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.
Conditions of Use
This book is licensed under a Creative Commons License (CC BY-NC-SA). You can download the ebook Calculus Volume 2 for free.
- Title
- Calculus Volume 2
- Publisher
- OpenStax
- Author(s)
- Edwin Jed Herman, Gilbert Strang
- Published
- 2024-02-05
- Edition
- 1
- Format
- eBook (pdf, epub, mobi)
- Pages
- 830
- Language
- English
- ISBN-10
- 1506698077
- ISBN-13
- 9781506698076
- License
- CC BY-NC-SA
- Book Homepage
- Free eBook, Errata, Code, Solutions, etc.
Preface Chapter 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 Chapter Review Key Terms Key Equations Key Concepts Review Exercises Chapter 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 Chapter Review Key Terms Key Equations Key Concepts Review Exercises Chapter 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 Chapter Review Key Terms Key Equations Key Concepts Review Exercises Chapter 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 Chapter Review Key Terms Key Equations Key Concepts Review Exercises Chapter 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 Chapter Review Key Terms Key Equations Key Concepts Review Exercises Chapter 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 Chapter Review Key Terms Key Equations Key Concepts Review Exercises Chapter 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 Chapter Review Key Terms Key Equations Key Concepts Review Exercises Appendix A Table of Integrals Appendix B Table of Derivatives Appendix C Review of Pre-Calculus Answer Key Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Index
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