Ordinary differential equations : mathematical tools for physicists
著者
書誌事項
Ordinary differential equations : mathematical tools for physicists
Springer, c2018
大学図書館所蔵 全2件
注記
Includes bibliographical references (p. 407-408)
内容説明・目次
内容説明
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.
目次
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
15. Electric Current and Charge transfer in finite and infinite arrays of Inductors
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
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