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This learning resource is built upon the online textbook, Calculus, vol 2, available free of charge from OpenStax University. The textbook material, itself, is provided in the PDF format. This means you should have a PDF reader, such as Acrobat Reader. It is available here for downloading, free of charge--tap the Acrobat Reader image to begin the installation process.

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Table of Contents

Chapter 1: Integration

1.1 Approximating Areas

1.2 The Definite Integral

1.3 The Fundamental Theorem of Calculus

1.4 Integration Formulas and the Net Change Theorem

1.5 Substitution

1.6 Integrals Involving Exponential and Logarithmic Functions

1.7 Integrals Resulting in Inverse Trigonometric Functions

Chapter 2: Applications of Integration

2.1 Areas between Curves

2.2 Determining Volumes by Slicing

2.3 Volumes of Revolution: Cylindrical Shells

2.4 Arc Length of a Curve and Surface Area

2.5 Physical Applications

2.6 Moments and Centers of Mass

2.7 Integrals, Exponential Functions, and Logarithms

2.8 Exponential Growth and Decay

2.9 Calculus of the Hyperbolic Functions

Chapter 3: Techniques of Integration

3.1 Integration by Parts

3.2 Trigonometric Integrals

3.3 Trigonometric Substitution

3.4 Partial Fractions

3.5 Other Strategies for Integration

3.6 Numerical Integration

3.7 Improper Integrals

Chapter 4: Introduction to Differential Equations

4.1 Basics of Differential Equations

4.2 Direction Fields and Numerical Methods

4.3 Separable Equations

4.4 The Logistic Equation

4.5 First-order Linear Equations

Chapter 5: Sequences and Series

5.1 Sequences

5.2 Infinite Series

5.3 The Divergence and Integral Tests

5.4 Comparison Tests

5.5 Alternating Series

5.6 Ratio and Root Tests

Chapter 6: Power Series

6.1 Power Series and Functions

6.2 Properties of Power Series

6.3 Taylor and Maclaurin Series

6.4 Working with Taylor Series

Chapter 7: Parametric Equations and Polar Coordinates

7.1 Parametric Equations

7.2 Calculus of Parametric Curves

7.3 Polar Coordinates

7.4 Area and Arc Length in Polar Coordinates

7.5 Conic Sections

Appendix A: Table of Integrals

Appendix B: Table of Derivatives

Appendix C: Review of Pre-Calculus

Appendix C: Review of Pre-Calculus

 

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Revised: June 06, 2015