© 2018

Ordinary Differential Equations

Mathematical Tools for Physicists


Table of contents

  1. Front Matter
    Pages i-xxii
  2. Raza Tahir-Kheli
    Pages 1-4
  3. Raza Tahir-Kheli
    Pages 5-12
  4. Raza Tahir-Kheli
    Pages 13-58
  5. Raza Tahir-Kheli
    Pages 59-73
  6. Raza Tahir-Kheli
    Pages 75-118
  7. Raza Tahir-Kheli
    Pages 119-194
  8. Raza Tahir-Kheli
    Pages 195-226
  9. Raza Tahir-Kheli
    Pages 227-255
  10. Raza Tahir-Kheli
    Pages 257-301
  11. Raza Tahir-Kheli
    Pages 303-316
  12. Raza Tahir-Kheli
    Pages 317-381
  13. Raza Tahir-Kheli
    Pages 383-401
  14. Raza Tahir-Kheli
    Pages 403-406
  15. Back Matter
    Pages 407-408

About this book


This textbook describes rules and procedures for the use of Differential Operators (DO) in Ordinary Differential Equations (ODE ). The book provides a detailed theoretical and numerical description of ODE. It presents a large variety of ODE and the chosen groups are used to solve a host of physical problems. Solving these problems is of interest primarily to students of science, such as physics, engineering, biology and chemistry. 

Scientists are greatly assisted by using the DO obeying several simple algebraic rules. The book describes these rules and, to help the reader, the vocabulary and the definitions used throughout the text are provided. A thorough description of the relatively straightforward methodology for solving ODE is given. The book provides solutions to a large number of associated problems. ODE that are integrable, or those that have one of the two variables missing in any explicit form are also treated with solved problems. The physics and applicable mathematics are explained and many associated problems are analyzed and solved in detail. Numerical solutions are analyzed and the level of exactness obtained under various approximations is discussed in detail.    


Theory and Practice of Ordinary Differential Equations Runge-Kutta Approximation Bernouilli Equation Clairaut Equation Lagrange Equation Euler Equation

Authors and affiliations

  1. 1.Department of PhysicsTemple UniversityPhiladelphiaUSA

About the authors

Raza A. Tahir-Kheli studied physics at Islamia College, Peshawar (Pakistan) before joining, in October 1955, Oriel College, University of Oxford. He completed the degrees of Master of Arts and Doctor of Philosophy in 1962.

His employment was:

 (1) Junior Demonstrator, Oxford University  October (1958) to  June (1960)

(2) Research Associate-Teaching, University of Pennsylvania, Department of Physics, (1962) to (1964).

(3) Atomic Energy Commission, Pakistan . (1964) to (1966)

(4) Temple University, Philadelphia  PA 19122. USA:

Assistant Professor of Physics, (1966)-(1968)

Associate Professor of Physics, (1968)-(1971)

Professor of Physics, (1971) to July, (2011)

Professor Emeritus (2011)

His other employments including sabbaticals were:

Royal Society Visiting Professor, Department of Theoretical Physics, University of Oxford (1982)

Two sabbaticals, at the Dept. of Theoretical Physics, University of Oxford

Professeur de Echange, Centre Scientifique, d'Orsay, France

Sabbatical at Department of Physics, University of California, at Santa Barbara.

Visiting Professor, Institut Laue -Langevin, Grenoble ,France

Sabbatical at Max-Planck Institut fuer Physik  

Bibliographic information

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