# Ordinary Differential Equations

## Mathematical Tools for Physicists

• Raza Tahir-Kheli
Book

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
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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

### Introduction

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.

### Keywords

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

#### Authors and affiliations

• Raza Tahir-Kheli
• 1