Workbook for Differential Equations

ISBN-10: 0470447516

ISBN-13: 9780470447512

Edition: 2010

List price: $77.95
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Description:

This book takes an informal approach and focuses on a few main concepts (modeling with DEs, special first order ODEs, linear DEs with constant coefficients, qualitative analysis of DEs, the theory of linear DEs, Laplace transforms, an introduction to PDEs, and series solutions of DEs) as opposed to covering every possible aspect of differential equations. A modular design is provided for easy access to certain topics, and every module begins by clearly stating the prerequisites and learning objectives. Graphical and pedagogical elements are abundant throughout, including highlighted notes that effectively remind readers about previously developed facts and boxed comments that guide readers through computations. Much of the classical content of a typical differential equations course is highly computational, and the necessary algorithms can be implemented in a computer algebra system (CAS), i.e. Mathematica, Maple, R, MathCAD, MuPAD, etc. This book is not specific to one CAS, and, whenever possible, the author includes programming projects with detailed specifications that require the reader to manually write CAS code to solve certain problems. In this fashion, readers gain a deeper connection to the material as well as learn a program that can be used to double check homework problems. This book is fast-moving without being terse, and it invites readers to become involved while promising to reward them with reading and learning skills that will serve them well in later technical courses. Applications are detailed, accurate, and appropriately woven throughout the text.
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Book details

List price: $77.95
Copyright year: 2010
Publisher: John Wiley & Sons, Limited
Publication date: 1/12/2010
Binding: Paperback
Pages: 350
Size: 8.25" wide x 10.75" long x 0.75" tall
Weight: 1.738
Language: English

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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