ENGLISH

Ordinary Differential Equations: Mathematical Tools for Physicists

By Raza Tahir-Kheli

Book information

Publisher
Springer International Publishing
Year
2018
ISBN
978-3-319-76405-4, 978-3-319-76406-1
Language
english
Format
PDF
Filesize
5 MB (5624343 bytes)
Edition
1st ed.
Pages
XXII, 408\423
Time added
2019-03-20 04:02:07
Physics; Mathematical Methods in Physics; Ordinary

Description

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. Front Matter ....Pages i-xxii Differential Operator (Raza Tahir-Kheli)....Pages 1-4 Some Definitions (Raza Tahir-Kheli)....Pages 5-12 Constant Coefficients (Raza Tahir-Kheli)....Pages 13-58 Variable Coefficients (Raza Tahir-Kheli)....Pages 59-73 Green’s Function Laplace Transforms (Raza Tahir-Kheli)....Pages 75-118 Special Types of Differential Equations (Raza Tahir-Kheli)....Pages 119-194 Special Situations (Raza Tahir-Kheli)....Pages 195-226 Oscillatory Motion (Raza Tahir-Kheli)....Pages 227-255 Resistors, Inductors, Capacitors (Raza Tahir-Kheli)....Pages 257-301 Numerical Solution (Raza Tahir-Kheli)....Pages 303-316 Frobenius Solution (Raza Tahir-Kheli)....Pages 317-381 Answer to Assigned Problems (Raza Tahir-Kheli)....Pages 383-401 Answer to Additional Assigned Problems (Raza Tahir-Kheli)....Pages 403-406 Back Matter ....Pages 407-408

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