Differential Equations with Applications and Historical Notes, Third Edition

✍ Scribed by George F. Simmons

• Publisher: CRC Press;Chapman and Hall/CRC
• Year: 2017
• Tongue: English
• Leaves: 763
• Series: Textbooks in Mathematics
• Edition: 3ed.
• Category: Library

✦ Synopsis

Fads are as common in mathematics as in any other human activity, and it is always difficult to separate the enduring from the ephemeral in the achievements of one’s own time. An unfortunate effect of the predominance of fads is that if a student doesn’t learn about such worthwhile topics as the wave equation, Gauss’s hypergeometric function, the gamma function, and the basic problems of the calculus of variations―among others―as an undergraduate, then he/she is unlikely to do so later.

The natural place for an informal acquaintance with such ideas is a leisurely introductory course on differential equations. Specially designed for just such a course, Differential Equations with Applications and Historical Notes takes great pleasure in the journey into the world of differential equations and their wide range of applications. The author―a highly respected educator―advocates a careful approach, using explicit explanation to ensure students fully comprehend the subject matter.

With an emphasis on modeling and applications, the long-awaited Third Edition of this classic textbook presents a substantial new section on Gauss’s bell curve and improves coverage of Fourier analysis, numerical methods, and linear algebra. Relating the development of mathematics to human activity―i.e., identifying why and how mathematics is used―the text includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout.

• Provides an ideal text for a one- or two-semester introductory course on differential equations
• Emphasizes modeling and applications
• Presents a substantial new section on Gauss’s bell curve
• Improves coverage of Fourier analysis, numerical methods, and linear algebra
• Relates the development of mathematics to human activity―i.e., identifying why and how mathematics is used
• Includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout
• Uses explicit explanation to ensure students fully comprehend the subject matter

 

✦ Table of Contents

Content: Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Suggestions for the Instructor
About the Author
1: The Nature of Differential Equations. Separable Equations
1 Introduction
2 General Remarks on Solutions
3 Families of Curves. Orthogonal Trajectories. 4 Growth, Decay, Chemical Reactions, and Mixing 5 Falling Bodies and Other Motion Problems
6 The Brachistochrone. Fermat and the Bernoullis. Appendix A: Some Ideas From the Theory of Probability: The Normal Distribution Curve (or Bell Curve) and Its Differential Equation2: First Order Equations
7 Homogeneous Equations
8 Exact Equations
9 Integrating Factors
10 Linear Equations
11 Reduction of Order. 12 The Hanging Chain. Pursuit Curves 13 Simple Electric Circuits
3: Second Order Linear Equations
14 Introduction
15 The General Solution of the Homogeneous Equation. 16 The Use of a Known Solution to find Another 17 The Homogeneous Equation with Constant Coefficients
18 The Method of Undetermined Coefficients.