Mathematics in physics and technics. An introduction with 572 problems and solutions. (Q1310304)

This book assumes that the reader is already familiar with advanced mathematical topics such as differential and integral calculus, vector calculus, ordinary and partial differential equations, integral equations, and probability and statistics. The goal of the book is to illustrate with examples and exercises how to find mathematical formulations of physical and technical problems. Many exercises are taken from classical physics and the reader is expected to have considerable knowledge of all areas of physics. The mathematical topics are not elementary: on page 19 the authors introduce Padé approximations; Stirling's formula for the Gamma function is used in an example on page 20, and the Riemann Zeta function appears in an exercises on page 21. There are 572 exercises from many areas of applied mathematics, physics, and engineering. Solutions are provided in a 50 page long appendix. Each section starts with a brief introduction of theory, covering equations and formulas that are needed to solve the exercises. There are few proofs but plenty of references to the mathematical literature where the topics can be studied in more depth. Each section ends with a collection of problems of various degrees of difficulty. None of them are of the ``plug these values into the formula'' variety. Two examples; (1) A copper wire of \(1mm\) thickness is carrying a current of \(20A\) A cross-wind in blowing on the wire with a velocity of \(5m/s\). On average, how much warmer than the oncoming air is the surface of the wire? (2) In a slow steady rain, 10 water droplets per \(m^ 2\) and per second are hitting the ground. What is the probability that an area of \(10cm^ 2\) is still completely dry 5 minutes after it started to rain? In solving the problems in the book the reader has to learn to sometimes accept incomplete descriptions of problems, and to sometimes neglect unimportant circumstances in constructing mathematical models.