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CITATION

Bronson, Richard and Costa, Gabriel. Schaum's Outline of Differential Equations, 4th Edition. McGraw-Hill, 2014.

Schaum's Outline of Differential Equations, 4th Edition

Authors: Richard Bronson and Gabriel Costa

Published:  March 2014

eISBN: 9780071822862 0071822860 | ISBN: 9780071824859
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  • Cover
  • Video Content
  • Title Page
  • Copyright Page
  • Contents
  • Chapter 1 Basic Concepts
  • Differential Equations
  • Notation
  • Solutions
  • Initial-Value and Boundary-Value Problems
  • Chapter 2 An Introduction to Modeling and Qualitative Methods
  • Mathematical Models
  • The “Modeling Cycle”
  • Qualitative Methods
  • Chapter 3 Classifications of First-Order Differential Equations
  • Standard Form and Differential Form
  • Linear Equations
  • Bernoulli Equations
  • Homogeneous Equations
  • Separable Equations
  • Exact Equations
  • Chapter 4 Separable First-Order Differential Equations
  • General Solution
  • Solutions to the Initial-Value Problem
  • Reduction of Homogeneous Equations
  • Chapter 5 Exact First-Order Differential Equations
  • Defining Properties
  • Method of Solution
  • Integrating Factors
  • Chapter 6 Linear First-Order Differential Equations
  • Method of Solution
  • Reduction of Bernoulli Equations
  • Chapter 7 Applications of First-Order Differential Equations
  • Growth and Decay Problems
  • Temperature Problems
  • Falling Body Problems
  • Dilution Problems
  • Electrical Circuits
  • Orthogonal Trajectories
  • Chapter 8 Linear Differential Equations: Theory of Solutions
  • Linear Differential Equations
  • Linearly Independent Solutions
  • The Wronskian
  • Nonhomogeneous Equations
  • Chapter 9 Second-Order Linear Homogeneous Differential Equations with Constant Coefficients
  • Introductory Remark
  • The Characteristic Equation
  • The General Solution
  • Chapter 10 nth-Order Linear Homogeneous Differential Equations with Constant Coefficients
  • The Characteristic Equation
  • The General Solution
  • Chapter 11 The Method of Undetermined Coefficients
  • Simple Form of the Method
  • Generalizations
  • Modifications
  • Limitations of the Method
  • Chapter 12 Variation of Parameters
  • The Method
  • Scope of the Method
  • Chapter 13 Initial-Value Problems for Linear Differential Equations
  • Chapter 14 Applications of Second-Order Linear Differential Equations
  • Spring Problems
  • Electrical Circuit Problems
  • Buoyancy Problems
  • Classifying Solutions
  • Chapter 15 Matrices
  • Matrices and Vectors
  • Matrix Addition
  • Scalar and Matrix Multiplication
  • Powers of a Square Matrix
  • Differentiation and Integration of Matrices
  • The Characteristic Equation
  • Chapter 16 e[sup(At)]
  • Definition
  • Computation of e[sup(At)]
  • Chapter 17 Reduction of Linear Differential Equations to a System of First-Order Equations
  • An Example
  • Reduction of an n[sup(th)] Order Equation
  • Reduction of a System
  • Chapter 18 Graphical and Numerical Methods for Solving First-Order Differential Equations
  • Qualitative Methods
  • Direction Fields
  • Euler’s Method
  • Stability
  • Chapter 19 Further Numerical Methods for Solving First-Order Differential Equations
  • General Remarks
  • Modified Euler’s Method
  • Runge–Kutta Method
  • Adams–Bashford–Moulton Method
  • Milne’s Method
  • Starting Values
  • Order of a Numerical Method
  • Chapter 20 Numerical Methods for Solving Second-Order Differential Equations Via Systems
  • Second-Order Differential Equations
  • Euler’s Method
  • Runge–Kutta Method
  • Adams–Bashford–Moulton Method
  • Chapter 21 The Laplace Transform
  • Definition
  • Properties of Laplace Transforms
  • Functions of Other Independent Variables
  • Chapter 22 Inverse Laplace Transforms
  • Definition
  • Manipulating Denominators
  • Manipulating Numerators
  • Chapter 23 Convolutions and the Unit Step Function
  • Convolutions
  • Unit Step Function
  • Translations
  • Chapter 24 Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transforms
  • Laplace Transforms of Derivatives
  • Solutions of Differential Equations
  • Chapter 25 Solutions of Linear Systems by Laplace Transforms
  • The Method
  • Chapter 26 Solutions of Linear Differential Equations with Constant Coefficients by Matrix Methods
  • Solution of the Initial-Value Problem
  • Solution with No Initial Conditions
  • Chapter 27 Power Series Solutions of Linear Differential Equations with Variable Coefficients
  • Second-Order Equations
  • 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
  • Chapter 28 Series Solutions Near a Regular Singular Point
  • Regular Singular Points
  • Method of Frobenius
  • General Solution
  • Chapter 29 Some Classical Differential Equations
  • Classical Differential Equations
  • Polynomial Solutions and Associated Concepts
  • Chapter 30 Gamma and Bessel Functions
  • Gamma Function
  • Bessel Functions
  • Algebraic Operations on Infinite Series
  • Chapter 31 An Introduction to Partial Differential Equations
  • Introductory Concepts
  • Solutions and Solution Techniques
  • Chapter 32 Second-Order Boundary-Value Problems
  • Standard Form
  • Solutions
  • Eigenvalue Problems
  • Sturm–Liouville Problems
  • Properties of Sturm–Liouville Problems
  • Chapter 33 Eigenfunction Expansions
  • Piecewise Smooth Functions
  • Fourier Sine Series
  • Fourier Cosine Series
  • Chapter 34 An Introduction to Difference Equations
  • Introduction
  • Classifications
  • Solutions
  • Appendix A: Laplace Transforms
  • Appendix B: Some Comments about Technology
  • Introductory Remarks
  • T1-89
  • Mathematica
  • Answers to Supplementary Problems
  • Index
  • For Download