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Ordinary differential equations an introduction to the fundamentals

Ordinary Differential Equations: An Introduction to the Fundamentals is a rigorous yet remarkably accessible textbook ideal for an introductory course in ordinary differential equations.

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Bibliographic Details
Main Author: Howell, Kenneth B. (Author)
Format: Book
Language:English
Published: Boca Raton CRC Press, Taylor & Francis Group [2016]
Series:Textbooks in mathematics
Subjects:
Differential equations
Mathematics
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Table of Contents:
  • I. The Basics
  • The starting point: basic concepts and terminology
  • Integration and differential equations
  • II. First-Order Equations
  • Some basics about first-order equations
  • Separable first-order equations
  • Linear first-order equations
  • Simplifying through substitution
  • The exact form and general integrating factors
  • Slope fields: graphing solutions without the solutions
  • Euler's numerical method
  • The art and science of modeling with first-order equations
  • III. Second- and Higher-Order Equations
  • Higher-order equations: extending first-order concepts
  • Higher-order linear equations and the reduction of order method
  • General solutions to homegeneous linear differential equations
  • Verifying the big theorems and an introduction to differential operators
  • Second-order homogeneous linear equations with constant coeffieients
  • Springs: Part I
  • Arbitrary homogeneous linear equations with constant coefficients
  • Eyler equations
  • Nonhomogeneous equations in general
  • Method of undetermined coefficients (aka: method of educated guess)
  • Springs: Part II
  • Variation of parameters (a better reduction of order method)
  • IV. The Laplace Transform
  • The Laplace transform (intro)
  • Differentiation and the Laplace transform
  • The Inverse Laplace transform
  • Convolution
  • Piecewise-defined functions and periodic functions
  • Delat functions
  • V. Power Series and Modified Power Series Solutions
  • Series solutions: preliminaries
  • Power series solutions I: basic computational methods
  • Power series solutions II: generalizations and theory
  • Modified power series solutions and the basic method of Frobenius
  • The big theorem on the Frobenius method, with applications
  • Validating the method of Frobenius
  • VI. Systems of Differential Equations (A Brief Introduction)
  • Systems of differential equations: a starting point
  • Critical points, direction fields and trajectories.

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