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Elementary Differential Equations

ISBN-10: 0534368417
ISBN-13: 9780534368418
Edition: 2000
List price: $280.95 Buy it from $110.62
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Description: This text has been written in clear and accurate language that students can read and comprehend. The author has minimized the number of explicitly state theorems and definitions, in favor of dealing with concepts in a more conversational manner.  More...

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Book details

List price: $280.95
Copyright year: 2000
Publisher: Brooks/Cole
Publication date: 10/28/1999
Binding: Hardcover
Pages: 900
Size: 8.25" wide x 10.50" long x 1.25" tall
Weight: 2.882
Language: English

This text has been written in clear and accurate language that students can read and comprehend. The author has minimized the number of explicitly state theorems and definitions, in favor of dealing with concepts in a more conversational manner. This is illustrated by over 250 worked out examples. The problems are extremely high quality and are regarded as one of the text's many strengths. This book also allows the instructor to select the level of technology desired. Trench has simplified this by using the symbols C and L. C exercises call for computation and/or graphics, and L exercises are laboratory exercises that require extensive use of technology. Several sections include informal advice on the use of technology. The instructor who prefers not to emphasize technology can ignore these exercises.

Introduction
Some Applications Leading to Differential Equations
Basic Concepts
Direction Fields for First Order Equations
First Order Equations
Linear First Order Equations
Separable Equations
Existence and Uniqueness of Solutions of Nonlinear Equations
Transformation of Nonlinear Equations into Separable Equations
Exact Equations
Integrating Factors
Numerical Methods
Euler's Method
The Improved Euler Method and Related Methods
The Runge-Kutta Method
Applications Of First Order Equations
Growth and Decay
Cooling and Mixing
Elementary Mechanics
Autonomous Second Order Equations
Applications to Curves
Linear Second Order Equations
Homogeneous Linear Equations
Constant Coefficient Homogeneous Equations
Nonhomogenous Linear Equations
The Method of Undetermined Coefficients I
The Method of Undetermined Coefficients II
Reduction of Order
Variation of Parameters
Applications Of Linear Second Order Equations
Spring Problems I
Spring Problems II
The RLC Circuit
Motion Under a Central Force
Series Solutions Of Linear Second Order Equations
Review of Power Series
Series Solutions Near an Ordinary Point I
Series Solutions Near an Ordinary Point II
Regular Singular Points; Euler Equations
The Method of Frobenius I
The Method of Frobenius II
The Method of Frobenius III
Laplace Transforms
Introduction to the Laplace Transform
The Inverse Laplace Transform
Solution of the Initial Value Problems
The Unit Step Function
Constant Coefficient Equations with Piecewise Continuous Forcing Functions
Convolution
Constant Coefficient Equations with Impulses
Linear Higher Order Equations
Introduction to Linear Higher Order Equations
Higher Order Constant Coefficient Homogeneous Equations
Undetermined Coefficients for Higher Order Equations
Variation of Parameters for Higher Order Equations
Linear Systems Of Differential Equations
Introduction to Systems of Differential Equations
Linear Systems of Differential Equations
Basic Theory of Homogenous Linear Systems
Constant Coefficient Homogeneous Systems I
Constant Coefficient Homogenous Systems II
Constant Coefficient Homogenous Systems III
Variation of Parameters for Nonhomogenous Linear Systems
Answers To Selected Exercises
Index

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