Ordinary Differential Equations
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Ordinary Differential Equations: An Introduction to the Fundamentals(Textbooks in Mathematics)

Ordinary Differential Equations: An Introduction to the Fundamentals(Textbooks in Mathematics)


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About the Book

Ordinary Differential Equations: An Introduction to the Fundamentals is a rigorous yet remarkably accessible textbook ideal for an introductory course in ordinary differential equations. Providing a useful resource both in and out of the classroom, the text: Employs a unique expository style that explains the how and why of each topic covered Allows for a flexible presentation based on instructor preference and student ability Supports all claims with clear and solid proofs Includes material rarely found in introductory texts Ordinary Differential Equations: An Introduction to the Fundamentals also includes access to an author-maintained website featuring detailed solutions and a wealth of bonus material. Use of a math software package that can do symbolic calculations, graphing, and so forth, such as Maple™ or Mathematica®, is highly recommended, but not required.

Table of Contents:
The Starting Point: Basic Concepts and Terminology. Integration and Differential 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. Higher-Order Equations: Extending First-Order Concepts. Higher-Order Linear Equations and the Reduction of Order Method. General Solutions to Homogeneous Linear Differential Equations. Verifying the Big Theorems and an Introduction to Differential Operators. Second-Order Homogeneous Linear Equations with Constant Coefficients. Springs: Part I. Arbitrary Homogeneous Linear Equations with Constant Coefficients. Euler 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). The Laplace Transform (Intro). Differentiation and the Laplace Transform. The Inverse Laplace Transform. Convolution. Piecewise-Defined Functions and Periodic Functions. Delta Functions. 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. Systems of Differential Equations: A Starting Point. Critical Points, Direction Fields and Trajectories. Appendix: Author’s Guide to Using This Text. Answers to Selected Exercises.

About the Author :
Kenneth B. Howell earned bachelor degrees in both mathematics and physics from Rose-Hulman Institute of Technology, and master’s and doctoral degrees in mathematics from Indiana University. For more than thirty years, he was a professor in the Department of Mathematical Sciences of the University of Alabama in Huntsville (retiring in 2014). During his academic career, Dr. Howell published numerous research articles in applied and theoretical mathematics in prestigious journals, served as a consulting research scientist for various companies and federal agencies in the space and defense industries, and received awards from the College and University for outstanding teaching. He is also the author of Principles of Fourier Analysis (Chapman & Hall/CRC, 2001).


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Product Details
  • ISBN-13: 9781498734219
  • Publisher: Taylor & Francis Ltd
  • Publisher Imprint: CRC Press
  • Language: English
  • Sub Title: An Introduction to the Fundamentals
  • ISBN-10: 1498734219
  • Publisher Date: 07 Dec 2018
  • Binding: Digital (delivered electronically)
  • Series Title: Textbooks in Mathematics


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Ordinary Differential Equations: An Introduction to the Fundamentals(Textbooks in Mathematics)
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Ordinary Differential Equations: An Introduction to the Fundamentals(Textbooks in Mathematics)
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