Fundamentals of Differential Equations and Boundary Value Problems eBook (7e) : 9780134462219

Fundamentals of Differential Equations and Boundary Value Problems eBook (7e)

Nagle,K et al
Published by
Pearson Higher Ed USA
Title type
NZ/Pacific customers only
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About the book: For one-semester sophomore- or junior-level courses in Differential Equations. Fundamentals of Differential Equations and Boundary Value Problems presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. This flexible text allows instructors to adapt to various course emphases (theory, methodology, applications, and numerical methods) and to use commercially available computer software. 

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Table of contents
  • 1.   Introduction
  • 2.   First-Order Differential Equations
  • 3.   Mathematical Models and Numerical Methods Involving First Order Equations
  • 4.   Linear Second-Order Equations
  • 5.   Introduction to Systems and Phase Plane Analysis
  • 6.   Theory of Higher-Order Linear Differential Equations
  • 7.   Laplace Transforms
  • 8.   Series Solutions of Differential Equations
  • 9.   Matrix Methods for Linear Systems
  • 10.   Partial Differential Equations
  • 11.   Eigenvalue Problems and Sturm-Liouville Equations
  • 12.   Stability of Autonomous Systems
  • 13.   Existence and Uniqueness Theory
  • Appendix A Review of Integration Techniques
  • Appendix B Newton's Method
  • Appendix C Simpson's Rule
  • Appendix D Cramer's Rule
  • Appendix E Method of Least Squares
  • Appendix F Runge-Kutta Procedure for n Equations
  • Appendix G Software for Analyzing Differential Equations
Features & benefits
  • Students learn the basic theory of differential equations while exploring a variety of modern applications in science and engineering.
    • Modernised treatment of the introduction to systems chapter and phase plane analysis increases student comprehension of the material.
    • Flexible organisation allows for various course configurations and emphasis (theory, applications and techniques, and concepts).
    • Motivating Problems begin most chapters with a discussion of a physics or engineering problem
    • Applications-driven sections are included in the chapter on linear second-order equations.
    • Review of Linear Algebraic Equations and Matrices -- The chapter on matrix methods for linear systems (Chapter 9) begins with two introductory sections on the theory of linear algebraic systems and matrix algebra.
    • Review of Integration Techniques appendix provides a review of the methods for integrating functions analytically. This offers students a useful refresh prior to beginning the differential equations course.          
    • NEW! Examples have been added dealing with variation of parameters, Laplace transforms, the Gamma function, and eigenvectors (among others).
  • Robust opportunities for exercises and assignments give instructors flexibility and students a wide range of practice.
    • 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.
    • Exercises, which are graduated in difficulty and varied by type, include a wide variety of applications such as barometric pressure, compound interest, the mathematical equivalence of an impulse force and a velocity boost.
    • Chapter Summaries and Review Problems at the end of each chapter help students comprehend fully the learning and promote knowledge retention.
    • Technical Writing Exercises help students develop their communication skills, an essential aspect of professional activity.
    • Optional use of Mathematica®, MATLAB®, and Maple computer software gives students opportunity to conduct numerical experiments and tackle realistic applications that give additional insights into the subject.
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