# MA139-15 Analysis 2

Department
Warwick Mathematics Institute
Level
Keith Ball
Credit value
15
Module duration
10 weeks
Assessment
Multiple
Study location
University of Warwick main campus, Coventry

##### Introductory description

Mathematical Analysis is the heart of modern Mathematics. This module is the second in a series of modules where the subject of Analysis is rigorously developed.

##### Module aims

The principal aim is to develop Analysis in dimension 1, with much greater precision and rigour than the students had at school. While the high-school Analysis is focusing on problem solving methods, the university-level Analysis is switching the focus to the mathematical concepts and clarity of thought.

##### Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

• Differentiability
• Higher order derivatives
• Taylor's Theorem
• Taylor's Series
• Riemann Integration
• Fundamental Theorem of Calculus
• Improper integrals
##### Learning outcomes

By the end of the module, students should be able to:

• learn differentiability, including higher derivatives and properties of differentiable functions
• develop the working knowledge of Taylor's series and theorem, ultimately understanding representability of a function by a power series
• develop a good working knowledge of the construction of the Riemann integral
• understand and apply the fundamental properties of the integral such as integrability of continuous functions on bounded intervals or the Fundamental Theorem of Calculus

M. Hart, Guide to Analysis, Macmillan.
M. Spivak, Calculus, Benjamin. R.G Bartle and D.R Sherbert, Introduction to Real Analysis (4th Edition), Wiley (2011)
L. Alcock, How to think about Analysis, Oxford University Press (2014)

##### Subject specific skills

Analysis gives first-year undergraduates a first excursion in to pure mathematics. The students will gain a new perspective and a deeper understanding of familiar mathematics which they have seen in school (e.g. real numbers, functions and differentiation). In Analysis, these concepts are developed with mathematical rigour, which characterises much of university mathematics to follow.

##### Transferable skills

Students will acquire key reasoning and problem solving skills, empower them to address new problems with confidence.

## Study time

Type Required
Lectures 30 sessions of 1 hour (33%)
Online learning (independent) 9 sessions of 1 hour (10%)
Private study 52 hours (57%)
Total 91 hours
##### Private study description

Working on assignments, going over lecture notes, text books, exam revision.

## Costs

No further costs have been identified for this module.

You do not need to pass all assessment components to pass the module.

Students can register for this module without taking any assessment.

##### Assessment group D
Weighting Study time
Assignments 15% 20 hours
In-person Examination 85% 39 hours
##### Assessment group R
Weighting Study time
In-person Examination - Resit 100%
##### Feedback on assessment

Marked homework (both assessed and formative) is returned and discussed in smaller classes. Exam feedback is given.

## Courses

This module is Core for:

• Year 1 of UMAA-G105 Undergraduate Master of Mathematics (with Intercalated Year)
• Year 1 of G100 Mathematics
• Year 1 of G100 Mathematics
• Year 1 of G100 Mathematics
• Year 1 of G100 Mathematics
• Year 1 of G103 Mathematics (MMath)
• Year 1 of G103 Mathematics (MMath)
• Year 1 of UMAA-G106 Undergraduate Mathematics (MMath) with Study in Europe
• Year 1 of UMAA-G1N2 Undergraduate Mathematics and Business Studies (with Intercalated Year)
• Year 1 of UMAA-GL11 Undergraduate Mathematics and Economics
• Year 1 of UECA-GL12 Undergraduate Mathematics and Economics (with Intercalated Year)
• Year 1 of UMAA-G101 Undergraduate Mathematics with Intercalated Year