﻿ Contemporary Calculus |Contemporary Calculus

Contemporary Calculus

A free, open-source calculus textbook by Dale Hoffman. Typeset in LaTeX and with additional contributions by Jeff Eldridge.

Now Available

• Chapters 0–3 (Differential Calculus)

• Chapters 4–8 (Integral Calculus)

Source Files

• Chapters 0–5: download (*.zip, 36.8MB, updated 8/1/2016)

Chapter 0 (Welcome to Calculus)

• Section 0.1 (A Preview of Calculus): download
• Section 0.2 (Lines in the Plane): download
• Section 0.3 (Functions and Their Graphs): download
• Section 0.4 (Combinations of Functions): download

Chapter 1 (Limits and Continuity)

• Section 1.0 (Tangent Lines, Velocities, Growth) download
• Section 1.1 (The Limit of a Function): download
• Section 1.2 (Properties of Limits): download
• Section 1.4 (Definition of Limit): download

Chapter 2 (The Derivative)

• Section 2.0 (Introduction to Derivatives) download
• Section 2.1 (The Definition of Derivative): download
• Section 2.2 (Derivatives: Properties and Formulas): download
• Section 2.3 (More Differentiation Patterns): download
• Section 2.4 (The Chain Rule): download
• Section 2.5 (Applications of the Chain Rule): download
• Section 2.8 (Linear Approximation and Differentials): download
• Section 2.9 (Implicit and Logarithmic Differentiation): download

Chapter 3 (Derivatives and Graphs)

• Section 3.1 (Finding Maximums and Minimums): download
• Section 3.2 (Mean Value Theorem): download
• Section 3.3 (The First Derivative and the Shape of f): download
• Section 3.4 (The Second Derivative and the Shape of f): download
• Section 3.5 (Applied Maximum and Minimum Problems): download
• Section 3.6 (Asymptotic Behavior of Functions): download

Chapter 4 (The Integral)

• Section 4.1 (Sigma Notation and Riemann Sums): download
• Section 4.2 (The Definite Integral): download
• Section 4.3 (Properties of the Definite Integral): download
• Section 4.4 (Areas, Integrals and Antiderivatives): download
• Section 4.5 (The Fundamental Theorem of Calculus): download
• Section 4.7 (First Applications of Definite Integrals): download
• Section 4.8 (Using Tables [and Technology] to Find Antiderivatives): download
• Section 4.9 (Approximating Definite Integrals): download

Chapter 5 (Applications of Definite Integrals)

• Section 5.1 (Volumes by Slicing): download
• Section 5.2 (Volumes: Disks and Washers): download
• Section 5.3 (Arclengths and Surface Areas): download
• Section 5.6 Moments and Centers of Mass): download

Chapter 6 (Differential Equations)

• Section 6.1 (Introduction to Differential Equations): download
• Section 6.2 (The Differential Equation y = f'(x)): download
• Section 6.4 (Exponential Growth and Decay): download
• Section 6.5 (Heating, Cooling and Mixing): download

Chapter 7 (Transcendental Functions)

• Section 7.3 (Inverse Trigonometric Functions): download
• Section 7.4 (Derivatives of Inverse Trigonometric Functions): coming soon
• Section 7.5 (Integrals Involving Inverse Trigonometric Functions): download
• Section 7.6 (Calculus Done Right): coming soon
• Section 7.7 (Hyperbolic Functions): coming soon

Chapter 8 (Integration Techniques)

• Section 8.1 (Finding Antiderivatives: A Review): download
• Section 8.2 (Integration by Parts): download
• Section 8.3 (Partial Fraction Decomposition): download
• Section 8.5 (Integrals of Trigonometric Functions): download
• Section 8.6 (Integration Tactics): problems only download

Chapter 9 (Sequences and Series)

• Section 9.2 (Limits of Sequences): download
• Section 9.4 (Geometric and Harmonic Series): download
• Section 9.6 (Integral Test and P-Test): download
• Section 9.9 (Absolute Convergence and the Ratio Test): download

Chapter 10 (Power Series)

• Section 10.1 (Power Series Centered at x = 0): download
• Section 10.2 (Power Series Centered at x = a): download
• Section 10.3 (Representing Functions as Power Series): download
• Section 10.4 (MacLaurin and Taylor Series): download
• Section 10.5 (Approximation Using Taylor Polynomials): download