous applications in designing. This content is intended to cure that need by providing graduate designing understudies (particularly electrical designing) with a course in the fundamental hypothesis of complex factors, which thus is crucial for the comprehension of change hypothesis. Assuming decent information on analytics, the book bargains clearly and thoroughly with significant numerical ideas, finding some kind of harmony between absolutely numerical medicines that are excessively broad for the architect, and books of applied designing which may neglect to pressure huge numerical thoughts. The content is partitioned into two essential parts: The initial segment (Chapters 1–7) is committed to the hypothesis of complex factors and starts with a diagram of the construction of framework investigation and a clarification of fundamental numerical and designing terms. Part 2 treats the establishment of the hypothesis of a mind boggling variable, revolved around the Cauchy-Riemann conditions. The following three sections — conformal planning, complex reconciliation, and limitless arrangement — pave the way to an especially significant part on multivalued capacities, clarifying the ideas of solidness, branch focuses, and riemann surfaces. Various charts delineate the actual utilizations of the numerical ideas included.
| 5. “Elements of the Theory of Functions (Dover Books on Mathematics)” by Konrad Knopp and F Bagemihl
“Elements of the Theory of Functions (Dover Books on Mathematics)” Book Review: This well-known#160;book gives a reasonable and brief audit of general capacity hypothesis by means of complex factors. Appropriate for undergrad math majors, the treatment investigates just those themes that are easiest but at the same time are generally significant for the improvement of the hypothesis. Requirements incorporate information on the establishments of genuine examination and of the components of scientific math. The content starts with a prologue to the arrangement of complex numbers and their tasks. At that point the idea of sets of numbers, the cutoff idea, and firmly related issues are stretched out to complex amounts. Last sections inspect the rudimentary capacities, including judicious and straight capacities, remarkable and mathematical capacities, and a few others just as their inverses, including the logarithm and the cyclometric capacities. Various models explain the fundamental thoughts, and verifications are communicated in an immediate way without penance of fulfillment or meticulousness.
| 6. “Complex Variables and Transform Calculus” by MRahman
“Complex Variables and Transform Calculus” Book Review: In light of a progression of talks given by the creator this content is intended for college understudies with a comprehension of vector analytics, arrangement methods of customary and fractional differential conditions and rudimentary information on essential changes. It will likewise be an important reference to researchers and architects who need to know the essential numerical improvement of the hypothesis of complex factors to take care of field issues. The hypotheses given are all around represented with models.
| 7. “Handbook of Multivalued Analysis: Volume I: Theory: 1 (Mathematics and Its Applications)” by Shouchuan Hu and Nikolaos S Papageorgiou
“Handbook of Multivalued Analysis: Volume I: Theory: 419 (Mathematics and Its Applications)” Book Review: A wide range of uses that this hypothesis gives. We notice that the current writing regarding this matter incorporates the books of J. P. Aubin, J. P. Aubin-A. Cellina, J. P. Aubin-H. Frankowska, C. Castaing-M. Valadier, K. Deimling, M. Kisielewicz and E. Klein-A. Thompson. Notwithstanding, these books either manage one specific area of the subject or present principally the limited dimensional parts of the hypothesis. In this volume, we have made a decent attempt to give a significantly more complete image of the subject, to incorporate some significant new improvements that happened lately and a point by point catalog. Albeit the introduction of the subject requires some information in different territories of numerical investigation, we have intentionally made this book pretty much independent, with the assistance of an all-encompassing reference section in which we have accumulated a few fundamental thoughts and results from geography, measure hypothesis and nonlinear practical examination. In this volume we present the hypothesis of the subject, while in the second volume we will talk about predominantly applications. This volume is separated into eight sections. The progression of parts follows pretty much the authentic improvement of the subject. We start with the topological hypothesis, trailed by the quantifiability investigation of multifunctions. Part 3 arrangements with the hypothesis of droning and accretive administrators. The firmly related subjects of the degree hypothesis and fixed purposes of multifunctions are introduced in Chapters 4 and 5, individually.
