A Workbook for Differential Equations

by Schrö; der, Bernd S. W.

• ISBN13: 9780470447512
• ISBN10: 0470447516
• Edition: 1st
• Format: Paperback
• Copyright: 2009-12-02
• Publisher: Wiley

Summary

Through an informal approach, A Workbook for Differential Equations presents the main concepts of differential equations. The text includes a modular design, stating the prerequisites and learning objectives. The reference contains graphical and pedagogical elements, highlighted notes, and boxed-comments for better understanding. This book provides programming projects, requiring students to manually write CAS code, emphasizing the importance of manually working on computations, applications, and models rather than simply memorizing the formulas and content. Including activities, PowerPoint slides, solutions, and more, this textbook is vital for students studying differential equations.

Author Biography

Bernd S. W. Schröder, PhD, is Edmundson/Crump Professor and Academic Director in the Program of Mathematics and Statistics at Louisiana Tech University. Dr. Schröder has authored more than thirty journal articles in his areas of research interest, which include ordered sets, probability theory, graph theory, harmonic analysis, computer science, and education. He is the author of Mathematical Analysis: A Concise Introduction, also published by Wiley.

Table of Contents

Preface

Modeling with Differential Equations

Terminology

Differential Equations Describing Populations

Remarks on Modeling with Differential Equations

Newton's Law of Cooling

Loaded Horizontal Beams

Some Special First Order Ordinary Differential Equations

Separable Differential Equations

Linear First Order Differential Equations

Bernoulli Equations

Homogeneous Equations

Exact Differential Equations

Projects

How to Review and Remember

Review of First Order Differential Equations

Before Module 3 Oscillating Systems and Hanging Cables

Spring-Mass-Systems

LRC Circuits

The Simple Pendulum

Suspended Cables

Projects

Linear Differential Equations with Constant Coefficients

Homogeneous Linear Differential Equations with Constant Coefficients

Solving Initial and Boundary Value Problems

Designing Oscillating Systems

The Method of Undetermined Coefficients

Variation of Parameters

Cauchy-Euler Equations

Some Results on Boundary Value Problems

Projects

Qualitative and Numerical Analysis of Differential Equations

Direction Fields and Autonomous Equations

From Visualization to Algorithm: Euler's Method

Runge-Kutta Methods

Finite Difference Methods for Second Order Boundary Value Problems

Linear Differential Equations-Theory

Existence and Uniqueness of Solutions

Linear Independence for Vectors

Matrices and Determinants

Linear Independence for Functions

The General Solution of Homogeneous Equations

Before Module 6 Coupled Electrical and Mechanical Systems

Multi-Loop Circuits and Kirchhoff's Laws

Coupled Spring-Mass-Systems

Laplace Transforms

Introducing the Laplace Transform

Solving Differential Equations with Laplace Transforms

Systems of Linear Differential Equations

Expanding the Transform Table

Discontinuous Forcing Terms

Complicated Forcing Functions and Convolutions

Projects

Before Module 7 Vibration and Heat

Vibrating Strings

The Heat Equation

The Schrodinger Equation

Introduction to Partial Differential Equations

Separation of Variables

Fourier Polynomials and Fourier Series

Fourier Series and Separation of Variables

Bessel and Legendre Equations

Series Solutions of Differential Equations

Expansions About Ordinary Points

Legendre Polynomials

Expansions about Singular Points

Bessel Functions

Reduction of Order

Projects

Systems of Linear Differential Equations

Existence and Uniqueness of Solutions

Matrix Algebra

Diagonalizable Systems with Constant Coefficients

Non-Diagonalizable Systems with Constant Coefficients

Qualitative Analysis

Variation of Parameters

Outlook on the Theory: Matrix Exponentials and the Jordan Normal Form

Background

Tables

Hints and Solutions for Selected Problems

Activities

Bibliography

Index

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