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Fundamentals of Differential Equations and Boundary Value Problems, 4/E
Kent B. Nagle, Late, University of South Florida
Edward B. Saff, Vanderbilt University
Arthur David Snider, University of South Florida

ISBN-10: 0321145712
ISBN-13: 9780321145710

Publisher: Addison-Wesley
Copyright: 2004
Format: Cloth Bound w/CD-ROM; 944 pp
Status: Out of Print

Suggested retail price: $133.33
This item is out of print and is no longer available for purchase.

Fundamentals of Differential Equations, Sixth Edition is designed for a one-semester sophomore or junior-level course. Fundamentals of Differential Equations and Boundary Value Problems, Fourth Edition, contains enough material for a two-semester course that covers and builds on boundary-value problems. These tried-and-true texts help students understand the methods and concepts they will need to successfully complete engineering courses. The new texts retain the features that have made previous editions successful, while integrating recent advances in teaching and learning.

The Fundamentals of Differential Equations and 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.
  • The chapter regarding the introduction to systems and phase plane analysis has been modernized to better facilitate student understanding of the material.
  • 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.
  • 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.
  • An updated Instructor's MAPLE/Matlab/Mathematica Manual, tied to development of the text, with suggestions on incorporating MAPLE, Matlab and Mathematica into the courses, and including sample worksheets for labs, is available.
  • Interactive Differential Equations CD included with every copy of the book.

  • Chapters 4 (Linear Second Order Equations) and 5 (Introduction to Systems and Phase Plane Analysis) have been substantially rewritten and tightened.
  • New Group Projects have been added.
  • The exercises have been tightened and updated.
  • MyMathLab is now available for this text for the first time. All of the text's electronic resources and the IDE content can be found in MyMathLab.

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

1. Introduction.

Background.

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 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.

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.

Convolution.

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.

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.



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.



11. Eigenvalue Problems and Sturm-Liouville Equations.

Introduction: Heat Flow in a Nonuniform Wire.

Eigenvalues and Eigenfunctions.

Regular Sturm-Liouville Boundary Value Problems.

Nonhomogeneous Boundary Value Problems and the Fredholm Alternative.

Solution by Eigenfunction Expansion.

Green's Functions.

Singular Sturm-Liouville Boundary Value Problems.

Oscillation and Comparison Theory.



12. Stability of Autonomous Systems.

Introduction: Competing Species.

Linear Systems in the Plane.

Almost Linear Systems.

Energy Methods.

Lyapunov's Direct Method.

Limit Cycles and Periodic Solutions.

Stability of Higher-Dimensional Systems.



13. Existence and Uniqueness Theory.

Introduction: Successive Approximations.

Picard's Existence and Uniqueness Theorem.

Existence of Solutions of Linear Equations.

Continuous Dependence of Solutions.



Appendices.

Newton's Method.

Simpson's Rule.

Cramer's Rule.

Method of Least Squares.

Runge-Kutta Precedure for n Equations.



Answers to Odd-Numbered Problems.


Index.

    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 ofDifferential 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).

  • 0321419219Fundamentals of Differential Equations with Boundary Value Problems with IDE CD (Saleable Package), 5/E
    Nagle, Saff & Snider
    © 2008 | Addison-Wesley | Cloth Bound w/CD-ROM; 944 pages | Instock
    ISBN-10: 0321419219 | ISBN-13: 9780321419217
    Brief Description

For Differential Equations


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