2013/14 Undergraduate Module Catalogue

MATH2016 Analysis

15 creditsClass Size: 200

Module manager: Dr Kevin Houston
Email: K.Houston@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2013/14

Pre-requisite qualifications

(MATH1010 and taken MATH1026) or (MATH1050 and MATH1055) or equivalent

This module is mutually exclusive with

MATH2015	Analysis 2
MATH2090	Real and Complex Analysis

This module is approved as an Elective

Module summary

This module aims to develop the ideas of continuity, differentiability and integrability and in particular show how they can be extended to complex valued functions. It will develop students' ability to appreciate the importance of proofs, and to understand and write them.

Objectives

On completion of this module, students should be able to:
a) use the epsilon-delta formulation to show that a function is continuous;
b) calculate upper and lower Riemann sums;
c) apply convergence tests to series of real and complex numbers and evaluate the radius of convergence of power series;
d) use the Cauchy-Riemann equations to decide where a given function is analytic;
e) compute standard contour integrals using the fundamental theorem of the calculus, Cauchy's theorem or Cauchy's integral formula;
f) classify the singularities of analytic functions and to compute, in the case of a pole, its order and residue;
g) evaluate typical definite integrals by using the calculus of residues.

Syllabus

1. Epsilon-delta definition of continuity for a function of a real variable.
2. Riemann integration for real valued functions. Formal properties of the integral. The Fundamental Theorem of the Calculus.
3. Basic ideas of complex function theory. Limits, continuity, analytic functions, Cauchy-Riemann equations.
4. Contour integrals. Cauchy's theorem, Cauchy's integral formula.
5. Power series. Analytic functions represented as Taylor or Laurent series. Singularities. Orders of poles, Cauchy's residue theorem, evaluation of definite integrals.

Teaching methods

Delivery type	Number	Length hours	Student hours
Workshop	10	1.00	10.00
Lecture	33	1.00	33.00
Private study hours			107.00
Total Contact hours			43.00
Total hours (100hr per 10 credits)			150.00

Private study

Studying notes between lectures: 53 hours
Doing problems: 40 hours
Exam preparation: 14 hours

Opportunities for Formative Feedback

Regular problems sheets

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
Written Work	*	15.00
Total percentage (Assessment Coursework)		15.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 30 mins	85.00
Total percentage (Assessment Exams)		85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 13/02/2014

Disclaimer

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