MA20219: Analysis 2B
[Page last updated: 03 August 2022]
Academic Year:  2022/23 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Intermediate (FHEQ level 5) 
Period: 
 Semester 2

Assessment Summary:  EX 100% 
Assessment Detail:  
Supplementary Assessment: 
 Likeforlike reassessment (where allowed by programme regulations)

Requisites: 
Before taking this module you must take MA20218

Learning Outcomes:
 After taking this unit students should be able to:
* state definitions and theorems in real and complex analysis and present proofs of the main theorems
* construct their own proofs of simple unseen results and of simple propositions
* present mathematical arguments in a precise, lucid and grammatical fashion
* apply definitions and theorems to simple examples
* give a geometric interpretation of multivariate differentiation
* evaluate simple contour integrals in the complex plane.

Aims:  To extend the theory of differentiation from functions of one real variable to functions of several real variables and to functions of one complex variable. To understand the relationship between these theories, their geometrical interpretation, and their application through examples.

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

Content:  Frechet derivative as best linear approximation, partial and directional derivatives.
Continuous differentiability, Jacobian matrix, chain rule, higher order partial derivatives, equality of continuous 2nd derivatives. Exterior derivative of a 1form (covector field), divergence and curl of a vector field, Hessian, stationary points and second derivative test, Taylor's theorem.
Complex differentiable functions and the CauchyRiemann equations, Curves in C, contour integrals. Primitives, Cauchy's theorem, Cauchy's Integral Formula, representation by power series. Liouville's Theorem, Fundamental Theorem of Algebra. Principal parts, Residue Theorem.

Programme availability: 
MA20219 is Compulsory on the following programmes:
Department of Computer Science
 USCMAFB20 : BSc(Hons) Computer Science and Mathematics (Year 2)
 USCMAAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 2)
 USCMAKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 2)
 USCMAFM14 : MComp(Hons) Computer Science and Mathematics (Year 2)
 USCMAAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 2)
 USCMAKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 2)
Department of Mathematical Sciences
 USMAAFB13 : BSc(Hons) Mathematics (Year 2)
 USMAAAB14 : BSc(Hons) Mathematics with Study year abroad (Year 2)
 USMAAKB14 : BSc(Hons) Mathematics with Year long work placement (Year 2)
 USMAAFB01 : BSc(Hons) Mathematics and Statistics (Year 2)
 USMAAAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 2)
 USMAAKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 2)
 USMAAFM14 : MMath(Hons) Mathematics (Year 2)
 USMAAAM15 : MMath(Hons) Mathematics with Study year abroad (Year 2)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 2)
Department of Physics
 USXXAFB03 : BSc(Hons) Mathematics and Physics (Year 2)
 USXXAAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 2)
 USXXAKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 2)
 USXXAFM01 : MSci(Hons) Mathematics and Physics (Year 2)
 USXXAAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 2)
 USXXAKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 2)
MA20219 is Optional on the following programmes:
Department of Economics
 UHESAFB04 : BSc(Hons) Economics and Mathematics (Year 2)
 UHESAFB04 : BSc(Hons) Economics and Mathematics (Year 3)
 UHESAAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 2)
 UHESAAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 4)
 UHESAKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 2)
 UHESAKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 4)
 UHESACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 2)
 UHESACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 4)
Department of Mathematical Sciences
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 2)
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 3)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 2)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 2)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
 USMAAFB05 : BSc(Hons) Statistics (Year 3)
 USMAAAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
 USMAAKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)

Notes:  This unit catalogue is applicable for the 2022/23 academic year only. Students continuing their studies into 2023/24 and beyond should not assume that this unit will be available in future years in the format displayed here for 2022/23.
 Programmes and units are subject to change 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 prerequisite rules.
 Find out more about these and other important University terms and conditions here.
