Calculus Volume 2

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Gilbert Strang, Massachusetts Institute of Technology

Pub Date: 2016

ISBN 13: 978-1-9381680-6-2

Publisher: OpenStax

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Table of Contents

Preface 
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 
Index 

About the Book

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.

About the Contributors

Author(s)

Gilbert Strang was an undergraduate at MIT and a Rhodes Scholar at Balliol College, Oxford. His Ph.D. was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. He is a Professor of Mathematics at MIT, an Honorary Fellow of Balliol College, and a member of the National Academy of Sciences.

He was the President of SIAM during 1999 and 2000, and Chair of the Joint Policy Board for Mathematics. He received the von Neumann Medal of the US Association for Computational Mechanics, and the Henrici Prize for applied analysis. The first Su Buchin Prize from the International Congress of Industrial and Applied Mathematics, and the Haimo Prize from the Mathematical Association of America, were awarded for his contributions to teaching around the world.