A First Course in Ordinary Differential Equations: Analytical and Numerical Methods

✍ Scribed by Martin Hermann, Masoud Saravi (auth.)

• Publisher: Springer India
• Year: 2014
• Tongue: English
• Leaves: 300
• Edition: 1
• Category: Library

✦ Synopsis

This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered.
The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed that the reader has a basic grasp of elementary calculus, in particular methods of integration, and of numerical analysis. Physicists, chemists, biologists, computer scientists and engineers whose work involves solving ODEs will also find the book useful as a reference work and tool for independent study. The book has been prepared within the framework of a German–Iranian research project on mathematical methods for ODEs, which was started in early 2012.

✦ Table of Contents

Front Matter....Pages i-xiv
Basic Concepts of Differential Equations....Pages 1-9
First-Order Differential Equations....Pages 11-44
Second-Order Differential Equations....Pages 45-92
Laplace Transforms....Pages 93-118
Systems of Linear Differential Equations....Pages 119-144
Power Series Solutions....Pages 145-188
Numerical Methods for Initial Value Problems....Pages 189-240
Shooting Methods for Linear Boundary Value Problems....Pages 241-277
Back Matter....Pages 279-288

✦ Subjects

Ordinary Differential Equations; Numerical Analysis; Applications of Mathematics; Mathematical Applications in the Physical Sciences; Continuum Mechanics and Mechanics of Materials; Mathematical Physics