49 Best Books on Calculus

We have compiled a list of the Best Reference Books on Calculus, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of Calculus Books with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Calculus below.

1. Calculus

 
1."Calculus - Single and Multivariable" by Hughes-Hallett
“Calculus – Single and Multivariable” Book Review: The aim of the book is to provide a balanced introduction to calculus that blends modeling and practical skills. It delves into a range of topics including the 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 with detailed explanations. Mathematical concepts such as differentiation, integration, and calculus of vector fields are used as tools throughout the book. Additionally, the book provides visual support for fundamental concepts through graphical, numerical, symbolic, and verbal explanations.

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2."Calculus" by James Stewart
“Calculus” Book Review: This book presents calculus in a technical manner with well-written chapters that cover topics like functions and limits, derivatives, integrals, inverse functions, polar coordinates, infinite sequence and series, vectors, partial derivatives, and vector calculus. Chapters also focus on the applications of differentiation, integration, and techniques of integration, and cover many applications of calculus such as differential equations, parametric equations, multiple integrals, and second-order differential equations. The content is comprehensive, precise, and includes many real-world examples.

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3."Calculus Vol. I" by T M Apostol
“Calculus Vol. I” Book Review: This book strikes a balance between theoretical and technical concepts of calculus. It begins with a thorough explanation of integration and then moves on to differentiation, with the aim of displaying the real link between integrals and derivatives. The book also includes discussions of linear algebra as well as the mean-value theorems and their applications. The featured theorems are illustrated with their proofs, followed by geometric or intuitive discussions. Many exercises are included in this text for self-assessment and practice.

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4."Calculus Vol. II" by T M Apostol
“Calculus Vol. II” Book Review: This book takes a theoretical and technical approach, starting with a historical introduction to calculus. The chapters cover major topics related to linear analysis as well as nonlinear analysis, with a final section featuring unique topics such as set functions, elementary probability, calculus of probabilities, and numerical analysis. The book thoroughly explains theorems with their proofs and applications, and each chapter includes plenty of examples and exercises.

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5."Calculus and Analytic Geometry" by G B Thomas and R L Finney
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6."Multivariable Calculus" by James Stewart
“Multivariable Calculus” Book Review: This book aims to provide readers with a comprehensive understanding of calculus and help them develop technical proficiency. It covers a range of topics including parametric equations, infinite sequences and series, vectors and geometry in space, vector functions, partial derivatives, multiple integrals, vector calculus, and second-order differential equations. The content is well-organized and easy to follow, featuring clear and precise explanations. The book is also a great resource for improving mathematical skills and is supported by numerous relatable examples.

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7."Multivariable Calculus" by James Stewart
“Multivariable Calculus” Book Review: The primary focus of this book is to present calculus from a technical perspective. The chapters are concise, accurate, and enriched with practical real-world examples. The book delves into various topics, such as parametric equations, infinite sequences and series, vectors and geometry in space, vector functions, partial derivatives, multiple integrals, vector calculus, and second-order differential equations. The text also highlights the applications and significance of these concepts. It contains a variety of exercises and solved and unsolved problems that make it ideal for individuals with a mathematical background or students pursuing a career in mathematics.

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8."Multivariable Calculus" by William L Briggs and Lyle Cochran
“Multivariable Calculus” Book Review: This book provides readers with a reader-friendly understanding of the fundamental principles and key concepts of multivariable calculus. It serves as a strong foundation in calculus, allowing readers to tackle advanced multivariable calculus concepts with ease. The book emphasizes the use of geometrical concepts for better explanation of related topics. The chapters are compact, creative, and efficient. Additionally, it features numerous figures, questions, and exercises. The book also highlights future developments and opportunities in multivariable calculus.

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9."Multivariable Calculus" by C Henry Edwards and David E Penney
“Multivariable Calculus” Book Review: The primary goal of this book is to provide in-depth information on all aspects of calculus. It presents the latest ideas and discoveries in multivariable calculus while also highlighting the use of geometrical concepts and methods in calculus. The book also introduces calculator and computer technology while presenting major topics related to them. It is suitable for undergraduate courses in calculus.

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10."Multivariable Calculus" by James Stewart
“Multivariable Calculus” Book Review: This book provides a comprehensive coverage of multivariable calculus, featuring various aspects, examples, and applications. The book begins by explaining parametric equations, polar coordinates, and infinite sequences and series in detail, followed by an extensive coverage of vectors and geometry of space, vector functions, partial derivatives, multiple integrals, vector calculus, and second-order differential equations. The technical view-point of the topics is illustrated, and the book includes many problems and exercises for self-study and practice. The readers can enhance their mathematical and technical skills through this book.