|8. “Differential Equations with Introduction to Laplace Transform” by Apurba Narayan Das|
| 9. “Introduction to Radon Transforms: With Elements of Fractional Calculus and Harmonic Analysis (Encyclopedia of Mathematics and its Applications)” by Boris Rubin
“Introduction to Radon Transforms: With Elements of Fractional Calculus and Harmonic Analysis (Encyclopedia of Mathematics and its Applications)” Book Review: The Radon transform represents a function on a manifold by its integrals over certain submanifolds. Integral transformations of this kind have a wide range of applications in modern analysis, integral and convex geometry, medical imaging, and many other areas. Reconstruction of functions from their Radon transforms requires tools from harmonic analysis and fractional differentiation. This comprehensive introduction contains a thorough exploration of Radon transforms and related operators when the basic manifolds are the real Euclidean space, the unit sphere, and the real hyperbolic space. Radon-like transforms are discussed not only on smooth functions but also in the general context of Lebesgue spaces. Applications, open problems, and recent results are also included. The book will be useful for researchers in integral geometry, harmonic analysis, and related branches of mathematics, including applications. The text contains many examples and detailed proofs, making it accessible to graduate students and advanced undergraduates.
| 10. “Stability Theory of Differential Equations (Dover Books on Mathematics)” by Richard Bellman
“Stability Theory of Differential Equations (Dover Books on Mathematics)” Book Review: Reasonable for cutting edge students and graduate understudies, this was the primary English-language text to offer point by point inclusion of boundedness, strength, and asymptotic conduct of straight and nonlinear differential conditions. It stays an exemplary guide, highlighting material from unique exploration papers, including the creator’s own investigations. The direct condition with steady and nearly constant coefficients gets inside and out consideration that incorporates parts of grid hypothesis. No past associate with the hypothesis is fundamental, since creator Richard Bellman determines the outcomes in network hypothesis all along. With respect to the steadiness of nonlinear frameworks, aftereffects of the direct hypothesis are utilized to drive the consequences of Poincaré and Liapounova. Teacher Bellman at that point studies significant outcomes concerning the boundedness, dependability, and asymptotic conduct of second-request straight differential conditions. The last parts investigate critical nonlinear differential conditions whose arrangements might be totally depicted regarding asymptotic conduct. Just genuine arrangements of genuine conditions are thought of, and the treatment accentuates the conduct of these arrangements as the free factor increments unbounded.
|11. “Advanced Calculus for Users” by Alain Robert
Book Review: This book is very useful for physicists and engineers in the field of advanced calculus. The book also presents the concepts of linearization, derivative and differential forms, finite dimensional vector spaces, functional analysis basics, infinite dimensional function spaces, convergence concepts for sequences and series of functions, fourier series and various concepts of historical applications.
3. Differential Calculus and Vector Calculus
|1. “Calculus of Variations (Dover Books on Mathematics)” by Isarel M Gelfand and S V Fomin
“Calculus of Variations (Dover Books on Mathematics)” Book Review: This book is designed for engineers, physicists. And also for applied mathematicians at advanced undergraduate and graduate levels. It includes canonical equations, variational principles of mechanics, and conservation laws. It also includes the theory of fields and sufficient conditions,the application of variational methods. Later it focuses on direct methods in the calculus of variations. It contains a generous number of exercises and diagrams.
|2. “Essential Calculus with Applications (Dover Books on Mathematics)” by Richard A Silverman
“Essential Calculus with Applications (Dover Books on Mathematics)” Book Review: This book is designed for engineers, physicists. And also for applied mathematicians at advanced undergraduate and graduate levels. The required chapters are starting from differential calculus with a discussion of the key concept of function. Then it continues with derivatives and limit, velocity, continuous and differentiable functions. It also includes indefinite integral, local extrema, and concrete optimization problems, integral calculus. Later it focuses on Riemann integral, improper integrals, differential equations, and their applications. The final chapter is devoted to the differential calculus of functions of several variables. The book contains numerous problems and answers.
