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Fundamentals of Differential Equations bound with IDE CD (Saleable Package), 7/E
R. Kent Nagle, Late, University of South Florida
Edward B. Saff, Vanderbilt University
Arthur David Snider, University of South Florida

ISBN-10: 0321410483
ISBN-13: 9780321410481

Publisher: Addison-Wesley
Copyright: 2008
Format: Cloth Bound w/CD-ROM; 768 pp
Published: 10/08/2007

Suggested retail price: $124.00
Not available for purchase at this time.

Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. Available in two versions, these flexible texts offer the instructor many choices in syllabus design, course emphasis (theory, methodology, applications, and numerical methods), and in using commercially available computer software.


Fundamentals of Differential Equations, Seventh Edition is suitable for a one-semester sophomore- or junior-level course. Fundamentals of Differential Equations with Boundary Value Problems, Fifth Edition, contains enough material for a two-semester course that covers and builds on boundary value problems. The Boundary Value Problems version consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm-Liouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory).


  • Applications-driven sections are included in the chapter on linear second-order equations.
  • Modernized treatment of the chapter on the introduction to systems and phase plane analysis increases student comprehension of the material.
  • Group Projects relating to the material covered appear at the end of each chapter. They may involve more challenging applications, delve deeper into theory, or introduce more advanced topics.
  • The expanded coverage of dynamical systems is consistent with the level of the text.
  • The phase line is covered at the beginning of the text.
  • Updated Instructor Manuals for MAPLE/Matlab/Mathematica, tied to the development of the text, Included are suggestions on incorporating these technologies into the courses, along with sample worksheets for labs.
  • Interactive Differential Equations CD-ROM is included with every new copy of the book.

  • Expanded Group Projects at the end of each chapter provide more applications to the biological sciences and to economics. The new projects enhance students' problem-solving abilities as well as broaden their appreciation for the power of the subject.
  • Enhanced Exercise Sets now include a selection of more challenging exercises.
  • New section (4.7) on Variable-Coefficient Equations anticipates how the structure and theory become generalized to the variable-coefficient case, while continuing to defer a more rigorous exposition of this topic to Chapter 6. This new section also includes a discussion of Cauchy-Euler equations and the Reduction-of-Order technique. Together with the enduring qualitatively-oriented Section 4.8, which guides the reader to speculate intelligently on the approximate behavior of variable coefficient and nonlinear equations, these two sections afford a broader overview of second-order equations and provide instructors the flexibility to proceed immediately to the applications sections.
  • New section (5.5) describing recent applications of differential equations techniques to biological systems and public health issues. These case studies demonstrate the potential for applying classical techniques of phase plane analysis and computer simulations.

1. Introduction

Background

Solutions and Initial Value Problems

Direction Fields

The Approximation Method of Euler

Chapter Summary

Technical Writing Exercises

Group Projects for Chapter 1

            A. Taylor Series Method

            B. Picard's Method

            C. Magnetic Dipole

            D. The Phase Line

 

2. First-Order Differential Equations

Introduction: Motion of a Falling Body

Separable Equations

Linear Equations

Exact Equations

Special Integrating Factors

Substitutions and Transformations

Chapter Summary

Technical Writing Exercises

Group Projects for Chapter 2

            A. Differential Equations in Clinical Medicine

            B. Torricelli's Law of Fluid Flow

            C. The Snowplow Problem

            D. Two Snowplows

            E. Clairaut Equations and Singular Solutions

            F. Multiple Solutions of a First-Order Initial Value Problem

            G. Designing a Solar Collector

            H. Asymptotic Behavior of Solutions to Linear Equations

            I. Utility Functions and Risk Aversion

 

3. Mathematical Models and Numerical Methods Involving First Order Equations

Mathematical Modeling

Compartmental Analysis

Heating and Cooling of Buildings

Newtonian Mechanics

Electrical Circuits

Improved Euler's Method

Higher-Order Numerical Methods: Taylor and Runge-Kutta

Chapter Summary

Technical Writing Exercises

Group Projects for Chapter 3

            A. Dynamics of HIV Infection

            B. Aquaculture

            C. Curve of Pursuit

            D. Aircraft Guidance in a Crosswind

            E. Feedback and the Op Amp

            F. Bang-Bang Controls

            G. Market Equilibrium: Stability and Time Paths

            H. Stability of Numerical Methods

            I. Period Doubling and Chaos

 

