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)
- download (PDF, 18.6MB, updated 9/10/2018)
- purchase hard copy (about $8 plus tax and shipping via Amazon, 9/10/2018 printing)
Chapters 4–8 (Integral Calculus)
- download (PDF, 23.1MB, updated 9/10/2018)
- purchase a hard copy (about $7 plus tax and shipping, 9/10/2018 printing)
Links
Source Files
- Chapters 0–5: download (*.zip, 36.8MB, updated 8/1/2016)
Table of Contents
Chapter 0 (Welcome to Calculus)
- All of Chapter 0: download
- 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
- Section 0.5 (Mathematical Language): download
- Chapter 0 Odd Answers: download
Chapter 1 (Limits and Continuity)
- All of Chapter 1: download
- 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 1.3 (Continuous Functions): download
- Section 1.4 (Definition of Limit): download
- Chapter 4 Odd Answers: download
Chapter 2 (The Derivative)
- All of Chapter 2: download
- 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 2.6 (Related Rates): download
- Section 2.7 (Newton’s Method): download
- Section 2.8 (Linear Approximation and Differentials): download
- Section 2.9 (Implicit and Logarithmic Differentiation): download
- Chapter 2 Odd Answers: download
Chapter 3 (Derivatives and Graphs)
- All of Chapter 3: download
- 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
- Section 3.7 (L’Hôpital’s Rule): download
- Chapter 3 Odd Answers: download
Chapter 4 (The Integral)
- All of Chapter 4: download
- Section 4.0 (Area): download
- 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 4.6 (Finding Antiderivatives): 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 4 Odd Answers: download
Chapter 5 (Applications of Definite Integrals)
- All of Chapter 5: download
- Section 5.1 (Volumes by Slicing): download
- Section 5.2 (Volumes: Disks and Washers): download
- Section 5.3 (Arclengths and Surface Areas): download
- Section 5.4 (More Work): download
- Section 5.5 (Volumes: Tubes): download
- Section 5.6 Moments and Centers of Mass): download
- Section 5.7 (Improper Integrals): download
- Section 5.8 (Additional Applications): download
- Chapter 5 Odd Answers: download
Chapter 6 (Differential Equations)
- Section 6.1 (Introduction to Differential Equations): download
- Section 6.2 (The Differential Equation y = f'(x)): download
- Section 6.3 (Separable Equations): download
- Section 6.4 (Exponential Growth and Decay): download
- Section 6.5 (Heating, Cooling and Mixing): download
- Chapter 6 Odd Answers: download
Chapter 7 (Transcendental Functions)
- Section 7.1 (One-to-One Functions): download
- Section 7.2 (Inverse Functions): download
- 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 7 Odd Answers: download
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 8.4 (Trigonometric Substitution): download
- Section 8.5 (Integrals of Trigonometric Functions): download
- Section 8.6 (Integration Tactics): problems only download
- Section 8.7 (Approximating Antiderivatives): download
- Chapter 8 Odd Answers: download
Chapter 9 (Sequences and Series)
- Section 9.1 (Sequences): download
- Section 9.2 (Limits of Sequences): download
- Section 9.3 (Infinite Series): download
- Section 9.4 (Geometric and Harmonic Series): download
- Section 9.5 (An Interlude): download
- Section 9.6 (Integral Test and P-Test): download
- Section 9.7 (Comparison Tests): download
- Section 9.8 (Alternating Series): download
- Section 9.9 (Absolute Convergence and the Ratio Test): download
- Chapter 9 Odd Answers: 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
- Chapter 10 Odd Answers: download
Chapter 11 (Polar and Parametric Curves)
- Section 11.1 (Polar Coordinates): download
- Section 11.2 (Calculus in Polar Coordinates): download
- Section 11.3 (Parametric Equations): download
- Section 11.4 (Calculus with Parametric Equations): download
- Chapter 11 Odd Answers: download
More coming soon…