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Programme & Unit Catalogues

## MA20219: Analysis 2B

Academic Year: 2015/6
Owning Department/School: Department of Mathematical Sciences
Credits: 6
Level: Intermediate (FHEQ level 5)
Period: Semester 2
Assessment Summary: EX 100%
Assessment Detail:
• Examination (EX 100%)
Supplementary Assessment: MA20219 Mandatory extra work (where allowed by programme regulations)
Requisites: Before taking this module you must take MA10207 AND take MA10209 AND take MA10210 AND take MA20218
Description: Aims:
To complete the rigorous theory of elementary multivariate calculus begun in Analysis 2A. To illustrate the geometrical meaning and potential applications of the main results through examples.

Learning Outcomes:
After taking this unit, students should be able to:
* state definitions and theorems in real analysis and present proofs of the main theorems
* construct their own proofs of simple unseen results and construct proofs of simple propositions
* Present mathematical arguments in a precise, lucid and grammatical fashion.
* Apply definitions and theorems to simple examples.
* Apply mathematics rigorously to problems from geometry and physics.
* Give a geometrical and physical interpretation of multivariate calculus.

Skills:
Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F (in tutorials).

Content:
Vector fields: div, curl, grad. Del operator, second order derivatives.
Line integrals: arc length, work integrals, conservative vector fields; criteria for the existence of a potential.
Multiple Riemann integration: criteria for integrability, exchanging the order of integration (Fubini), volume integrals for semi-convex domains, statement (without proof) of the change of variables formula, Cartesian, polar and cylindrical coordinates for the change of variables formula.
Parametrised surfaces: surface area, surface integrals, change of variables for surface integrals, surface integrals independent of parametrisation.
Divergence theorem for semi-convex domains in R3, Green's theorem, oriented surfaces, Stokes' theorem, geometric interpretation of div, curl and grad, Green's identities.
Programme availability:

#### MA20219 is Compulsory on the following programmes:

Department of Computer Science
• USCM-AFB20 : BSc(Hons) Computer Science and Mathematics (Year 2)
• USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 2)
• USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 2)
• USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 2)
• USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 2)
• USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 2)
Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 2)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 2)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 2)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 2)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 2)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 2)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 2)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 2)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 2)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 2)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 2)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 2)
Department of Physics
• USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 2)
• USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 2)
• USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 2)
• USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 2)
• USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 2)
• USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 2)

#### MA20219 is Optional on the following programmes:

Department of Mathematical Sciences
• USMA-AFB05 : BSc(Hons) Statistics (Year 2)
• USMA-AFB05 : BSc(Hons) Statistics (Year 3)
• USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 2)
• USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
• USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 2)
• USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)

Notes:
* This unit catalogue is applicable for the 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.