|3. “Differential Forms: A Complement to Vector Calculus” by Weintraub|
|4. “Differential Calculus in Normed Linear Spaces (Texts and Readings in Mathematics)” by Kalyan Mukherjea
“Differential Calculus in Normed Linear Spaces (Texts and Readings in Mathematics)” Book Review: This book consists of topics on advanced calculus from a geometric point of view. Chapters mentioned are linear transformation between normed linear spaces, the Inverse and Implicit function theorems, convergence of sequences and series of real numbers. Applications and examples are included for students’ practice. This book can be useful for mathematics, physics and engineering students.
|5. “Complex Analysis With Vector Calculus” by Cooray T M J A
“Complex Analysis With Vector Calculus” Book Review: Result of many years of research from the author, this book provides a clear explanation on the topic of Complex Analysis of Vector Calculus. This book is targeted for undergraduate engineering students enrolled in a course of engineering mathematics. Other important chapters contained in the book include algebra and its operations on vector and scalar fields and many more related concepts. A variety of examples and questions have been provided throughout the book to easen the understanding of the reader.
|6. “Essential Calculus with Applications (Dover Books on Mathematics)” by Richard A Silverman
“Essential Calculus with Applications (Dover Books on Mathematics)” Book Review: This book explains calculus not only helps in solving mathematical problems but also problems in the diverse fields of physics, biology and economics and many more of them. Written by a noted mathematician, this book provides a wider exposure of Calculus to undergraduate students. Starting from basics, the author described topics like sets, inequalities, absolute value, mathematical induction etc. Moving to a more advanced level, topics like velocity, continuous and differentiable functions, the indefinite integral, local extrema, and concrete optimization problems are covered in the book. Last chapter is completely devoted to differential calculus of functions of several variables.
|7. “Vector Analysis (Undergraduate Texts in Mathematics)” by Klaus Jänich and L Kay
“Vector Analysis (Undergraduate Texts in Mathematics)” Book Review: This Book covers modern vector analysis and describes the classical notion and understanding of the theory of Vector Analysis. It covers all the concepts of classical vector analysis in Euclidean space. It also introduces newer concepts like de Rham Cohomology, Hodge theory, elementary differential geometry, and basic duality in the same. Prerequisite needed to start this book is calculus and linear algebra. Ample amount of illustrations, exercises and tests are also provided in the book.
|8. “Multivariable Calculus With Vectors” by Hartley Rogers
“Multivariable Calculus With Vectors” Book Review: This book is for students studying in the third semester or taking fourth and fifth quarters of the calculus course. Advanced topic of multivariate calculus is covered extensively in the book. Other topics that are covered in the book include modeling physical phenomena, developing geometric intuition etc. A variety of examples and questions have been provided throughout the book to easen the understanding of the reader.
4. Multivariable Calculus
|1. “Multivariable Calculus” by Clark Bray
“Multivariable Calculus” Book Review: The book is basically for the students of sciences and engineering, seeking deep knowledge on multivariable calculus. The chapters of this book feature multivariable functions along with different ways for their geometrical representation. The topics like gravitational, electric, and magnetic fields, linear algebra, derivative transformation and Jacobian matrices are discussed in detail. The manipulating multivariable equations and Maxwell’s laws are clearly explained. The book also highlights the relationship between featured physical ideas and vector calculus theorems of Gauss and Stokes. For better understanding of the readers, the substantial applications of multivariable calculus are mentioned.
| 2. “Multivariable Calculus” by Ron Larson and Bruce H Edwards
“Multivariable Calculus” Book Review: The book focuses on conceptual as well as technological aspects of multivariable calculus. The chapters of this book are comprehensive, precise, and contain proper definitions and detailed theory of featured concepts. The topics like vectors, geometry of space, vector-valued functions, multiple integration, and vector analysis are explained efficiently. Many exercises and questions are included in this text for self-study and self-assessment of the readers. To give the book’s content visual support several applications and real world examples of multivariable calculus are mentioned. The book will be valuable for the students and teachers of mathematics.
