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  5. Differential Equations and Boundary Value Problems: Computing and Modeling (Tech Update)

Differential Equations and Boundary Value Problems: Computing and Modeling (Tech Update), 5th edition

  • C Henry Edwards
  • David E. Penney
  • David Calvis

Published by Pearson (January 1st 2018) - Copyright © 2019

5th edition

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For one-semester sophomore- or junior-level courses in Differential Equations.

This package includes MyLab Math. This Tech Update is completely compatible with the (c)2015 version of the text.

The right balance between concepts, visualization, applications, and skills – now available with MyLab Math

Differential Equations: Computing and Modeling provides the conceptual development and geometric visualization of a modern differential equations course that is essential to science and engineering students. It balances traditional manual methods with the new, computer-based methods that illuminate qualitative phenomena – a comprehensive approach that makes accessible a wider range of more realistic applications.

The book starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout. For the first time, MyLab™ Math is available for the 5th Edition, providing online homework with immediate feedback, the complete eText, and more.

Reach every student by pairing this text with MyLab Math

MyLab™ Math is the teaching and learning platform that empowers instructors to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student.

0134995988 / 9780134995984   Differential Equations and Boundary Value Problems: Computing and Modeling Media Update and MyLab Math with Pearson eText -- Title-Specific Access Card Package, 5/e

Package consists of:

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  • 0134872975 / 9780134872971  MyLab Math plus Pearson eText – Standalone Access Card - for Differential Equations and Boundary Value Problems: Computing and Modeling Media Update

Table of contents

1. First-Order Differential Equations

1.1 Differential Equations and Mathematical Models

1.2 Integrals as General and Particular Solutions

1.3 Slope Fields and Solution Curves

1.4 Separable Equations and Applications

1.5 Linear First-Order Equations

1.6 Substitution Methods and Exact Equations


2. Mathematical Models and Numerical Methods

2.1 Population Models

2.2 Equilibrium Solutions and Stability

2.3 Acceleration—Velocity Models

2.4 Numerical Approximation: Euler’s Method

2.5 A Closer Look at the Euler Method

2.6 The Runge—Kutta Method


3. Linear Equations of Higher Order

3.1 Introduction: Second-Order Linear Equations

3.2 General Solutions of Linear Equations

3.3 Homogeneous Equations with Constant Coefficients

3.4 Mechanical Vibrations

3.5 Nonhomogeneous Equations and Undetermined Coefficients

3.6 Forced Oscillations and Resonance

3.7 Electrical Circuits

3.8 Endpoint Problems and Eigenvalues


4. Introduction to Systems of Differential Equations

4.1 First-Order Systems and Applications

4.2 The Method of Elimination

4.3 Numerical Methods for Systems


5. Linear Systems of Differential Equations

5.1 Matrices and Linear Systems

5.2 The Eigenvalue Method for Homogeneous Systems

5.3 A Gallery of Solution Curves of Linear Systems

5.4 Second-Order Systems and Mechanical Applications

5.5 Multiple Eigenvalue Solutions

5.6 Matrix Exponentials and Linear Systems

5.7 Nonhomogeneous Linear Systems


6. Nonlinear Systems and Phenomena

6.1 Stability and the Phase Plane

6.2 Linear and Almost Linear Systems

6.3 Ecological Models: Predators and Competitors

6.4 Nonlinear Mechanical Systems

6.5 Chaos in Dynamical Systems


7. Laplace Transform Methods

7.1 Laplace Transforms and Inverse Transforms

7.2 Transformation of Initial Value Problems

7.3 Translation and Partial Fractions

7.4 Derivatives, Integrals, and Products of Transforms

7.5 Periodic and Piecewise Continuous Input Functions

7.6 Impulses and Delta Functions


8. Power Series Methods

8.1 Introduction and Review of Power Series

8.2 Series Solutions Near Ordinary Points

8.3 Regular Singular Points

8.4 Method of Frobenius: The Exceptional Cases

8.5 Bessel’s Equation

8.6 Applications of Bessel Functions


9. Fourier Series Methods and Partial Differential Equations

9.1 Periodic Functions and Trigonometric Series

9.2 General Fourier Series and Convergence

9.3 Fourier Sine and Cosine Series

9.4 Applications of Fourier Series

9.5 Heat Conduction and Separation of Variables

9.6 Vibrating Strings and the One-Dimensional Wave Equation

9.7 Steady-State Temperature and Laplace’s Equation


10. Eigenvalue Methods and Boundary Value Problems

10.1 Sturm—Liouville Problems and Eigenfunction Expansions

10.2 Applications of Eigenfunction Series

10.3 Steady Periodic Solutions and Natural Frequencies

10.4 Cylindrical Coordinate Problems

10.5 Higher-Dimensional Phenomena 

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