MA244 - Analysis III

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

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.

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) Assignments 15%
2 hour examination (April) 85%
D1 (Assessed/examined work) Assignments (G100 &G103 only) 15%
2 hour examination (April) (Overflow paper) 85%

Module availability

This module is available on the following courses:

Core
• Undergraduate Mathematics and Physics (MMathPhys) (FG31) - Year 2
• 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 Physics (BSc) (GF13) - Year 2
• Undergraduate Mathematics and Economics (GL11) - Year 2
• Undergraduate Mathematics and Economics (with Intercalated Year) (GL12) - Year 2
• Undergraduate Mathematics and Philosophy (GV17) - Year 2
• Undergraduate Mathematics and Philosophy with Specialism in Logic and Foundations (GV19) - Year 2
Optional Core
• Undergraduate Mathematics and Philosophy with Intercalated Year (GV18) - Year 2
Optional
• Postgraduate Taught Mathematics (Diploma plus MSc) (G1PC) - Year 1
• Postgraduate Taught Mathematics (Diploma plus MSc) (G1PC) - Year 2
• Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc) (G1PD) - Year 1
• Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc) (G1PD) - Year 2
• Undergraduate Discrete Mathematics (G4G1) - Year 2
• Undergraduate Discrete Mathematics (G4G3) - Year 2