Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as “the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories. “Another definition includes mathematics inspired by physics, known as physical mathematics.
About the Book
This book is the result of two courses offered in the Department of Applied and Engineering Physics at Cornell University. The goal of these courses was to cover a number of intermediate to advanced topics in applied mathematics required by science and engineering majors. The courses were initially intended for junior-level undergraduates enrolled in the Department of Applied Physics, but over the years have expanded to include physics, chemistry, astronomy, and biophysics students as well as students from other engineering departments.
It has also been taken by upper-level fresh men and sophomores, as well as graduate students who need math reinforcement. While teaching this course, I noticed a gap in the textbooks that seemed appropriate for undergraduate students in applied physics. There are many good books on introductory calculus. One example is Calculus and Analytic Geometry by Thomas and Finney, which we consider a prerequisite for this book.
There are also a number of excellent textbooks on advanced topics in mathematical physics, such as Mathematical Methods for Physicists by Arfken. Unfortunately, these advanced books are generally aimed at graduate students and do not work well for intermediate-level undergraduates. There seemed to be no intermediate book that could help the average student transition between these two levels. Our goal was to create a book that would fill this need.
Topics covered include intermediate topics such as linear algebra, tensors, curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace transforms, differential equations, Dirac and delta functions, and solving the Laplace equation.