MAT7101 Applied Functional Analysis

This course aims at familiarizing the students with the basic concepts, principles, methods of functional analysis and its applications. Functional analysis plays an important role in the applied sciences as well as in mathematics itself. Functional analysis develops the tools from calculus and linear algebra further to the more general setting where one has vector spaces comprising functions or general abstract infinite-dimensional vector spaces. The basic objects studied in functional analysis are vector spaces with a notion of distance between vectors, and continuous maps between such vector spaces. This interplay between the algebraic and analytic setting gives rise to many interesting and useful results, which have a wide range of applicability to diverse mathematical problems, such as from numerical analysis, differential and integral equations, optimization and approximation theory.

Course Objectives

• To develop the basic ideas of functional analysis.
• To apply the general results to specific problems.
• To apply Functional Analysis tools in solving problems in science and other areas of mathematics.

Learning Outcomes
Upon completion of this course a students should have developed competencies in:

• Developing basic ideas of functional analysis.
• Applying general results to specific problems.
• Extending ideas of analysis and algebra covered in other earlier courses and show how they are brought together in a more general form.
• Applying functional analysis in business mathematics, fixed point theory, Computer Science etc.