|3. “Integral Calculus For Beginners” by First and Joseph Edwards
“Integral Calculus For Beginners” Book Review: This book is designed for the engineering aspirants. This book provides the basic concepts of integral calculus. It also divided into notation, summation and applications, general method and standard forms, method of substitution, integration by parts, partial fractions, sundry standard methods, reduction formulae, miscellaneous methods, rectification, quadrature, surface and volumes of solids of revolution, second order elements of area miscellaneous applications, equations of the first order, equations of the second order, exact differential equations, linear differential equations with constant coefficient and orthogonal trajectories miscellaneous equations. And it also contains the single correct answers, multiple correct answers, multiple correct options, passage-based, matching types, assertion and reason, integer answer types with complete solutions.
|4. “Differential and Integral Calculus Vol. I” by N S Piskunov
“Differential and Integral Calculus Vol. I” Book Review: The book focuses on the fundamental concept of differential calculus that is the derivative. It will provide a base for studying various technical subjects. The chapters of this book contain a thorough discussion on variables, functions, limits, and continuity of a function. Each chapter contains several questions and problems. The content of this book is supported by many worked examples. It consists of many techniques and models for dealing with problem solving. The book will be suitable for the courses of mathematics in higher technical schools.
|5. “Differential and Integral Calculus Vol. II” by N S Piskunov
“Differential and Integral Calculus Vol. II” Book Review: The book aims at delivering thorough information on calculus. The chapters of this book majorly cover all the aspects of differential as well as integral calculus. Initially, topics like differential equations, multiple integrals, line integrals, surface integrals, and Fourier series are thoroughly explained. Moving further, the advanced topics like equations of mathematical physics, operational calculus and its applications, elements of probability and mathematical statistics, and matrices discussed in detail. The book will be beneficial of the students and teachers of mathematics.
|6. “Calculus: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability” by Tom M Apostol
“Calculus: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability” Book Review: This book is an introduction to calculus. It balances between theory and technique. The text states the difference between the integral and the derivative. It includes the proofs of all the important theorems. The volume introduces the mean-value theorems and their applications. It incorporates a treatment of linear algebra, and contains many new and easier exercises.
|7. “A Course in Multivariable Calculus and Analysis (Undergraduate Texts in Mathematics)” by Sudhir R Ghorpade and Balmohan V Limaye
“A Course in Multivariable Calculus and Analysis (Undergraduate Texts in Mathematics)” Book Review: This textbook gives exposition of multivariable calculus. The book includes analogues of basic results in one-variable calculus, such as the mean value theorem and the fundamental theorem of calculus. It examines topics such as monotonicity, monotonicity, and convexity. Each chapter contains detailed proofs of relevant results. It also has numerous examples and a wide collection of exercises. The book is for undergraduate and graduate students.
|8. “Multivariable Calculus, Linear Algebra and Differential Equations” by Stanley I Grossman
“Multivariable Calculus, Linear Algebra and Differential Equations” Book Review:
This textbook is for the second-year calculus course. It is divided into five parts. This includes multivariable calculus; linear algebra; introduction to intermediate calculus; differential equations; and review of Taylor polynomials, sequences, and series. The text contains some 5,500 exercises.
|9. “Multivariable Calculus, Linear Algebra and Differential Equations” by Stanley I Grossman|
| 10. “Multivariable Mathematics: United States Edition” by Richard E Williamson and Hale F Trotter
“Multivariable Mathematics: United States Edition” Book Review: This book explores the standard problem-solving techniques of multivariable mathematics. It also explores integrating vector algebra ideas with multivariable calculus and differential equations. The major topics discussed are the introduction of vector geometry and matrix algebra. Also, the early introduction of the gradient vector as the key to differentiability and optional numerical methods are included.
