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CITATION

Bronson, Richard. Schaum's Easy Outline of Differential Equations. McGraw-Hill, 2003.

Schaum's Easy Outline of Differential Equations

Authors: Richard Bronson

Published:  February 2003

eISBN: 9780071428460 0071428461 | ISBN: 9780071409674
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  • 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