Applied Differential Equations: The Primary Course, 1st Edition (Hardback) book cover

Applied Differential Equations

The Primary Course, 1st Edition

By Vladimir A. Dobrushkin

Chapman and Hall/CRC

731 pages | 191 B/W Illus.

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Hardback: 9781439851043
pub: 2014-12-16
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Description

A Contemporary Approach to Teaching Differential Equations

Applied Differential Equations: An Introduction presents a contemporary treatment of ordinary differential equations (ODEs) and an introduction to partial differential equations (PDEs), including their applications in engineering and the sciences. Designed for a two-semester undergraduate course, the text offers a true alternative to books published for past generations of students. It enables students majoring in a range of fields to obtain a solid foundation in differential equations.

The text covers traditional material, along with novel approaches to mathematical modeling that harness the capabilities of numerical algorithms and popular computer software packages. It contains practical techniques for solving the equations as well as corresponding codes for numerical solvers. Many examples and exercises help students master effective solution techniques, including reliable numerical approximations.

This book describes differential equations in the context of applications and presents the main techniques needed for modeling and systems analysis. It teaches students how to formulate a mathematical model, solve differential equations analytically and numerically, analyze them qualitatively, and interpret the results.

Reviews

"The author covers traditional material along with modern approaches for analyzing, solving, and visualizing ODEs. The topics are accompanied by mathematical software codes for some of the most popular packages … . The text contains a large number of examples from different areas … . It also includes advanced material for students who want to obtain a deeper knowledge on this subject. … the textbook contains a great number of exercises. In addition, each chapter ends with summary and review questions, making the text well-suited for self-study as well."

Zentralblatt MATH 1326

"Two notable aspects of the book are its comprehensiveness and tight integration with applications. … There is much to like about this book — lucid writing, clear development of the basic ideas, and a very large number of exercises with a good range of difficulty. … a very attractive text."

MAA Reviews, September 2015

Table of Contents

First-Order Equations

Introduction

Separable Equations

Equations with Homogeneous Coefficients

Exact Differential Equations

Integrating Factors

First-Order Linear Differential Equations

Equations Reducible to first Order

Existence and Uniqueness

Review Questions for Chapter 1

Applications of First Order ODE

Applications in Mathematics

Curves of Pursuit

Chemical Reactions

Population Models

Mechanics

Electricity

Applications in Physics

Thermodynamics

Flow Problems

Review Questions for Chapter 2

Mathematical Modeling and Numerical Methods

Mathematical Modeling

Compartment Analysis

Difference Equations

Euler’s Methods

Error Estimates

The Runge-Kutta Methods

Multistep Methods

Error Analysis and Stability

Review Questions for Chapter 3

Second-order Equations

Second and Higher Order Linear Equations

Linear Independence and Wronskians

The Fundamental Set of Solutions

Equations with Constant Coefficients

Complex Roots

Repeated Roots. Reduction of Order

Nonhomogenous Equations

Variation of Parameters

Operator Method

Review Questions for Chapter 4

Laplace Transforms

The Laplace Transform

Properties of the Laplace Transform

Convolution

Discontinuous and Impulse Functions

The Inverse Laplace Transform

Applications to Homogenous Equations

Applications to Non-homogenous Equations

Internal Equations

Review Questions for Chapter 5

Series of Solutions

Review of Power Series

The Recurrence

Power Solutions about an Ordinary Point

Euler Equations

Series Solutions Near a Regular Singular Point

Equations of Hypergeometric Type

Bessel’s Equations

Legendre’s Equation

Orthogonal Polynomials

Review Questions for Chapter 6

Applications of Higher Order Differential Equations

Boundary Value Problems

Some Numerical Methods

Dynamics

Dynamics of Rotational Motion

Harmonic Motion

Modeling: Forced Oscillations

Modeling of Electric Circuits

Some Variational Problems

Review Questions for Chapter 7

Appendix: Software Packages

Answers to Problems

Bibliography

Index

About the Author

Vladimir A. Dobrushkin is an associate of Brown University.

About the Series

Textbooks in Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations