There are multiple ways that each of these methods can be implemented in code. In this lab, we have tried to present a clear translation of each algorithm without worrying too much about making our solutions optimal with regard to amount of memory used or total number of computations performed. Also error-checking of the inputs to each function has been left out for brevity in this document.
Numerical methods are algorithms that approximate the solution of mathematical problems that have solutions which are not conveniently expressed in analytical form (that is, functions such as exponential, sine, etc.). Most real engineering problems do not have convenient analytical solutions. The problems that you study in your engineering courses are often simplified from the real mathematical problem to demonstrate a particular physical principle or to give you a basis upon which to judge a result that you obtain using a numerical method. Perhaps the best example of a successive approximation algorithm is Newton's Method for finding the roots of a function.
If you use a numerical method to solve a mathematical problem, be extremely careful that the solution returned by the computer program is in fact a plausible solution to your problem. The adage "garbage in -- garbage out" means that if you make mistakes in using the computer to solve the problem, then the solution you obtain is likely to be erroneous. Mathematics is a language to describe these problems. Thus engineers use mathematics as a tool for understanding concepts, not an end in itself.
The problems will be made available at the time of your team lab.