Chapter Two: Tools for Analysis

A theoretical investigation may get initiated by following the hints from the experimental observations, physical considerations or both. To arrive at a conclusion and to ensure its correctness, however, a theoretical undertaking nowadays may require both numerical and analytical computations. The compact analytical formulae have the advantages of clarity, insight, and convenience, while the numerical analysis provides the ultimate solution and the vivid graphical visualization. MATLAB offers the symbolic computation and reduces the overhead in programming and consequently, the time to get the answer, and the effort to visualize the result. This is useful at the beginning of a scientific endeavor when the problem may not be well defined, and quick answers on a few conjectures are desired. After the problem gets mathematically formulated and well defined, and an efficient code is geared toward production phase or even commercial application, C++ or its variants of internet ready programming languages such as Java, PhP, or Python is the recommended choice. Here, we start by introducing MATLAB for use in computer programming.