Introductory Differential Equations - 4th Edition - ISBN: 9780124172197, 9780124172821

Introductory Differential Equations

4th Edition

Authors: Martha Abell James Braselton
eBook ISBN: 9780124172821
Hardcover ISBN: 9780124172197
Imprint: Academic Press
Published Date: 22nd July 2014
Page Count: 530
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Description

Introductory Differential Equations, Fourth Edition, offers both narrative explanations and robust sample problems for a first semester course in introductory ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. The book provides the foundations to assist students in learning not only how to read and understand differential equations, but also how to read technical material in more advanced texts as they progress through their studies.

This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, and Fourier Series. It follows a traditional approach and includes ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple. Because many students need a lot of pencil-and-paper practice to master the essential concepts, the exercise sets are particularly comprehensive with a wide array of exercises ranging from straightforward to challenging. There are also new applications and extended projects made relevant to everyday life through the use of examples in a broad range of contexts.

This book will be of interest to undergraduates in math, biology, chemistry, economics, environmental sciences, physics, computer science and engineering.

Key Features

  • Provides the foundations to assist students in learning how to read and understand the subject, but also helps students in learning how to read technical material in more advanced texts as they progress through their studies.
  • Exercise sets are particularly comprehensive with a wide range of exercises ranging from straightforward to challenging.
  • Includes new applications and extended projects made relevant to "everyday life" through the use of examples in a broad range of contexts.
  • Accessible approach with applied examples and will be good for non-math students, as well as for undergrad classes.

Readership

Undergraduates in math, biology, chemistry, economics, environmental sciences, physics, computer science and engineering

