Course Summary
This course provides essential mathematical background for many subsequent courses in modern applied mathematics, pure mathematics, numerical analysis, statistics and operations research. Its aim is two fold. Firstly, it develops the foundation of mathematical analysis of functions of real variable in a rigorous manner, demonstrating how these ideas extend to many unfamiliar contexts and then extends the analysis of real functions of one variable to the analysis of functions of two or more real variables in a systematic manner. Secondly it provides sufficient background in the analysis of functions of a complex variable for you to study advanced engineering mathematics or aspects of probability theory. You will also become more familiar and comfortable with the language of abstract formalism and proof techniques that are present in all modern texts on analysis and its applications.