First Course in Differential Equations : With Modeling Applications

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  • Edition: 9th
  • Format: Hardcover
  • Copyright: 2008-05-14
  • Publisher: Brooks Cole
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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
Laplace Transforms
Answers for Selected Odd-Numbered Problems
Table of Contents provided by Publisher. All Rights Reserved.

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