Studies in Theoretical Physics, Volume 1:Fundamental mathematical methods is the first of the six-volume series in theoretical physics. It provides the mathematical methods that any physical sciences and engineering undergraduate might need in upper-division courses in classical mechanics, quantum mechanics, and electricity and magnetism. It is a book designed for a two-semester course in Mathematical Methods. The first eight chapters introduce series and sequences, complex numbers, functions and series, vectors, matrices and determinants, and differential and integral calculus of scalar and vector functions, suitable for the first semester of a two-semester sequence. The last eight chapters introduce the calculus of variations, linear algebra, power series substitution method for solving differential equations, partial differential equations, contour integrals, Laplace transforms, Fourier series, and Fourier transforms, suitable for the second semester. Unlike other books, this book has a section at the end of each chapter that focuses on solving problems using Mathematica.

Key Features

All selected topics provide the mathematical methods students would need in Classical Mechanics, Electricity and Magnetism, and Quantum Mechanics at the undergraduate level.
Modern 3D graphics are extensively used for 3D visualization and a better understanding of the topics covered and the example problems used.
Examples are selected to cover the applications in the subsequent volumes of Studies in Theoretical Physics.
Topics covered in sixteen chapters are intended for a two-semester sequence of undergraduate courses in Mathematical Methods. Each chapter also introduces Mathematica to the topics covered by re-solving most of the example problems considered in each chapter. Discussions are clear, brief, concise, and use simple English easy to understand by readers with English as a second language. The authors of this book have years of experience teaching many introductory and upper-division physics courses.