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Programme & Unit Catalogues

MA20219: Analysis 2B

Credits: 6
Level: Intermediate (FHEQ level 5)
Period: Semester 2
Assessment: EX 100%
Supplementary Assessment: MA20219 Mandatory extra work (where allowed by programme regulations)
Requisites: Before taking this unit 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-AFB13 : BSc (hons) Computer Science with Mathematics (Full-time) - Year 2
• USCM-AKB14 : BSc (hons) Computer Science with Mathematics (Full-time with Thick Sandwich Placement) - Year 2
• USCM-AAB14 : BSc (hons) Computer Science with Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
Department of Mathematical Sciences
• USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 2
• USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 2
• USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 2
• USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 2
• USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 2
• USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 2
• USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 2
• USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
Department of Physics
• USXX-AFB03 : BSc (hons) Mathematics and Physics (Full-time) - Year 2
• USXX-AKB04 : BSc (hons) Mathematics and Physics with Placement (Full-time with Thick Sandwich Placement) - Year 2
• USXX-AAB04 : BSc (hons) Mathematics and Physics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 2

MA20219 is Optional on the following programmes:

Department of Mathematical Sciences
• USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 2
• USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 2
• USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2

NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.