Elementary Differential Equations With Boundary Value Problems

, by Kohler, Werner E.; Johnson, Lee W.

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ISBN: 9780321121646 | 0321121643
Cover: Hardcover
Copyright: 1/1/2004

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Introduction to Differential Equations
Introduction
Direction Fields
First Order Linear Differential Equations
Existence and Uniqueness
First Order Linear Homogeneous Differential Equations
Nonhomogeneous Differential Equations
Introduction to Mathematical Models
Mixing Problems and Cooling Problems
First Order Nonlinear Differential Equations
Existence and Uniqueness
Separable First Order Equations
Exact Differential Equations
Bernoulli Equations
The Logistic Population Model
One-Dimensional Motion with Air Resistance
One-Dimensional Dynamics with Distance as the Independent Variable
Euler's Method
Second Order Linear Differential Equations
Introduction
Existence and Uniqueness
The General Solution of Homogeneous Equations
Fundamental Sets and Linear Independence
Constant Coefficient Homogeneous Equations
Real Repeated Roots
Reduction of Order
Complex Roots
Unforced Mechanical Vibrations
The General Solution of the Linear Nonhomogeneous Equation
The Method of Undetermined Coefficients
The Method of Variation of Parameters
Forced Mechanical Vibrations, Electrical Networks, and Resonance
Higher Order Linear Differential Equations
Existence and Uniqueness
The General Solution ofnth Order Linear Homogeneous Equation
Fundamental Sets and Linear Independence
Constant Coefficient Homogeneous Equations
Nonhomogeneous Linear Equations
First Order Linear Systems
The Calculus of Matrix Functions
Existence and Uniqueness
Homogeneous Linear Systems
Fundamental Sets and Linear Independence
Constant Coefficient Homogeneous Systems
Complex Eigenvalues
Repeated Eigenvalues
Nonhomogeneous Linear Systems
Euler's Method for Systems of Differential Equations
Diagonalization
Functions of a Matrix and the Exponential Matrix
Laplace Transforms
The Laplace Transform
Lapla
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Elementary Differential Equations With Boundary Value Problems

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Elementary Differential Equations With Boundary Value Problems

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