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11."Calculus and Analytic Geometry" by G B Thomas
“Calculus and Analytic Geometry” Book Review: This book is a comprehensive guide to calculus, beginning with derivatives and their applications, and then moving on to integration and its methods, along with applications of definite integrals. It covers transcendental and hyperbolic functions, sequences and infinite series, power series, partial derivatives, multiple integrals, and differential equations. The subsequent chapters cover plane analytic geometry, polar coordinates, vectors, vector functions, and their derivatives, and vector analysis. The book also includes illustrations, examples, and solved exercises. It is designed for undergraduate students and teachers.

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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 provides an in-depth coverage of electricity and magnetism, including electric field, Gauss’s law, electric potential, capacitance, resistance, Kirchhoff’s rules, and the law of Biot-Savart. It contains 100 examples with step-by-step solutions and explanations, as well as tables of equations, symbols, and units. The book provides a variety of examples to solve fundamental physics problems.

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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 presents a complete review of all the fundamentals of Advanced Calculus, along with clear and concise explanations of all the concepts. It includes 1,370 fully solved problems, covering topics such as 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.

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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: This book is a comprehensive guide that explores mathematical techniques for solving scientific and engineering problems. It takes a unified approach, drawing on distribution theory and introducing advanced topics relevant to both practitioners and researchers. The book aims to equip readers, both experts and non-experts, with practical and up-to-date mathematical tools for their research and analysis. This text is intended for graduate students and researchers in applied mathematics, physical sciences, and engineering. The clear explanations, accessible writing style, and numerous illustrations/examples also make it a useful self-study reference for anyone seeking to improve their understanding and proficiency in problem-solving techniques. While suitable for a general scientific and engineering audience, the book is mathematically rigorous.

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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: This is an ideal resource for undergraduate and graduate students in engineering and mathematics. The book provides a comprehensive introduction to Laplace transforms, including topics such as inverse transforms, convolution, and applications in circuit analysis and control systems. Each chapter includes numerous examples, solved problems, and practice exercises, making it easy for students to understand and apply the concepts. The book also features a helpful glossary of Laplace transform properties and a comprehensive index for quick reference. Overall, this book is an essential tool for mastering Laplace transforms.

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3."Fourier Transforms (Dover Books on Mathematics)" by Ian Naismith Sneddon
“Fourier Transforms (Dover Books on Mathematics)” Book Review: This book presents the theory of Fourier transformations and related topics in a format suitable for students and research workers interested in the boundary value problems of physics and engineering. The book focuses on applications rather than the theory itself. The first three chapters provide a general treatment of the fundamentals, although the foundation is not presented in its most extensive form. Instead, the primary theories are established for a specific class of functions that are broad enough to encompass most of those encountered in applied mathematics. The final seven chapters cover the application of the theory in solving boundary value and initial value problems in engineering and physics. The book is accessible to students with a strong foundation in advanced calculus, and no specific knowledge of physics is required. Each chapter begins with a discussion of the fundamental principles and the derivation of the basic equations. The author also includes properties of the Mellin, Laplace, and Hankel transformations, as well as a discussion of the Dirac delta function and other related topics.

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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: The book discusses the importance of complex variable theory in engineering and the need for a course for mechanical and applied mathematics specialists. The book “Fundamentals of Complex Analysis for Engineers with Applications to the Theory of Linear Systems” provides a thorough and clear explanation of the essential theory of complex variables. The book strikes a balance between purely mathematical treatments that may be too extensive for engineers and books on applied engineering that may overlook important mathematical ideas. Divided into two parts, the book covers topics such as conformal mapping, complex integration, and multivalued functions. The book includes various illustrations to demonstrate the practical applications of the mathematical concepts covered.

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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 book, widely known for its concise and comprehensive review of complex analysis, is suitable for undergraduate math majors. It covers only the most fundamental and relevant topics in the development of the theory, assuming a solid understanding of real analysis and mathematical logic. The text starts with an introduction to complex numbers and their operations, then extends the concepts of sets and limits to complex quantities. The final chapters examine elementary functions such as rational and linear functions, exponential and trigonometric functions, and their inverses, including logarithmic and cyclometric functions. The fundamental ideas are illustrated with numerous examples, and the proofs are presented in a direct and rigorous manner.

