Ordinary Differential Equations

Detalles Bibliográficos
Autor principal: Greenberg, Michael D.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2012.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title Page
  • Copyright
  • Contents
  • Preface
  • 1 First-Order Differential Equations
  • 1.1 Motivation And Overview
  • 1.1.1 Introduction
  • 1.1.2 Modeling
  • 1.1.3 The order of a differential equation
  • 1.1.4 Linear and nonlinear equations
  • 1.1.5 Ourplan
  • 1.1.6 Direction field
  • 1.1.7 Computer software
  • 1.2 Linear First-Order Equations
  • 1.2.1 The simplest case
  • 1.2.2 The homogeneous equation
  • 1.2.3 Solving the full equation by the integrating factor method
  • 1.2.4 Existence and uniqueness for the linear equation
  • 1.3 Applications Of Linear First-Order Equations
  • 1.3.1 Population dynamics
  • exponential model
  • 1.3.2 Radioactive decay
  • carbon dating
  • 1.3.3 Mixing problems
  • a one-compartment model
  • 1.3.4 The phase line, equilibrium points, and stability
  • 1.3.5 Electrical circuits
  • 1.4 Nonlinear First-Order Equations That Are Separable
  • 1.5 Existence And Uniqueness
  • 1.5.1 An existence and uniqueness theorem
  • 1.5.2 Illustrating the theorem
  • 1.5.3 Application to free fall
  • physical significance of nonuniqueness
  • 1.6 Applications Of Nonlinear First-Order Equations
  • 1.6.1 The logistic model of population dynamics
  • 1.6.2 Stability of equilibrium points and linearized stability analysis
  • 1.7 Exact Equations And Equations That Can Be Made Exact
  • 1.7.1 Exact differential equations
  • 1.7.2 Making an equation exact
  • integrating factors
  • 1.8 Solution By Substitution
  • 1.8.1 Bernoulli's equation
  • 1.8.2 Homogeneous equations
  • 1.9 Numerical Solution By Euler's Method
  • 1.9.1 Euler's method
  • 1.9.2 Convergence of Euler's method
  • 1.9.3 Higher-order methods
  • Chapter 1 Review
  • 2 Higher-Order Linear Equations
  • 2.1 Linear Differential Equations Of Second Order
  • 2.1.1 Introduction
  • 2.1.2 Operator notation and linear differential operators
  • 2.1.3 Superposition principle
  • 2.2 Constant-Coefficient Equations
  • 2.2.1 Constant coefficients
  • 2.2.2 Seeking a general solution
  • 2.2.3 Initial value problem
  • 2.3 Complex Roots
  • 2.3.1 Complex exponential function
  • 2.3.2 Complex characteristic roots
  • 2.4 Linear Independence
  • Existence, Uniqueness, General Solution
  • 2.4.1 Linear dependence and linear independence
  • 2.4.2 Existence, uniqueness, and general solution
  • 2.4.3 Abel's formula and Wronskian test for linear independence
  • 2.4.4 Building a solution method on these results
  • 2.5 Reduction Of Order
  • 2.5.1 Deriving the formula
  • 2.5.2 The method rather than the formula
  • 2.5.3 About the method of reduction of order
  • 2.6 Cauchy-Euler Equations
  • 2.6.1 General solution
  • 2.6.2 Repeated roots and reduction of order
  • 2.6.3 Complex roots
  • 2.7 The General Theory For Higher-Order Equations
  • 2.7.1 Theorems for nth-order linear equations
  • 2.7.2 Constant-coefficient equations
  • 2.7.3 Cauchy-Euler equations
  • 2.8 Nonhomogeneous Equations
  • 2.8.1 General solution

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