**Dale Hoffman**

**Bellevue College**

**dhoffman@bellevuecollege.edu**

**A free on-line calculus text**

**Many of these materials were developed for the Open Course Library Project of the Washington State Colleges as part of a Gates Foundation grant. The goal of this project was to create materials that would be FREE (on the web) to anyone who wanted to use or modify them (and not have to pay $200 for a calculus book). They have been used by several thousand students.**

The textbook sections, in color, are available free in pdf format at the bottom of this page.

Printed versions, in B&W, are available for Calculus I (chapters 0-3), II (chapters 4-8), and III (chapters 9-11) for about $18 each at Lulu.com.

Alternate printed versions reformatted in LaTex are available at CreateSpace.com and Amazon.com or free online at ContemporaryCalculus.com.

The links below are to pdf files. When you click on them, they will be downloaded to your computer. You will need Adobe Acrobat Reader to open them.

**Chapter 0 Learning Outcomes****0.1 Preview****0.2 Lines****0.3 Functions****0.4 Combinations of Functions****0.5 Mathematical Language****Chapter 0 Odd Answers**

**Chapter 1 -- Functions, Graphs, Limits and Continuity**

**Chapter 1 Learning Outcomes****1.0 Slopes & Velocities****1.1 Limit of a Function****1.2 Limit Properties****1.3 Continuous Functions****1.4 Formal Definition of Limit****Chapter 1 Odd Answers**

**Chapter 2 -- The Derivative**

**Chapter 2 Learning Outcomes****2.0 Slope of a Tangent Line****2.1 Definition of Derivative****2.2 Differentiation Formulas****2.3 More Differentiation Patterns****2.4 Chain Rule (!!!)****2.5 Using the Chain Rule****2.6 Related Rates****2.7 Newton's Method****2.8 Linear Approximation****2.9 Implicit Differentiation****Chapter 2 Odd Answers**

**Chapter 3 -- Derivatives and Graphs**

**Chapter 3 Learning Outcomes****3.1 Introduction to Maximums & Minimums****3.2 Mean Value Theorem****3.3 f' and the Shape of f****3.4 f'' and the Shape of f****3.5 Applied Maximums & Minimums****3.6 Asymptotes****3.7 L'Hospital's Rule****Chapter 3 Odd Answers**

**Chapter 4 -- The Integral**

**Chapter 4 Learning Outcomes****4.0 Introduction to Integrals****4.1 Sigma Notation & Riemann Sums****4.2 The Definite Integral****4.3 Properties of the Definite Integral****4.4 Areas, Integrals and Antiderivatives****4.5 The Fundamental Theorem of Calculus****4.6 Finding Antiderivatives****4.7 First Applications of Definite Integrals****4.8 Using Tables to Find Antiderivatives****4.9 Approximating Definite Integrals****Chapter 4 Odd Answers**

**Chapter 5 -- Applications of Definite Integrals**

**Chapter 5 Learning Outcomes****5.0 Introduction to Applications****5.1 Volumes****5.2 Arc Lengths & Surface Areas****5.3 More Work****5.4 Moments & Centers of Mass****5.5 Additional Applications****Chapter 5 Odd Answers**

**Chapter 6 -- Introduction to Differential Equations**

**Chapter 6 Learning Outcomes****6.0 Introduction to Differential Equations****6.1 Differential Equation y'=f(x)****6.2 Separable Differential Equations****6.3 Exponential Growth, Decay & Cooling****Chapter 6 Odd Answers**

**Chapter 7 -- Inverse Trigonometric Functions**

**Chapter 7 Learning Outcomes****7.0 Introduction to Transcendential Functions****7.1 Inverse Functions****7,2 Inverse Trigonometric Functions****7.3 Calculus with Inverse Trigonometric Functions****Chapter 7 Odd Answers**

**Chapter 8 -- Improper Integrals and Integration Techniques**

**Chapter 8 Learning Outcomes****8.0 Introduction Improper Integrals & Integration Techniques****8.1 Improper Integrals****8.2 Integration Review****8.3 Integration by Parts****8.4 Partial Fraction Decomposition****8.5 Trigonometric Substitution****8.6 Trigonometric Integrals****Chapter 8 Odd Answers**

**Chapter 9 Learning Outcomes****9.1 Polar Coordinates****9.2 Calculus with Polar Coordinates****9.3 Parametric Equations****9.4 Calculus with Parametric Equations****9.4.5 Bezier Curves****9.5 Conic Sections****9.6 Properties of the Conic Sections****Chapter 9 Odd Answers**

**Chapter 10 Learning Outcomes****10.0 Introduction to Sequences & Series****10.1 Sequences****10.2 Infinite Series****10.3 Geometric and Harmonic Series****10.3.5 An Interlude and Introduction****10.4 Positive Term Series: Integral & P-Tests****10.5 Positive Term Series: Comparison Tests****10.6 Alternating Sign Series****10.7 Absolute Convergence and the Ratio Test****10.8 Power Series****10.9 RepresentingFunctions with Power Series****10.10 Taylor and Maclaurin Series****10.11 Approximation Using Taylor Polynomials****10.12 Fourier Series****Chapter 10 Odd Answers**

**Chapter 11 Learning Outcomes****11.0 Moving Beyond Two Dimensions****11.1 Vectors in the Plane****11.2 Rectangular Coordinates in Three Dimensions****11.3 Vectors in Three Dimensions****11.4 Dot Product****11.5 Cross Product****11.6 Lines and Planes inThree Dimensions****11.7 Vector Reflections****Appendix -- Sketching in 3D****Chapter 11 Odd Answers**

**12.0 Introduction to Vector-Valued Functions****12.1 Vector-Valued Functions and Curves in Space****12.2 Derivatives & Antiderivatives of Vector-Valued Functions****12.3 Arc Length and Curvature of Space Curves****12.4 Cylindrical & Spherical Coordinate Systems in 3D****Chapter 12 Odd Answers**

**13.0 Introduction to Functions of Several Variables****13.1 Functions of Two or More Variables****13.2 Limits and Continuity****13.3 Partial Derivatives****13.4 Tangent Planes and Differentials****13.5 Directional Derivatives and the Gradient****13.6 Maximums and Minimums****13.7 Lagrange Multiplier Method****13.8 Chain Rule****Chapter 13 Odd Answers**

**14.0 Introduction to Double Integrals****14.1 Double Integrals over Rectangular Domains****14.2 Double Integrals over General Domains****14.3 Double Integrals in Polar Coordinates****14.4 Applications of Double Integrals****14.5 Surface Area****14.6 Triple Integrals and Applications****14.7 Triple Integrals in Cylindrical and Spherical Coordinates****14.8 Changing Variables in Double and Triple Integrals****Chapter 14 Odd Answers**

**15.0 Introduction to Vector Calculus****15.1 Vector Fields****15.2 Divergence, Curl and Del in 2D****15.3 Line Integrals****A Message****15.4 Fundamental Theorem of Line Integrals and Potential Functions****15.4.5 Theorems of Green, Stokes and Gauss: Discrete Introdutions****15.5 Green's Theorem****15.6 Divergence and Curl in 3D****15.7 Parametric Surfaces****15.8 Surface Integrals****15.9 Stokes' Theorem****15.10 Gauss/Divergence Theorem****Chapter 15 Odd Answers**

This work by Dale Hoffman for Washington State Colleges is licensed under a Creative Commons Attribution 3.0 United States License. You are free to print, use, mix or modify these materials as long as you credit the original to Dale Hoffman. MSWord versions are available from the author.

last modified August 25, 2016