Transform Techniques in Physics
Some of the most powerful tools for solving problems in physics are transform methods. The idea is that one can transform the problem at hand to a new problem in a different space, hoping that the problem in the new space is easier to solve. A more familiar example in physics comes from quantum mechanics. Similar transform constructions occur for many other type of problems. The chapter deals with a study of Laplace transforms, which are useful in the study of initial value problems, particularly for linear ordinary differential equations with constant coefficients. It explains the study of Fourier transforms. These will provide an integral representation of functions defined on the real line. The chapter looks at the convolution operation and its Fourier transform. The integral/sum of the square of a function is the integral/sum of the square of the transform.