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First Course in Differential Equations : With Modeling Applications,9780495108245
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First Course in Differential Equations : With Modeling Applications

by
Edition:
9th
ISBN13:

9780495108245

ISBN10:
0495108243
Format:
Hardcover
Pub. Date:
5/14/2008
Publisher(s):
Cengage Learning
Includes 2-weeks free access to
step-by-step solutions for this book.
Step-by-Step solutions are actual worked out problems to the questions at the end of each chapter that help you understand your homework and study for your exams. Chegg and eCampus are providing you two weeks absolutely free. 81% of students said using Step-by-Step solutions prepared them for their exams.

Questions About This Book?

What version or edition is this?
This is the 9th edition with a publication date of 5/14/2008.
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  • The Used copy of this book is not guaranteed to include any supplemental materials. Typically, only the book itself is included.

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Summary

A First Course in Differential Equations with Modeling Applications, 9th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.

Table of Contents

Introduction to Differential Equations
Definitions and Terminology
Initial-Value Problems
Differential Equations as Mathematical Models
Chapter 1 in Review
First-Order Differential Equations
Solution Curves Without a Solution
Separable Variables
Linear Equations
Exact Equations and Integrating Factors
Solutions by Substitutions
A Numerical Method
Chapter 2 in Review
Modeling with First-Order Differential Equations
Linear Models
Nonlinear Models
Modeling with Systems of First-Order Differential Equations
Chapter 3 in Review
Higher-Order Differential Equations
Preliminary Theory- Linear Equations
Reduction of Order
Homogeneous Linear Equations with Constant Coefficients
Undetermined Coefficients- Superposition Approach
Undetermined Coefficients- Annihilator Approach
Variation of Parameters
Cauchy-Euler Equation
Solving Systems of Linear Differential Equations by Elimination
Nonlinear Differential Equations
Chapter 4 in Review
Modeling with Higher-Order Differential Equations
Linear Models: Initial-Value Problems
Linear Models: Boundary-Value Problems
Nonlinear Models
Chapter 5 in Review
Series Solutions of Linear Equations
Solutions About Ordinary Points
Solutions About Singular Points
Special Functions
Chapter 6 in Review
Laplace Transform
Definition of the Laplace Transform
Inverse Transform and Transforms of Derivatives
Operational Properties I
Operational Properties II
Dirac Delta Function
Systems of Linear Differential Equations
Chapter 7 in Review
Systems of Linear First-Order Differential Equations
Preliminary Theory
Homogeneous Linear Systems
Nonhomogeneous Linear Systems
Matrix Exponential
Chapter 8 in Review
Numerical Solutions of Ordinary Differential Equations
Euler Methods
Runge-Kutta Methods
Multistep Methods
Higher-Order Equations and Systems
Second-Order Boundary-Value Problems
Chapter 9 in Review
Gamma Function
Matrices
Laplace Transforms
Answers for Selected Odd-Numbered Problems
Table of Contents provided by Publisher. All Rights Reserved.


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