Fundamentals of Differential Equations / Edition 5

Fundamentals of Differential Equations / Edition 5

2.0 2
by R. Kent Nagle, Edward B. Saff, Arthur David Snider

ISBN-10: 0201338688

ISBN-13: 9780201338683

Pub. Date: 11/11/1999

Publisher: Addison-Wesley

This text is in a flexible one-semester text that spans a variety of topics in the basic theory as well as applications of differential equations.  See more details below


This text is in a flexible one-semester text that spans a variety of topics in the basic theory as well as applications of differential equations.

Product Details

Publication date:
Edition description:
Older Edition
Product dimensions:
8.31(w) x 9.50(h) x 1.36(d)

Table of Contents

(Most chapters end with a Chapter Summary, Review Problems and Group Projects.)

1. Introduction.


Solutions and Initial Value Problems.

Direction Fields.

The Approximation Method of Euler.

2. First Order Differential Equations.

Introduction: Motion of a Falling Body.

Separable Equations.

Linear Equations.

Exact Equations.

Special Integrating Factors.

Substitutions and Transformations.

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.

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.

Qualitative Considerations for Variable-Coefficient and Nonlinear Equations.

A Closer Look at Free Mechanical Vibrations.

A Closer Look at Forced Mechanical Vibrations.

5. Introduction to Systems andPhase Plane Analysis.

Interconnected Fluid Tanks.

Elimination Method for Systems with Constant Coefficients.

Solving Systems and Higher-Order Equations Numerically.

Introduction to the Phase Plane.

Coupled Mass-Spring Systems.

Electrical Systems.

Dynamical Systems, Poincaré Maps, and Chaos.

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.

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.


Impulses and the Dirac Delta Function.

Solving Linear Systems with Laplace Transforms.

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.

9. Matrix Methods for Linear Systems.


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.

10. Partial Differential Equations.

Introduction: A Model for Heat Flow.

Method of Separation of Variables.

Fourier Series.

Fourier Cosine and Sine Series.

The Heat Equation.

The Wave Equation.

Laplace's Equation.


Newton's Method.

Simpson's Rule.

Cramer's Rule.

Method of Least Squares.

Runge-Kutta Precedure for n Equations.

Answers to Odd-Numbered Problems.


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Fundamentals of Differential Equations 2 out of 5 based on 0 ratings. 2 reviews.
Guest More than 1 year ago
I think this book is okay. I don't think that it is really horrible, but some of the definitions and theorems could be stated better and more understandable. This book will get you through, but don't buy the solutions manual.
Guest More than 1 year ago
I had this book at a community college.this book is very wordy and confusing. the instructor is the only way i got thru the course. avoid it if you can