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Schaum's Easy Outline of Differential Equations
CITATION
Bronson, Richard
.
Schaum's Easy Outline of Differential Equations
. McGraw-Hill, 2003.
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Schaum's Easy Outline of Differential Equations
Authors:
Richard Bronson
Published:
February 2003
eISBN:
9780071428460 0071428461
|
ISBN:
9780071409674
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Book Description
Table of Contents
Copyright
Contents
Chapter 1 Basic Concepts and Classifying Differential Equations
Differential Equations
Notation
Solutions
Initial-Value and Boundary-Value Problems
Standard and Differential Forms
Linear Equations
Bernoulli Equations
Homogeneous Equations
Separable Equations
Exact Equations
Chapter 2 Solutions of First-Order Differential Equations
Separable Equations
Homogeneous Equations
Exact Equations
Linear Equations
Bernoulli Equations
Solved Problems
Chapter 3 Applications of First-Order Differential Equations
Growth and Decay Problems
Temperature Problems
Falling Body Problems
Dilution Problems
Electrical Circuits
Orthogonal Trajectories
Solved Problems
Chapter 4 Linear Differential Equations: Theory of Solutions
Linear Differential Equations
Linearly Independent Solutions
The Wronskian
Nonhomogeneous Equations
Chapter 5 Solutions of Linear Homogeneous Differential Equations with Constant Coef •cients
The Characteristic Equation
General Solution for Second-Order Equations
General Solution for nth-Order Equations
Solved Problems
Chapter 6 Solutions of Linear Nonhomogeneous Equations and Initial-Value Problems
The Method of Undetermined Coef •cients
Variation of Parameters
Initial-Value Problems
Solved Problems
Chapter 7 Applications of Second-Order Linear Differential Equations
Spring Problems
Electrical Circuit Problems
Buoyancy Problems
Classifying Solutions
Solved Problems
Chapter 8 Laplace Transforms and Inverse Laplace Transforms
Definition of the Laplace Transform
Properties of Laplace Transforms
Definition of the Inverse Laplace Transform
Manipulating Denominators
Manipulating Numerators
Convolutions
Unit Step Function
Translations
Solved Problems
Chapter 9 Solutions by Laplace Transforms
Laplace Transforms of Derivatives
Solutions of Linear Differential Equations with Constant Coefficients
Solutions of Linear Systems
Solved Problems
Chapter 10 Matrices and the Matrix Exponential
Matrices and Vectors
Matrix Addition
Scalar and Matrix Multiplication
Powers of a Square Matrix
Differentiation and Integration of Matrices
The Characteristic Equation of a Matrix
Definition of the Matrix Exponential eAt
Computation of the Matrix Exponential eAt
Solved Problems
Chapter 11 Solutions of Linear Differential Equations with Constant Coef •cients by Matrix Methods
Reduction of Linear Differential Equations to a First-Order System
Solution of the Initial-Value Problem
Solution with No Initial Conditions
Solved Problems
Chapter 12 Power Series Solutions
Second-Order Linear Equations with Variable Coef •cients
Analytic Functions and Ordinary Points
Solutions Around the Origin of Homogeneous Equations
Solutions Around the Origin of Nonhomogeneous Equations
Initial-Value Problems
Solutions Around Other Points
Regular Singular Points
Method of Frobenius
Solved Problems
Chapter 13 Gamma and Bessel Functions
Gamma Function
Bessel Functions
Algebraic Operations on Infinite Series
Solved Problems
Chapter 14 Numerical Methods for First-Order Differential Equations
Direction Fields
Euler’s Method
General Remarks Regarding Numerical Methods
Modified Euler’s Method
Runge-Kutta Method
Adams-Bashforth-Moulton Method
Milne’s Method
Order of a Numerical Method
Numerical Methods for Systems
Solved Problems
Chapter 15 Boundary-Value Problems and Fourier Series
Second-Order Boundary-Value Problems
Eigenvalue Problems
Sturm-Liouville Problems
Eigenfunction Expansions
Fourier Sine Series
Fourier Cosine Series
Solved Problems
Appendix Laplace Transforms
Index