Worldwide Differential Calculus

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David B. Massey– Northeastern University

ISBN-10: 0-9842071-9-8
ISBN-13:  978-0-9842071-9-0
565 Pages
©2019 Worldwide Center of Mathematics, LLC

Digital | $19.95
Print | $39.95 + shipping

 

Features

 

contents

 

Supplements

Introduction

Differential Calculus is the study of instantaneous rates of change; these rates of change are known as derivatives. 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  • Margin side-remarks and historical references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 Average Rates of Change
  • 1.1.1 Exercises
  • 1.2 Prelude to IROC's
  • 1.2.1 Exercises
  • 1.3 Limits and Continuity
  • 1.3.1 Limits
  • 1.3.2 Continuous Functions
  • 1.3.3 Limits involving Infinity
  • 1.3.4 Exercises
  • 1.4 IROC's and the Derivative
  • 1.4.1 Exercises
  • 1.5 Extrema and the Mean Value Theorem
  • 1.5.1 Exercises
  • 1.6 Higher-Order Derivatives
  • 1.6.1 Exercises
  • Appendix 1.A Technical Matters
  • 1.A.1 Properties of Real Numbers and Extended Real Numbers
  • 1.A.2 Functions
  • 1.A.3 Proofs of Theorems on Limits and Continuity
  • 1.A.4 Proofs of Theorems on Differentiability and Continuity
  • 2.1 The Power Rule and Linearity
  • 2.1.1 Exercises
  • 2.2 The Product and Quotient Rules
  • 2.2.1 Exercises
  • 2.3 The Chain Rule and Inverse Functions
  • 2.3.1 Exercises
  • 2.4 The Exponential Function
  • 2.4.1 Exercises
  • 2.5 The Natural Logarithm
  • 2.5.1 Exercises
  • 2.6 General Exponential and Logarithmic Functions
  • 2.6.1 Exercises
  • 2.7 Trigonometric Functions: Sine and Cosine
  • 2.7.1 Exercises
  • 2.8 The Other Trigonometric Functions
  • 2.8.1 Exercises
  • 2.9 Inverse Trig Functions
  • 2.9.1 Exercises
  • 2.10 Implicit Functions
  • 2.10.1 Exercises
  • Appendix 2.A Technical Matters
  • 3.1 Related Rates
  • 3.1.1 Exercises
  • 3.2 Graphing
  • 3.2.1 Exercises
  • 3.3 Optimization
  • 3.3.1 Exercises
  • 3.4 Linear Approximation
  • 3.4.1 Exercises
  • 3.5 l'Hôpital's Rule
  • 3.5.1 Exercises
  • Appendix 3.A Technical Matters
  • 4.1 What is a Differential Equation?
  • 4.1.1 Exercises
  • 4.2 Anti-derivatives
  • 4.2.1 Exercises
  • 4.3 Separable Differential Equations
  • 4.3.1 Exercises
  • 4.4 Applications of Differential Equations
  • 4.4.1 Exercises
  • 4.5 Approximating Solutions
  • 4.5.1 Exercises
  • Appendix A Parameterized Curves and Motion
  • A.1 Parameterized Curves
  • A.1.1 Exercises
  • Appendix B Tables of Derivative Formulas
  • Appendix C Answers to Odd-Numbered Problems

 

 

Supplements

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

Worldwide Differential Calculus Study Guide ($4.95) go >
The study guide for Worldwide Differential Calculus contains a full-length video lecture for each section of the textbook, ideas and definitions, formulas and theorems, remarks and warnings, and example problems for each topic. It also contains margin side-remarks and historical references.

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

The Mathematician’s Blueprint: Differential Calculus ($2.95) go >
The Mathematician’s Blueprint provides advice and support to students learning differential calculus. It contains recommendations, helpful calculator tips and tricks, and a comprehensive formula sheet with example problems.

WebAssign go >
Worldwide Differential 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.