4. Linear Second-Order Equations

Introduction: The Mass-Spring Oscillator

Homogeneous Linear Equations; The General Solution

Auxiliary Equations with Complex Roots

Nonhomogeneous Equations: The Method of Undetermined Coefficients

The Superposition Principle and Undetermined Coefficients Revisited

Variation of Parameters

Variable-Coefficient Equations

Qualitative Considerations for Variable-Coefficient and Nonlinear Equations

A Closer Look at Free Mechanical Vibrations

A Closer Look at Forced Mechanical Vibrations

Chapter Summary

Technical Writing Exercises

Group Projects for Chapter 4

            A. Nonlinear Equations Solvable by First-Order Techniques

            B. Apollo Reentry

            C. Simple Pendulum

            D. Linearization of Nonlinear Problems

            E. Convolution Method

            F. Undetermined Coefficients Using Complex Arithmetic

            G. An Alternative to the Method of Undetermined Coefficients

            H. Asymptotic Behavior of Solutions

 

5. Introduction to Systems and Phase Plane Analysis

Interconnected Fluid Tanks

Elimination Method for Systems with Constant Coefficients

Solving Systems and Higher-Order Equations Numerically

Introduction to the Phase Plane

Applications to Biomathematics: Epidemic and Tumor Growth Models

Coupled Mass-Spring Systems

Electrical Systems

Dynamical Systems, Poincaré Maps, and Chaos

Chapter Summary

Technical Writing Exercises

Group Projects for Chapter 5

            A. Designing a Landing System for Interplanetary Travel

            B. Things That Bob

            C. Hamiltonian Systems

            D. Strange Behavior of Competing Species - Part 1

            E. Cleaning Up the Great Lakes

 

6. Theory of Higher-Order Linear Differential Equations

Basic Theory of Linear Differential Equations

Homogeneous Linear Equations with Constant Coefficients

Undetermined Coefficients and the Annihilator Method

Method of Variation of Parameters

Chapter Summary

Technical Writing Exercises

Group Projects for Chapter 6

            A. Computer Algebra Systems and Exponential Shift

            B. Justifying the Method of Undetermined Coefficients

            C. Transverse Vibrations of a Beam

 

7. Laplace Transforms

Introduction: A Mixing Problem

Definition of the Laplace Transform

Properties of the Laplace Transform

Inverse Laplace Transform

Solving Initial Value Problems

Transforms of Discontinuous and Periodic Functions

Convolution

Impulses and the Dirac Delta Function

Solving Linear Systems with Laplace Transforms

Chapter Summary

Technical Writing Exercises

Group Projects for Chapter 7

            A. Duhamel's Formulas

            B. Frequency Response Modeling

            C. Determining System Parameters

 

8. Series Solutions of Differential Equations

Introduction: The Taylor Polynomial Approximation

Power Series and Analytic Functions

Power Series Solutions to Linear Differential Equations

Equations with Analytic Coefficients

Cauchy-Euler (Equidimensional) Equations

Method of Frobenius

Finding a Second Linearly Independent Solution

Special Functions.

Chapter Summary

Technical Writing Exercises

Group Projects for Chapter 8

            A. Spherically Symmetric Solutions to Shrodinger's Equation for the Hydrogen Atom

            B. Airy's Equation

            C. Buckling of a Tower

            D. Aging Spring and Bessel Functions

 

9. Matrix Methods for Linear Systems

Introduction

Review 1: Linear Algebraic Equations

Review 2: Matrices and Vectors

Linear Systems in Normal Form

Homogeneous Linear Systems with Constant Coefficients

Complex Eigenvalues

Nonhomogeneous Linear Systems

The Matrix Exponential Function

Chapter Summary

Technical Writing Exercises

Group Projects for Chapter 9

            A. Uncoupling Normal Systems

            B. Matrix Laplace Transform Method

            C. Undamped Second-Order Systems

            D. Strange Behavior of Competing Species - Part II

 

Appendices

A. Newton's Method

B. Simpson's Rule

C. Cramer's Rule

D. Method of Least Squares

E. Runge-Kutta Precedure for n Equations

 

Answers to Odd-Numbered Problems

Index

For Differential Equations


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