Schaum's Outline of Differential Equations, Fifth Edition /

Schaum's Outline of Differential Equations, Fifth Edition is the go-to study guide for all students of science who need to learn or refresh their knowledge of differential equations. With an outline format that facilitates quick and easy review and mirrors your course in scope and sequence, thi...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Bronson, Richard (Autor), Costa, Gabriel B. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, N.Y. : McGraw Hill LLC, [2022]
Edición:Fifth edition.
Temas:
Differential equations > Outlines, syllabi, etc.
Differential equations > Problems, exercises, etc.
Differential equations.
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title Page
  • Copyright Page
  • Dedication
  • 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 eAt
  • Definition
  • Computation of eAt
  • Chapter 17 Reduction of Linear Differential Equations to a System of First-Order Equations
  • An Example
  • Reduction of an nth 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
  • Chapter 35 Solving Differential Equations Using Mathematica
  • Introduction
  • Chapter 36 Solving Systems of Differential Equations via Eigenvalues Using Mathematica
  • Introduction
  • Terminology
  • Chapter 37 Qualitative Methods
  • Introduction
  • Terminology
  • Chapter 38 Euler?s Method Using Microsoft Excel?
  • The Method
  • Chapter 39 Some Interesting Modeling Problems
  • Examples
  • APPENDIX Laplace Transforms
  • ANSWERS TO SUPPLEMENTARY PROBLEMS
  • INDEX.

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