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6."Complex Variables and Transform Calculus" by MRahman
“Complex Variables and Transform Calculus” Book Review: This is a comprehensive textbook that covers complex variables and transform calculus topics. The book is organized into twelve chapters that cover topics such as complex functions, analytic functions, conformal mappings, contour integration, Fourier series, Laplace transforms, and Z-transforms. The book is aimed at students pursuing undergraduate and graduate degrees in mathematics, physics, engineering, and related fields. The author provides numerous examples and exercises throughout the book, making it a useful resource for both self-study and classroom use. The book is highly recommended for anyone seeking a solid foundation in complex variables and transform calculus.

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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: The theory of complex variables has many practical applications. While existing literature on the subject includes works by 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, these books generally focus on specific areas or limited dimensional aspects of the theory. In this volume, we aim to provide a more comprehensive picture of the subject, including recent developments and a detailed index. Although some background in other areas of mathematical analysis is required, we have intentionally made this book relatively self-contained, with the help of an extensive appendix that collects some basic ideas and results from topology, measure theory, and nonlinear functional analysis. This volume covers the theory of the subject, while the second volume will focus mainly on applications. The book is divided into eight chapters, following the historical development of the subject. We begin with the topological theory, followed by the quantitative analysis of multifunctions. Chapter 3 deals with the theory of monotone and accretive operators. The closely related subjects of degree theory and fixed points of multifunctions are presented in Chapters 4 and 5, respectively.

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8."Differential Equations with Introduction to Laplace Transform" by Apurba Narayan Das
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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: This comprehensive introduction delves into the Radon transform and its various applications in modern analysis, integral and convex geometry, medical imaging, and other areas. The book offers a thorough exploration of the Radon transform and related operators, with a focus on the real Euclidean space, the unit sphere, and the real hyperbolic space. It also discusses Radon-like transforms on smooth functions and in the general context of Lebesgue spaces. The book contains many examples, detailed proofs, and covers applications, open problems, and recent results. It will be useful for researchers in integral geometry, harmonic analysis, and related branches of mathematics, including applications, as well as graduate students and advanced undergraduates.

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10."Stability Theory of Differential Equations (Dover Books on Mathematics)" by Richard Bellman
“Stability Theory of Differential Equations (Dover Books on Mathematics)” Book Review: This classic guide is suitable for advanced and graduate students, providing detailed coverage of the boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. The text includes material from original research papers, including the author’s own studies. The book delves deeply into the linear equation with constant and nearly constant coefficients, which includes aspects of matrix theory. No previous experience with the theory is required, as the author derives the results in matrix theory along the way. The stability of nonlinear systems is studied, and the results of linear theory are used to derive the results of Poincaré and Liapounova. The author then examines important results concerning the boundedness, stability, and asymptotic behavior of second-order linear differential equations. The final chapters explore significant nonlinear differential equations, and their solutions are fully described in terms of asymptotic behavior. Only real solutions of real equations are considered, and the treatment emphasizes the behavior of these solutions as the independent variable increases without bound.

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11."Advanced Calculus for Users" by Alain Robert
Book Review: This book is a useful resource for physicists and engineers studying advanced calculus. It covers topics such as linearization, derivatives and differential forms, finite dimensional vector spaces, basics of functional analysis, infinite dimensional function spaces, convergence concepts for sequences and series of functions, Fourier series, and various concepts with historical applications.

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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 intended for advanced undergraduate and graduate engineers, physicists, and applied mathematicians. It covers canonical equations, variational principles of mechanics, and conservation laws. The theory of fields and sufficient conditions, along with the application of variational methods, are also included. The later part of the book is dedicated to direct methods in the calculus of variations. It is supplemented with a generous number of exercises and diagrams for enhanced understanding.

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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 applied mathematicians at advanced undergraduate and graduate levels. It covers the fundamental topics, beginning with differential calculus, where the key concept of functions is discussed. It then moves on to derivatives and limits, velocity, continuous and differentiable functions. The book includes topics such as indefinite integral, local extrema, and concrete optimization problems, integral calculus, Riemann integral, improper integrals, differential equations, and their applications. Finally, the book focuses on the differential calculus of functions of several variables. The book features numerous problems with answers.

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3."Differential Forms: A Complement to Vector Calculus" by Weintraub
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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 presents advanced calculus topics from a geometric perspective. The chapters cover linear transformations between normed linear spaces, the Inverse and Implicit function theorems, and the convergence of sequences and series of real numbers. The book includes a range of applications and examples for students to practice, and it is suitable for mathematics, physics, and engineering students.

