The mathematical analysis is the branch of mathematics concerned with the theoretical foundations of numerical algorithms for the solution of problems arising in scientific applications. The subject addresses a variety of questions ranging from the approximation of function and integrals to the approximate solution of algebraic, transcendental, differential and integrals equations, with particular emphasis on the stability, accuracy, efficient and reliability of numerical algorithms. In this course, there is a selection of exercises; all these exercises are theoretical, students are urged to apply all the methods described in this module to some simple examples to see what happens. A few of exercises will be found to require some heavy algebraic manipulation. The main objective of this module is to help student to solve and analyse power system and renewable energy problems.