# MA244 - Analysis III

**Module code:**MA244**Module name:**Analysis III**Department:**Mathematics Institute**Credit:**12

Content and teaching | Assessment | Availability

## Module content and teaching

###### Principal aims

The aims of the module are: 1. To develop a good working knowledge of the construction of the integral of regulated functions; 2. to study the continuity, differentiability and integral of the limit of a uniformly convergent sequence of functions; 3. to use the concept of norm in a vector space to discuss convergence and continuity there.

###### Principal learning outcomes

At the end of this module you should be able to: 1. Understand the need for a rigorous theory of integration, and that this can be developed for regulated functions by approximating the area under the graph by rectangles; 2. understand uniform and pointwise convergence of functions together with properties of the limit function; 3. be able to prove the main results of integration: any continuous function can be integrated on a bounded interval and the Fundamental Theorem of Calculus; 4. prove and apply the Contraction Mapping Theorem.

###### Departmental link

http://go.warwick.ac.uk/MA244/

###### Other essential notes

Prerequisites: MA131 Analysis, MA106 Linear Algebra.

## Module assessment

Assessment group | Assessment name | Percentage |
---|---|---|

12 CATS (Module code: MA244-12) | ||

D (Assessed/examined work) | Weekly assignments | 15% |

3 hour examination (April) | 85% | |

D1 (Assessed/examined work) | Weekly Assignments (G100 &G103 only) | 15% |

3 hour examination (April) (Overflow paper) | 85% |

## Module availability

This module is available on the following courses:

###### Core

- Undergraduate Mathematics (BSc) (G100) - Year 2
- Undergraduate Mathematics with Intercalated Year (G101) - Year 2
- Undergraduate Mathematics (MMath) (G103) - Year 2
- Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 2
- Undergraduate Mathematics (MMath) with Study in Europe (G106) - Year 2
- Undergraduate Mathematics and Business Studies (with Intercalated Year) (G1N2) - Year 2
- Undergraduate Mathematics and Business Studies (G1NC) - Year 2
- Undergraduate Mathematics and Economics (GL11) - Year 2
- Undergraduate Mathematics and Economics (with Intercalated Year) (GL12) - Year 2
- Undergraduate Mathematics and Philosophy with Specialism in Logic and Foundations (GV19) - Year 2

###### Optional Core

- Undergraduate Mathematics and Philosophy (GV17) - Year 2
- Undergraduate Mathematics and Philosophy with Intercalated Year (GV18) - Year 2

###### Optional

- Postgraduate Taught Mathematics (Diploma plus MSc) (G1PC) - Year 2
- Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc) (G1PD) - Year 2
- Undergraduate Discrete Mathematics (G4G1) - Year 2
- Undergraduate Discrete Mathematics (G4G3) - Year 2