Two- or three-semester general calculus course to enhance student learning

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Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.

✨Contents of the Application✨

1 Integration

Introduction

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

Key Terms

Key Equations

Key Concepts

Chapter Review Exercises

2 Applications of Integration

Introduction

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

Key Terms

Key Equations

Key Concepts

Chapter Review Exercises

3 Techniques of Integration

Introduction

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

Key Terms

Key Equations

Key Concepts

Chapter Review Exercises

4 Introduction to Differential Equations

Introduction

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

Key Terms

Key Equations

Key Concepts

Chapter Review Exercises

5 Sequences and Series

Introduction

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

Key Terms

Key Equations

Key Concepts

Chapter Review Exercises

6 Power Series

Introduction

6.1 Power Series and Functions

6.2 Properties of Power Series

6.3 Taylor and Maclaurin Series

6.4 Working with Taylor Series

Key Terms

Key Equations

Key Concepts

Chapter Review Exercises

7 Parametric Equations and Polar Coordinates

Introduction

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

Key Terms

Key Equations

Key Concepts

Chapter Review Exercises

A | Table of Integrals

B | Table of Derivatives

C | Review of Pre-Calculus

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