Mathematical Method in Physics Darterrius Sims
- ISBN: 9781788820639
- Edition: 1st
- ©Year: 2020
- List Price : 150
About the Book
Mathematical Physics is a significant discipline, concerned with the interface of mathematics and physics. There are several distinct branches of Mathematical Physics and these roughly corresponded to particular historical periods. Mathematics and physics have interacted fruitfully for centuries. Physics has been a constant source of interesting mathematical problems, and these problems have often required new mathematics for their solution. Conversely, advances in mathematics have found surprising and impressive applications in physics. Mathematics may be considered as a logical relationship language developed upon the concept/definition of one. From this one, we can logically define two, three, etc. which we call numbers. Hencea number is some relationship to one. Once we have whole numbers then we can define add, subtract, multiply and divide. Fractions, squares, cubes, etc, all became possible, as moreand more complexly defined relationships between numbers evolved. Ordinary differential equations are equations to be solved in which the unknown element is a function, rather than a number, and in which the known information relates that function to its derivatives. Few such equations admit an explicit answer, but there is a wealth of qualitative information describing the solutions and their dependence on the defining equation. There are many important classes of differential equations for which detailed information is available. Fourier series are used extensively in engineering, especially for processing images and other signals. Finding the coefficients of a Fourier series is the same as doing a spectral analysis of a function. The Fourier series is a mathematical tool used for analyzing an arbitrary periodic function by decomposing it into a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short. This book is intended partly to serve as a textbook cum reference for the course Engineering Physics taught at the undergraduate level in engineering colleges all over the country. The other purpose of the book is to serve as a reference bookfor research workers in theoretical physics and signal processing.
Contents: 1. Introduction, 2. VectorandTensor Analysis, 3. Ordinary Differential Equations, 4. Matrix Algebra, 5. Fourier Series and Integrals, 6. Linear Vector Spaces, 7. Functions of Complex Variable, 8. The Calculus of Variations, 9.The LaplaceTransformation, 10. Partial Differential Equations.
Darterrius Sims read Mathematics at St John's College and proceeded to a Ph.D. there in theoretical and experimental nuclear physics. Fie was involved in the experimental discovery of a number of the early baryonic resonances. Flaving been Senior Tutor at Clare College, where he has taught physics and mathematics for nearly forty years, he has served on many committees concerned with teaching and examining of these subjects at all levels of tertiary and undergraduate education. Fie is also one of the authors of 200 Puzzling Physics Problems. Darterrius Sims became a Research Associate with a special interest in star-formation processes and the structure of star-forming regions. In particular his research has concentrated on the physics of jets and outflows from young stars. Fie has considerable experience of teaching mathematics and physics to undergraduate and pre-university students.