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## Calculus Books

### Calculus Books

#### Single Variable Calculus MIT

This book explains the following topics: Derivatives, Derivatives, slope, velocity, rate of change, Limits, continuity, Trigonometric limits, Derivatives of products, quotients, sine, cosine, Chain rule, Higher derivatives, Implicit differentiation, inverses, Exponential and log, Logarithmic differentiation, hyperbolic functions, Applications of Differentiation, Linear and quadratic approximations ,Curve sketching, Max-min problems, Newton�s method and other applications, Mean value theorem, Inequalities, Differentials, antiderivatives, Differential equations, separation of variables, Integration, Techniques of Integration.

Author(s): NAPages

#### Exercises and Problems in Calculus

This is a set of exercises and problems for a standard beginning calculus. A fair number of the exercises involve only routine computations, many of the exercises and most of the problems are meant to illuminate points that in my experience students have found confusing.

Author(s): 374Pages

#### A Brief Introduction to Calculus

These notes are intended as a brief introduction to some of the main ideas and methods of calculus. Topics covered includes: Functions and Graphs, Linear Functions, Lines, and Linear Equations, Limits, Continuity, Linear Approximation, Introduction to the Derivative, Product, Quotient, and Chain Rules, Derivatives and Rates, Increasing and Decreasing Functions, Concavity, Optimization, Exponential and Logarithmic Functions, Antiderivatives, Integrals.

Author(s): 69Pages

#### Calculus with Theory Lecture Notes

This note emphasizes careful reasoning and understanding of proofs. It assumes knowledge of elementary calculus. Topics covered includes: Integers and exponents, Square roots, and the existence of irrational numbers, The Riemann condition, Properties of integrals, Integrability of bounded piecewise-monotonic functions, Continuity of the square root function, Rational exponents, The fundamental theorems of calculus, The trigonometric functions, The exponential and logarithm functions, Integration, Taylor's formula, Fourier Series.

Author(s): NAPages

#### Calculus, Applications and Theory

This note covers following topics: The Real Numbers, Basic Geometry And Trigonometry, The Complex Numbers, Functions Of One Variable, Derivatives, Properties And Applications Of Derivatives, Antiderivatives And Differential Equations, The Integral, Infinite Series, Vector Valued Functions, Limits And Derivatives, Line Integrals, Functions Of More Than One Variable, Linear Algebra, Vector Calculus.

Author(s): 635Pages

#### Lecture Notes for Math by Dr. Vitaly A. Shneidman

This note covers following topics: Continuity and Limits, Continuous Function, Derivatives, Derivative as a function, Differentiation rules, Derivatives of elementary functions, Trigonometric functions, Implicit differentiation, Inverse Functions, Logarithmic functions and differentiation, Monotonicity, Area between two curves.

Author(s): 163Pages

#### Applied Advanced Calculus Lecture Notes by Jan Vrbik

This note explains following topics: Ordinary Differential Equations, First-Order Differential Equations, Second Order Differential Equations, Third and Higher-Order Linear ODEs, Sets of Linear, First-Order, Constant-Coefficient ODEs,Power-Series Solution, Vector Analysis, Complex Analysis, Complex Analysis, Complex Functions.

Author(s): 136Pages

#### 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): 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.

Author(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): 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.

Author(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.

Author(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.

Author(s): NAPages

#### 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): 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.

Author(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.

Author(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): 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.

Author(s): NAPages

#### Calculus Lecture Notes

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

Author(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.

Author(s): 153Pages

#### Calculus in Context

Calculus in Context is the product of the Five College Calculus Project. Besides the introductory calculus text, the product includes computer software and a Handbook for Instructors.

Author(s): NAPages

#### Lecture Notes in Calculus (PDF 206P)

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

Author(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

Author(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

Author(s): 135Pages

#### Calculus Course Notes

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

Author(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): 566Pages 292Pages