| 11. “Multivariable Dynamic Calculus on Time Scales” by Martin Bohner and Svetlin G Georgiev
“Multivariable Dynamic Calculus on Time Scales” Book Review: This book offers an overview of recent developments of multivariable dynamic calculus on time scale. It covers topics from parameter-dependent integrals to partial differentiation on time scales. The chapters provide a pathway to this active area of research. The text is for students and researchers in mathematics and the physical sciences. The book presents a clear and well-organized treatment of the concept behind the mathematics and solution techniques. Also, includes many practical examples and exercises.
| 12. “An Introduction to Multivariable Analysis from Vector to Manifold” by Piotr Mikusinski and Michael D Taylor
“An Introduction to Multivariable Analysis from Vector to Manifold” Book Review: This text provides various ways of handling some of the useful concepts encountered in dealing with the machinery of multivariable analysis and differential forms on manifolds. It is useful for students and researchers in the above fields. The major topics discussed are systematic exposition, brief development of linear algebra in Rn and supported by numerous examples and exercises from the computational to the theoretical. There are chapters covering the wedge product, differential forms, and the generalized Stokes’ theorem. It includes bibliography and comprehensive index Core topics in multivariable analysis. The volume is for senior undergraduates and graduate studies in differential geometry and for analysis in N dimensions.
| 13. “Derivatives and Integrals of Multivariable Functions” by Alberto Guzman
“Derivatives and Integrals of Multivariable Functions” Book Review: This text is for a one-semester course of advanced calculus of several variables. In the first three chapters, differentiability and derivatives are defined. It includes properties of derivatives reducible to the scalar and real-valued. The next following chapters proceed analogously through the development of integration theory. Also, properties of integrals of scalar functions are discussed. The text presents results about scalar integrals of vector functions. It also emphasizes the physical applications of the theory.
|14. “Stochastic Calculus and Applications” by R J Elliot
“Stochastic Calculus and Applications” Book Review: This book is thoroughly updated and is streamlined to reflect the upliftment in the field. This book gives the beginners a good overview of the topic through the modern general theory of random processes and stochastic integrals as used by systems theorists. This book is for electronic engineers and for those working in quantitative and mathematical finance. This book is equipped with proofs, problems and explanatory materials to increase the focus. This book covers topics like Measure and Integral, Probabilities and Expectation, Filtrations, Stopping Times and Stochastic Processes, Martingales in Discrete Time, Martingales in Continuous Time, The Progressive, Optional and Predictable σ-Algebras, Processes of Finite Variation, The Structure of Square Integrable Martingales, Quadratic Variation and Semimartingales, The Stochastic Integral, The Exponential Formula and Girsanov’s Theorem. This book also explains chapters like Lipschitz Stochastic Differential Equations, Backward Stochastic Differential Equations, Filtering, Optimal Control of Drifts and Jump Rates, Control of a Single Jump with detailed explanations.
5. Integral Calculus
|1. “Calculus of Variations (Dover Books on Mathematics)” by Isarel M Gelfand and S V Fomin
“Calculus of Variations (Dover Books on Mathematics)” Book Review: The aim of the book is to give a treatment of the elements of the calculus of variations in a form both easily understandable and sufficiently modern. It concentrates on physical applications of variational methods, e.g., canonical equations, variational principles of mechanics, and conservation laws. The book starts with a complete university level course in the subject, including the theory of fields and sufficient conditions for weak and strong extrema. Further, it explains the application of variational methods to the study of systems with infinite degrees of freedom. The book concludes with direct methods in the calculus of variations. It is valuable for advanced undergraduate and graduate students of mathematics and physics.
|2. “Calculus for Engineers and Students of Science – An Introduction to the Differential and Integral Calculus for the Use of Engineering and Technical Students” by John Stoney|
|3. “Calculus for Scientists and Engineers: An Analytical Approach” by K D Joshi
“Calculus for Scientists and Engineers: An Analytical Approach” Book Review: This book concentrates on the why of mathematics rather than how’s. It covers the wide range of course for the reader who is taking a first course in calculus. It provides deeper insights or required transition from calculus to analysis. It explains abstract concepts and helps beginners to overcome the intimidation which often felt when first confronting abstraction. It demonstrates the different techniques through numerous exercises with answers supplied at the end of the book.
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