Mathematics

Analysis 2

Module code: G5139
Level 4
15 credits in spring semester
Teaching method: Lecture, Workshop
Assessment modes: Coursework, Unseen examination

Analysis 2 continues directly from Analysis 1: studying functions of one variable. We will explore properties of these functions such as being continuous, differentiable and Riemann integrable.

While you may have seen some of these properties already in school, we will also give a mathematical definition of these properties. This enables us to prove theorems, which are true for all such functions.

By using mathematical arguments in these proofs, you will develop skills that will be important for your entire Mathematics degree. You will also look at many examples of functions and explore what these analytical tools can tell us about a particular function, e.g. using the derivatives of a function to get a good idea of the graph of the function, and be able to sketch it.

Module learning outcomes

• Calculate basic integrals and derivatives of functions of one real variable;
• Appreciate rigorous arguments in differential and integral calculus and be able to deploy them in solving problems in analysis;
• Understand the concepts and definitions of differentiable functions and Riemann integrable functions, provide and explain examples and counterexamples;
• Demonstrate knowledge of the definitions and the elementary properties of continuous and differentiable functions of one real variable.