Mathematical Methods for Physics

The book describes mathematical tools that allow to solve partial differential equations, typical of physical problems. Another original and unique feature of this book is the emphasis on the mathematical formulation of the problems, as well as the analysis of several alternative ways to solve them.

This book presents mathematical tools to solve partial differential equations, typical of physical problems. It explains in a detailed manner the process of solving the problems that typically arise in the context of physics. Although there are a large number of textbooks on this topic, few go so deep into the topic. One of the original and unique features of this book is emphasis on the mathematical formulation of the problems, as well as the analysis of several alternative ways to solve them. Importantly, the book provides a graphical analysis of the results when appropriate. It describes a wide scope of the problems, with detailed solutions and the methods involved, ranging from cases in one to three dimensions, from Cartesian to polar, cylindrical, and spherical coordinates and includes properties and applications of the Fourier transform to solve partial differential equations.

Autorentext

Farkhad G. Aliev is Echegaray Professor of Condensed Matter Physics at Universidad Autónoma de Madrid (UAM), Spain. He conducted research as a scientist at Lomonosov Moscow State University (19841995) and was a visiting professor and a senior researcher at UAM (19901995) and at Katholieke Universiteit Leuven (19951998). He leads the MAGNETRANS group at UAM, which focuses on dynamics in magnetic and superconducting nanostructures. He has been teaching a course on Mathematical Methods for Physics at UAM for several years.

Antonio Lara obtained his PhD in Condensed Matter Physics at the MAGNETRANS group (UAM) in 2017, under the super vision of Prof. Farkhad G. Aliev. During his doctoral studies, his research focused on magnetic dynamics, as well as superconducting vortex dynamics in hybrid magnetic/ superconducting systems at the nanoscale. He has taught problem-solving lessons on Mathematical Methods for Physics at UAM for several years. He has been awarded several prizes for young researchers at international conferences of Solid State Physics.

Inhalt

1. Harmonic Oscillator and Green's Function

2. Problems in One Dimension

3. Bidimensional Problems

4. Three-Dimensional Problems

5. Problems in Polar Coordinates

6. Problems in Cylindrical Coordinates

7. Problems in Spherical Coordinates

8. Fourier Transform and Its Applications