Ordinary Differential Equations , 1st ed. 2018
Mathematical Tools for Physicists

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.     

1. Ordinary Differential Equations: Theory and Practice.

2. The Runge-Kutta approximation: Linear Ordinary Differential Equation

3. Bernouilli Equation: Ordinary Differential Equation

4. Clairaut Equation: Ordinary Differential Equation

5. Lagrange Equation: Ordinary Differential Equation

6. Euler Equation: Ordinary Differential Equation

7. Method of Undetermined Coefficients: Linear Ordinary Differential Equation

8. Exact and Inexact  Differential Equations

9. Factorable Differential Equations

10. Order Reduction of Differential Equations

11. Under-Damped Anharmonic Motion

12. Critically Damped Anharmonic Motion

13. Over Damped Anharmonic Motion

14. Electric Current  and Charge transfer in finite and infinite arrays of Resistors

16. Electric Current and Charge transfer in finite and infinite arrays of Capacitors

17. Finite and Infinite arrays of Conductors, Inductors and Capacitors

18. Frobenius Solution

19. Bessels Equations

20. Numerical Solution 

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)

(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:

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  

Teaches differential equations in a comprehensive way to help both students and teachers of of physics, chemistry and engineering

Covers many physics- and engineering-related mathematical problems

Provides a large numbers of appropriate problems and worked out solutions