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Calculus Books

This section contains free e-books and guides on Calculus, some of the resources in this section can be viewed online and some of them can be downloaded.

Calculus Category

Calculus Books

Calculus with Applications by Daniel Kleitman

The note is intended as a one and a half term course in calculus for students who have studied calculus in high school. It is intended to be self contained, so that it is possible to follow it without any background in calculus, for the adventurous.

Author(s):

s NAPages

Calculus Lectures Notes by Gerald Hoehn

This note covers following topics of Integral and Differential Calculus: Differential Calculus: rates of change, speed, slope of a graph, minimum and maximum of functions, Derivatives measure instantaneous changes, Integral Calculus: Integrals measure the accumulation of some quantity, the total distance an object has travelled, area under a curve, volume of a region.

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s NAPages

Calculus by David Guichard

This book covers the following topics: Analytic Geometry, Instantaneous Rate Of Change: The Derivative, Rules For Finding Derivatives, Transcendental Functions, Curve Sketching, Applications of the Derivative, Integration, Techniques of Integration, Applications of Integration, Sequences and Series.

Author(s):

s 320Pages

Introduction to Calculus Notes

This note explains the following topics: Hyperbolic Trigonometric Functions, The Fundamental Theorem of Calculus, The Area Problem or The Definite Integral, The Anti-Derivative, Optimization, L'Hopital's Rule, Curve Sketching, First and Second Derivative Tests, The Mean Value Theorem, Extreme Values of a Function, Linearization and Differentials, Inverse Trigonometric Functions, Implicit Differentiation, The Chain Rule, The Derivative of Trig. Functions, The Differentiation Rules, Limits Involving Infinity, Asymptotes, Continuity, Limit of a function and Limit Laws, Rates of Change and Tangents to Curves.

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s NAPages

Caluclus 1 Lecture Notes

This note describes the following topics: Derivatives, Integrals, Limits, and Continuity, Types of Basic Functions, Graphing Piecewise Functions,  Graphing using Transformations, Composition of Functions, Derivatives and Rates of Change, Derivative of a Function, Differentation Formulas, Derivative of Trig Functions, The Chain Rule, Implicit Differentation, Applications of Differentiation, Find Max and Minimum Values, Extreme Value Theorem, Fermat's Theorem, Limits at Infinity, Asymptotes, Sketching Curves, The Mean Value Theorem, Integration, The Definite Integral, The Fundamental Theorem of Calculus, Indefinite Integrals and Applications, Integration by Substitution.

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s NAPages

Understanding Basic Calculus

In this book, much emphasis is put on explanations of concepts and solutions to examples. Topics covered includes: Sets, Real Numbers and Inequalities, Functions and Graphs, Limits, Differentiation, Applications of Differentiation, Integration, Trigonometric Functions, Exponential and Logarithmic Functions.

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s 292Pages

Calculus 1 Class Notes

This note explains the following topics: Functions and Their Graphs, Trigonometric Functions, Exponential Functions, Limits and Continuity, Differentiation, Differentiation Rules, Implicit Differentiation, Inverse Trigonometric Functions, Derivatives of Inverse Functions and Logarithms, Applications of Derivatives, Extreme Values of Functions, The Mean Value Theorem, Monotone Functions and the First Derivative Test, Integration, Sigma Notation and Limits of Finite Sums, Indefinite Integrals and the Substitution Method.

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s NAPages

Calculus I by Mei Qin Chen

Goals of this note is to have a good understanding of concepts of calculus and applications of calculus in sciences and engineering. Topics covered includes: polynomials and special functions, The Concept of Limit, Computation of Limit, Continuity and its Consequences, Limits Involving Infinity, Tangent Lines and Velocity, Computation of Derivatives, Derivatives of Trigonometric Functions.

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s NAPages

Lecture Notes On Advanced Calculus II

This lecture note explains the following topics:Sequences of Real Numbers, Limits of Sequences, Sequences which tend to &

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s 97Pages

Calculus for Computer Scientists Lecture Notes

This note explains the following topics: Calculus is probably not the most popular course for computer scientists. Calculus – FAQ, Real and complex numbers, Functions, Sequences, Series, Limit of a function at a point, Continuous functions, The derivative, Integrals, Definite integral, Applications of integrals, Improper integrals, Wallis’ and Stirling’s formulas, Numerical integration, Function sequences and series.

