Worldwide Integral Calculus

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David B. Massey– Northeastern University

ISBN-10: 0-9842071-5-5
ISBN-13: 978-0-9842071-5-2
657 Pages
©2019 Worldwide Center of Mathematics, LLC

Digital | $19.95
Print | $39.95 + shipping

 

Features

 

contents

 

Supplements

Introduction

Integral Calculus is the study of continuous sums of infinitesimal contributions; these continuous sums are known as integrals. This book is written by David B. Massey, Ph.D., an award-winning teacher and world-renowned research mathematician, who has been teaching college students for 30 years. He emphasizes intuitive ideas in conjunction with rigorous statements of theorems, and provides a large number of illustrative examples. In the accompanying videos, Dr. Massey lectures on the core material from each section.


Features

  • Written by an award-winning mathematics professor with 30 years of teaching experience
  • Down-to-Earth exposition, presented as it would be spoken in class
  • Completely rigorous definitions, statements of theorems, and proofs
  • Technical proofs at the end of each chapter, to avoid disrupting the exposition
  • Margin side-remarks and historical references
  • Hyperlinked table of contents, index, and cross-references
  • Embedded video links to full-length lectures
  • Video-solutions to select exercises
  • PDF format, compatible with all computers, tablets, and mobile devices
  • Low cost in electronic or print form

Contents

  • 1.1 Basic Anti-Differentiation
  • 1.1.1 Exercises
  • 1.2 Special Trig. Integrals and Trig
  • 1.2.1 Exercises
  • 1.3 Integration by Partial Fractions
  • 1.3.1 Exercises
  • 1.4 Integration using Hyperbolic Sine and Cosine
  • 1.4.1 Exercises
  • 2.1 Sums and Differences
  • 2.1.1 Exercises
  • 2.2 Prelude to the Definite Integral
  • 2.2.1 Exercises
  • 2.3 The Definite Integral
  • 2.3.1 Exercises
  • 2.4 The Fundamental Theorem of Calculus
  • 2.4.1 Exercises
  • 2.5 Improper Integrals
  • 2.5.1 Exercises
  • 2.6 Numerical Techniques
  • 2.6.1 Exercises
  • Appendix 2.A Technical Matters
  • 3.1 Displacement and Distance Traveled
  • 3.1.1 Exercises
  • 3.2 Area in the Plane
  • 3.2.1 Exercises
  • 3.3 Distance Traveled in Space and Arc Length
  • 3.3.1 Exercises
  • 3.4 Area Swept Out and Polar Coordinates
  • 3.4.1 Exercises
  • 3.5 Volume
  • 3.5.1 Exercises
  • 3.6 Surface Area
  • 3.6.1 Exercises
  • 3.7 Mass and Density
  • 3.7.1 Exercises
  • 3.8 Centers of Mass and Moments
  • 3.8.1 Exercises
  • 3.9 Work and Energy
  • 3.9.1 Exercises
  • 3.10 Hydrostatic Pressure
  • 3.10.1 Exercises
  • 4.1 Approximating Polynomials
  • 4.1.1 Exercises
  • 4.2 Approximation of Functions
  • 4.2.1 Exercises
  • 4.3 Error in Approximation
  • 4.3.1 Exercises
  • 4.4 Functions as Power Series
  • 4.4.1 Exercises
  • 4.5 Power Series as Functions I
  • 4.5.1 Exercises
  • 4.6 Power Series as Functions II
  • 4.6.1 Exercises
  • 4.7 Power Series Solutions
  • 4.7.1 Exercises
  • Appendix 4.A Technical Matters
  • 5.1 Theorems on Sequences
  • 5.1.1 Exercises
  • 5.2 Basic Theorems on Series
  • 5.2.1 Exercises
  • 5.3 Non-negative Series
  • 5.3.1 Exercises
  • 5.4 Series with Positive and Negative Terms
  • 5.4.1 Exercises
  • Appendix A An Introduction to Vectors and Motion
  • Appendix B Tables of Integration Formulas
  • Appendix C Answers to Odd-Numbered Exercises

 

 

Supplements

 

Worldwide Integral Calculus Solution Manual (Faculty) go >
Faculty may request the available free faculty digital resources online.

Worldwide Integral Calculus Study Guide ($4.95) go >

Worldwide Integral Calculus Video Playlist (Free) go >
Worldwide Integral Calculus features associated video selections made available free on the Center of Math YouTube Channel. Video links are directly embedded in the digital textbook.

WebAssign go >
Worldwide Multivariable Calculus is available with WebAssign. WebAssign is a powerful digital solution designed by educators to enrich the teaching and learning experience. WebAssign provides extensive content, instant assessment, and superior support.