Table of Contents

  • Preface
    • Technology
    • Applications
    • Style
    • Features
    • Pedagogical Features
    • Content
  • Chapter 1: Introduction to Differential Equations
    • Abstract
    • 1.1 Introduction to Differential Equations: Vocabulary
    • Exercises 1.1
    • 1.2 A Graphical Approach to Solutions: Slope Fields and Direction Fields
    • Exercises 1.2
    • Chapter 1 Summary: Essential Concepts and Formulas
    • Chapter 1 Review Exercises
  • Chapter 2: First-Order Equations
    • Abstract
    • 2.1 Introduction to First-Order Equations
    • Exercises 2.1
    • 2.2 Separable Equations
    • Exercises 2.2
    • 2.3 First-Order Linear Equations
    • Exercises 2.3
    • 2.4 Exact Differential Equations
    • Exercises 2.4
    • 2.5 Substitution Methods and Special Equations
    • Exercises 2.5
    • 2.6 Numerical Methods for First-Order Equations
    • Exercises 2.6
    • Chapter 2 Summary: Essential Concepts and Formulas
    • Chapter 2 Review Exercises
    • Differential Equations at Work
  • Chapter 3: Applications of First-Order Differential Equations
    • Abstract
    • 3.1 Population Growth and Decay
    • Exercises 3.1
    • 3.2 Newton’s Law of Cooling and Related Problems
    • Exercises 3.2
    • 3.3 Free-Falling Bodies
    • Exercises 3.3
    • Chapter 3 Summary: Essential Concepts and Formulas
    • Chapter 3 Review Exercises
    • Differential Equations at Work
  • Chapter 4: Higher Order Equations
    • Abstract
    • 4.1 Second-Order Equations: An Introduction
    • Exercises 4.1
    • 4.2 Solutions of Second-Order Linear Homogeneous Equations with Constant Coefficients
    • Exercises 4.2
    • 4.3 Solving Second-Order Linear Equations: Undetermined Coefficients
    • Exercises 4.3
    • 4.4 Solving Second-Order Linear Equations: Variation of Parameters
    • Exercises 4.4
    • 4.5 Solving Higher Order Linear Homogeneous Equations
    • Exercises 4.5
    • 4.6 Solving Higher Order Linear Equations: Undetermined Coefficients and Variation of Parameters
    • Exercises 4.6
    • 4.7 Cauchy-Euler Equations
    • Exercises 4.7
    • 4.8 Power Series Solutions of Ordinary Differential Equations
    • Exercises 4.8
    • 4.9 Series Solutions of Ordinary Differential Equations
    • Exercises 4.9
    • Chapter 4 Summary: Essential Concepts and Formulas
    • Chapter 4 Review Exercises
    • Differential Equations at Work
  • Chapter 5: Applications of Higher Order Differential Equations
    • Abstract
    • 5.1 Simple Harmonic Motion
    • 5.2 Damped Motion
    • 5.3 Forced Motion
    • 5.4 Other Applications
    • 5.5 The Pendulum Problem
    • Chapter 5 Summary: Essential Concepts and Formulas
    • Chapter 5 Review Exercises
    • Differential Equations at Work
  • Chapter 6: Systems of Differential Equations
    • Abstract
    • 6.1 Introduction
    • Exercises 6.1
    • 6.2 Review of Matrix Algebra and Calculus
    • Exercises 6.2
    • 6.3 An Introduction to Linear Systems
    • Exercises 6.3
    • 6.4 First-Order Linear Homogeneous Systems With Constant Coefficients
    • Exercises 6.4
    • 6.5 First-Order Linear Nonhomogeneous Systems: Undetermined Coefficients and Variation of Parameters
    • Exercises 6.5
    • 6.6 Phase Portraits
    • Exercises 6.6
    • 6.7 Nonlinear Systems
    • Exercises 6.7
    • 6.8 Numerical Methods
    • Exercises 6.8
    • Chapter 6 Summary: Essential Concepts and Formulas
    • Chapter 6 Review Exercises
    • Differential Equations at Work
  • Chapter 7: Applications of Systems of Ordinary Differential Equations
    • Abstract
    • 7.1 Mechanical and Electrical Problems With First-Order Linear Systems
    • Exercises 7.1
    • 7.2 Diffusion and Population Problems With First-Order Linear Systems
    • Exercises 7.2
    • 7.3 Nonlinear Systems of Equations
    • Exercises 7.3
    • Chapter 7 Summary: Essential Concepts and Formulas
    • Chapter 7 Review Exercises
    • Differential Equations at Work
  • Chapter 8: Introduction to the Laplace Transform
    • Abstract
    • 8.1 The Laplace Transform: Preliminary Definitions and Notation
    • Exercises 8.1
    • 8.2 The Inverse Laplace Transform
    • Exercises 8.2
    • 8.3 Solving Initial-Value Problems with the Laplace Transform
    • Exercises 8.3
    • 8.4 Laplace Transforms Of Several Important Functions
    • Exercises 8.4
    • 8.5 The Convolution Theorem
    • Exercises 8.5
    • 8.6 Laplace Transform Methods for Solving Systems
    • Exercises 8.6
    • 8.7 Some Applications Using Laplace Transforms
    • Chapter 8 Review Exercises
    • Differential Equations at Work
  • Answers to Selected Exercises
    • Exercises 1.1
    • Exercises 1.2
    • Chapter 1 Review Exercises
    • Exercises 2.1
    • Exercises 2.2
    • Exercises 2.3
    • Exercises 2.4
    • Exercises 2.5
    • Exercises 2.6
    • Chapter 2 Review Exercises
    • Exercises 3.1
    • Exercises 3.2
    • Exercises 3.3
    • Chapter 3 Review Exercises
    • Exercises 4.1
    • Exercises 4.2
    • Exercises 4.3
    • Exercises 4.4
    • Exercises 4.5
    • Exercises 4.6
    • Exercises 4.7
    • Exercises 4.8
    • Exercises 4.9
    • Chapter 4 Review Exercises
    • Exercises 5.1
    • Exercises 5.2
    • Exercises 5.3
    • Exercises 5.4
    • Exercises 5.5
    • Chapter 5 Review Exercises
    • Exercises 6.1
    • Exercises 6.2
    • Exercises 6.3
    • Exercises 6.4
    • Exercises 6.5
    • Exercises 6.6
    • Exercises 6.7
    • Exercises 6.8
    • Chapter 6 Review Exercises
    • Exercises 7.1
    • Exercises 7.2
    • Exercises 7.3
    • Chapter 7 Review Exercises
    • Exercises 8.1
    • Exercises 8.2
    • Exercises 8.3
    • Exercises 8.4
    • Exercises 8.5
    • Exercises 8.6
    • Exercises 8.7
    • Chapter 8 Review Exercises
  • Bibliography
  • Appendices
  • Index

Details

No. of pages:
530
Language:
English
Copyright:
© Academic Press 2014
Published:
Imprint:
Academic Press
eBook ISBN:
9780124172821
Hardcover ISBN:
9780124172197

About the Author

Martha Abell

Martha L. Abell and James P. Braselton are graduates of the Georgia Institute of Technology and the Ohio State University, respectively, and teach at Georgia Southern University, Statesboro where they have extensive experience in Mathematica-assisted instruction at both the undergraduate and graduate levels. In addition, they have given numerous presentations on Mathematica, throughout the United States and abroad. Other books by the authors include Differential Equations with Mathematica, Second Edition and Statistics with Mathematica. Martha became Dean of the College of Science and Mathematics at Georgia Southern University in 2014.

Affiliations and Expertise

Georgia Southern University, Statesboro, USA

James Braselton

Martha L. Abell and James P. Braselton are graduates of the Georgia Institute of Technology and the Ohio State University, respectively, and teach at Georgia Southern University, Statesboro. Martha recently received Georgia Southern's award for 'excellence in research and/or creative scholarly activity.' Both authors have extensive experience with using Mathematica as well as Mathematica-assisted instruction at both the undergraduate and graduate levels. In addition, they have given numerous presentations on Mathematica, throughout the United States and abroad. Other books by the authors include Differential Equations with Mathematica, Second Edition and Statistics with Mathematica. Martha Abell became Dean of the College of Science and Mathematics at Georgia Southern University, Statesboro, Georgia, in 2014.

Affiliations and Expertise

Georgia Southern University, Statesboro, USA