Author(s):

s 185Pages

First Semester Calculus

This note covers the following topics: Numbers and Functions, Derivatives, Limits and Continuous Functions, Graph Sketching and Max-Min Problems, Exponentials and Logarithms, The Integral, Applications of the integral.

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s 134Pages

Advanced Calculus Lecture Notes for Mathematics

These notes are not intended as a textbook. It is hoped however that they will minimize the amount of note taking activity which occupies so much of a student’s class time in most courses in mathmatics. Topics covered includes: The Real Number system & Finite Dimensional Cartesian Space, Limits, Continuity, and Differentiation, Riemann Integration, Differentiation of Functions of Several Variables.

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s 189Pages

Introductory Calculus Notes

The approach followed is quite different from that of standard calculus texts. We use natural, but occasionally unusual, definitions for basic concepts such as limits and tangents. Topics covered includes: Sets: Language and Notation, The Extended Real Line, Suprema, Infima, Completeness, Neighborhoods, Open Sets and Closed Sets, Trigonometric Functions, Continuity, The Intermediate Value Theorem, Inverse Functions, Tangents, Slopes and Derivatives, Derivatives of Trigonometric Functions, Using Derivatives for Extrema, Convexity, Integration Techniques.

Author(s):

s 330Pages

Advanced Calculus by Evelyn Silvia

This book covers the following topics: Field of Reals and Beyond, From Finite to Uncountable Sets, Metric Spaces and Some Basic Topology, Sequences and Series, Functions on Metric Spaces and Continuity, Riemann Stieltjes Integration.

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s NAPages

Course Material for Introductory Calculus

This lecture note covers the following topics: General linear homogeneous ODEs, Systems of linear coupled first order ODEs,Calculation of determinants, eigenvalues and eigenvectors and their use in the solution of linear coupled first order ODEs, Parabolic, Spherical and Cylindrical polar coordinate systems, Introduction to partial derivatives, Chain rule, change of variable, Jacobians with examples including polar coordinate systems, surfaces and Sketching simple quadrics.

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s NAPages

Calculus Lecture Notes

This lecture note explains Differential and Integral calculus of functions of one variable, including trigonometric functions.

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s 134Pages

Calculus Lecture Notes I

This lecture note explains the following topics: Methods of integration, Taylor polynomials, complex numbers and the complex exponential, differential equations, vector geometry and parametrized curves.

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s 153Pages

Lecture Notes in Calculus (PDF 206P)

This is useful notes for Calculus. This notes contain Real numbers, Functions, Derivatives, Integration theory and Sequences

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s 206Pages

Lecture Notes on the Lambda Calculus (PDF 106P)

This notes contains the details about The untyped lambda calculus, The Church-Rosser Theorem, Combinatory algebras, The Curry-Howard isomorphism, Polymorphism, Weak and strong normalization, Denotational semantics of PCF

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s 106Pages

Calculus Compact Lecture Notes (PDF 135P)

This notes contain Complex numbers, Proof by induction, Trigonometric and hyperbolic functions, Functions, limits, differentiation, Integration, Taylor’s theorem and series

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s 135Pages

Calculus Course Notes

This notes contains the following subcategories Calculus, Introduction to Number Theory and Vector Calculus

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s NAPages

Introduction to calculus

This book emphasizes the fundamental concepts from calculus and analytic geometry and the application of these concepts to selected areas of science and engineering. Topics covered includes: Sets, Functions, Graphs and Limits, Differential Calculus, Integral Calculus, Sequences, Summations and Products and Applications of Calculus.

Author(s):

s 566Pages

Calculus Made Easy

Calculus Made Easy has long been the most popular calculus primer, and this major revision of the classic math text makes the subject at hand still more comprehensible to readers of all levels. This is a book that explains the philosophy of the subject in a very simple manner, making it easy to understand even for people who are not proficient in math.

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s 292Pages

Calculus textbook

This book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications.

Author(s):

s NAPages