Calculus Volume 2

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The app guides students through the basic concepts of calculus and helps them understand how those concepts apply to their real lives and the world around them. The app is divided into three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.

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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

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

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

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

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

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

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

A | Table of Integrals

B | Table of Derivatives

C | Review of Pre-Calculus