A First Course in Ordinary Differential Equations

Analytical and Numerical Methods

  • Martin Hermann
  • Masoud Saravi

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Martin Hermann, Masoud Saravi
    Pages 1-9
  3. Martin Hermann, Masoud Saravi
    Pages 11-44
  4. Martin Hermann, Masoud Saravi
    Pages 45-92
  5. Martin Hermann, Masoud Saravi
    Pages 93-118
  6. Martin Hermann, Masoud Saravi
    Pages 119-144
  7. Martin Hermann, Masoud Saravi
    Pages 145-188
  8. Martin Hermann, Masoud Saravi
    Pages 189-240
  9. Martin Hermann, Masoud Saravi
    Pages 241-277
  10. Back Matter
    Pages 279-288

About this book


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.


Differential Equations Numerical Differential Equations Ordinary Differential Equations Runge-Kutta Methods Shooting Methods

Authors and affiliations

  • Martin Hermann
    • 1
  • Masoud Saravi
    • 2
  1. 1.Institute of Applied MathematicsFriedrich Schiller UniversityJenaGermany
  2. 2.Department of Mathematics Nour BranchIslamic Azad UniversityNourIran

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