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5."Complex Analysis With Vector Calculus" by Cooray T M J A
“Complex Analysis With Vector Calculus” Book Review: This book on Complex Analysis of Vector Calculus is the result of years of research by the author. It provides clear explanations of the topic and is aimed at undergraduate engineering students taking a course in engineering mathematics. The book also covers important chapters on algebra and operations on vector and scalar fields, along with other related concepts. A variety of examples and questions are included throughout the book to aid the reader’s understanding.

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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 how calculus is not only useful for solving mathematical problems, but also for solving problems in diverse fields such as physics, biology, economics, and more. Written by a renowned mathematician, it provides a comprehensive introduction to calculus for undergraduate students. The book begins with the basics, covering topics such as sets, inequalities, absolute value, and mathematical induction. It then progresses to more advanced topics like velocity, continuous and differentiable functions, the indefinite integral, local extrema, and concrete optimization problems. The final chapter is devoted entirely to the differential calculus of functions of several variables. The book also includes numerous exercises to aid in understanding the concepts.

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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 presents both classical and newer concepts in the theory of Vector Analysis. It covers all the classical vector analysis concepts in Euclidean space and introduces newer concepts such as de Rham Cohomology, Hodge theory, elementary differential geometry, and basic duality. The prerequisite for this book is calculus and linear algebra, and it contains ample illustrations, exercises, and tests.

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8."Multivariable Calculus With Vectors" by Hartley Rogers
“Multivariable Calculus With Vectors” Book Review: This book is designed for students studying in their third semester or taking the fourth and fifth quarters of a calculus course. It extensively covers advanced topics in multivariate calculus and other topics such as modeling physical phenomena and developing geometric intuition. The book includes a variety of examples and questions to help readers understand the concepts.

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4. Multivariable Calculus

 
1."Multivariable Calculus" by Clark Bray
“Multivariable Calculus” Book Review: This books designed for students of science and engineering who are seeking in-depth knowledge on multivariable calculus. Each chapter delves into the topic of multivariable functions and their various geometrical representations. The book covers a wide range of topics, including gravitational, electric, and magnetic fields, linear algebra, derivative transformation, Jacobian matrices, manipulating multivariable equations, and Maxwell’s laws. Additionally, it highlights the relationship between physical concepts and vector calculus theorems of Gauss and Stokes. To facilitate better comprehension, the book provides ample applications of multivariable calculus.

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2."Multivariable Calculus" by Ron Larson and Bruce H Edwards
“Multivariable Calculus” Book Review: This comprehensive book covers both the conceptual and technological aspects of multivariable calculus. Its chapters are precise and contain detailed definitions and theory of featured concepts, such as vectors, geometry of space, vector-valued functions, multiple integration, and vector analysis. It includes numerous exercises and questions for self-study and self-assessment. Real-world examples and applications of multivariable calculus are also given to support the book’s content visually. This book will be beneficial to both students and teachers of mathematics.

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3."Integral Calculus For Beginners" by First and Joseph Edwards
“Integral Calculus For Beginners” Book Review: This book is designed for engineering aspirants and provides an introduction to integral calculus. It covers various topics, including 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 and second orders, exact differential equations, linear differential equations with constant coefficient and orthogonal trajectories, and miscellaneous equations. The book also includes single correct answers, multiple correct answers, multiple correct options, passage-based, matching types, assertion and reason, and integer answer types with complete solutions.

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4."Differential and Integral Calculus Vol. I" by N S Piskunov
“Differential and Integral Calculus Vol. I” Book Review: This book focuses on the fundamental concept of differential calculus, i.e., the derivative, which provides a base for studying various technical subjects. Its chapters contain thorough discussions on variables, functions, limits, and continuity of a function. The book includes numerous questions, problems, and worked examples. It presents several techniques and models for problem-solving and is suitable for courses in mathematics at higher technical schools.

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5."Differential and Integral Calculus Vol. II" by N S Piskunov
“Differential and Integral Calculus Vol. II” Book Review: This book aims to provide comprehensive information on calculus and covers all aspects of differential and integral calculus. It begins by discussing topics such as differential equations, multiple integrals, line integrals, surface integrals, and Fourier series. It then moves on to more advanced topics, such as equations of mathematical physics, operational calculus and its applications, elements of probability and mathematical statistics, and matrices. This book will benefit both students and teachers of mathematics.

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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 serves as an introduction to calculus and balances theory and technique. It explains the difference between the integral and the derivative and includes proofs of all important theorems. It introduces mean-value theorems and their applications and also covers linear algebra. The book contains numerous new and easier exercises.

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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 provides an exposition of multivariable calculus and 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, numerous examples, and a wide collection of exercises. This book is suitable for both undergraduate and graduate students.

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8."Multivariable Calculus, Linear Algebra and Differential Equations" by Stanley I Grossman
“Multivariable Calculus, Linear Algebra and Differential Equations” Book Review: This book is a comprehensive textbook for undergraduate mathematics students. The book covers topics in multivariable calculus, linear algebra, and differential equations. It includes chapters on vector analysis, partial differentiation, multiple integrals, vector calculus, linear algebra, ordinary differential equations, and partial differential equations. The author provides clear explanations and examples, as well as numerous exercises to reinforce concepts. This textbook is an ideal resource for students seeking a solid foundation in these fundamental areas of mathematics.

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9."Multivariable Calculus, Linear Algebra and Differential Equations" by Stanley I Grossman
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10."Multivariable Mathematics: United States Edition" by Richard E Williamson and Hale F Trotter
“Multivariable Mathematics: United States Edition” Book Review: This book delves into standard techniques for solving problems in multivariable mathematics. It also explores the integration of vector algebra concepts with multivariable calculus and differential equations. The book covers major topics such as the introduction of vector geometry and matrix algebra. Additionally, it includes an early introduction to the gradient vector as the key to differentiability and optional numerical methods.

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11."Multivariable Dynamic Calculus on Time Scales" by Martin Bohner and Svetlin G Georgiev
“Multivariable Dynamic Calculus on Time Scales” Book Review: This book provides an overview of recent developments in multivariable dynamic calculus on time scales, covering topics from parameter-dependent integrals to partial differentiation on time scales. The chapters offer a clear and well-organized treatment of the concepts behind the mathematics and solution techniques, making it useful for students and researchers in mathematics and the physical sciences. The book also includes many practical examples and exercises, providing a pathway to this active area of research.

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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 book presents various ways to handle useful concepts encountered in the machinery of multivariable analysis and differential forms on manifolds. It is intended for students and researchers in the above fields and covers core topics in multivariable analysis. The book includes a systematic exposition, a brief development of linear algebra in Rn, and numerous examples and exercises ranging from computational to theoretical. Chapters cover the wedge product, differential forms, and the generalized Stokes’ theorem. The book also includes a bibliography and comprehensive index and is suitable for senior undergraduates and graduate students in differential geometry and analysis in N dimensions.

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13."Derivatives and Integrals of Multivariable Functions" by Alberto Guzman
“Derivatives and Integrals of Multivariable Functions” Book Review: This textbook is intended for a one-semester course on advanced calculus of several variables. The first three chapters introduce the concept of differentiability and derivatives, including properties that are reducible to the scalar and real-valued cases. The subsequent chapters follow a similar development for integration theory, including discussions on the properties of integrals of scalar functions. The book also covers results on scalar integrals of vector functions, with an emphasis on physical applications of the theory.

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14."Stochastic Calculus and Applications" by R J Elliot
“Stochastic Calculus and Applications” Book Review: This updated book presents a streamlined and modern general theory of random processes and stochastic integrals, suitable for beginners and experts in electronic engineering and quantitative finance. It covers a wide range of topics, including 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. Additionally, the book includes chapters on Lipschitz Stochastic Differential Equations, Backward Stochastic Differential Equations, Filtering, Optimal Control of Drifts and Jump Rates, and Control of a Single Jump. The book provides proofs, explanatory materials, and problems to enhance the reader’s understanding and focus.

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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 goal of this book is to present a modern and comprehensible treatment of the elements of the calculus of variations, with a focus on their physical applications. This includes canonical equations, variational principles of mechanics, and conservation laws. Beginning with a thorough university-level course in the subject, the book covers the theory of fields and provides adequate conditions for weak and strong extrema. It also discusses the application of variational methods to systems with infinite degrees of freedom. Finally, the book concludes with direct methods in the calculus of variations. Advanced undergraduate and graduate students of mathematics and physics will find this book valuable.

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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
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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 focuses on the reasons behind mathematical concepts rather than the methods used to solve problems. It encompasses a wide range of topics suitable for readers taking their first course in calculus, and offers deeper insights for those transitioning from calculus to analysis. It clarifies abstract concepts and helps beginners overcome the intimidation often felt when encountering abstraction for the first time. The book illustrates various techniques through a plethora of exercises, and provides answers at the end of the book.

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We have put a lot of effort into researching the best books on Calculus and came out with a recommended list and their reviews. If any more book needs to be added to this list, please email us. We are working on free pdf downloads for books on Calculus and will publish the download link here. Fill out this Calculus books pdf download" request form for download notification.

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