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MA20223: Vector calculus and partial differential equations

[Page last updated: 20 April 2021]

Academic Year: 2021/2
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%
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA10236
Description: Aims:
To complete the theory of vector calculus leading up to the fundamental integral theorems (the divergence theorem, Green's theorem, and Stokes' theorem). To introduce Fourier series, the three basic classes of linear PDEs (characterised by the Laplace, heat and wave equations), and the method of separation of variables.

Learning Outcomes:
After taking this unit, students should be able to:
* Use the fundamental integral theorems of vector calculus (the divergence theorem, Green's theorem, and Stokes' theorem)
* Demonstrate familiarity with the basic properties of Fourier series
* Solve the Laplace, heat, and wave equation in simple domains using separation of variables.
* Write the relevant mathematical arguments in a precise and lucid fashion.

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

Content:
Directional derivatives, gradients, potentials, line integrals (revision), divergence, curl, surface and volume integrals, curvilinear coordinates.
Integral theorems (divergence, Green, Stokes).
Fourier series: formal introduction, convergence theorem; Fourier cosine and sine series.
Partial differential equations: classification of linear second order PDEs; separation of variables for Laplace's equation in 2D, and heat and wave equation in one space dimension; d'Alembert formula for wave equation. Elementary potential theory and conservation laws.

Programme availability:
NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2021

MA20223 is Compulsory on the following programmes:

Department of Mathematical Sciences
  • 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)
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)

MA20223 is Optional on the following programmes:

Department of Mathematical Sciences
  • USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 2)
  • USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
  • USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 2)
  • USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
  • USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 2)
  • USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
  • USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 2)
  • USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
  • USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 2)
  • USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
  • USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 2)
  • USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
  • 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)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 2)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 2)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 2)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)

Notes:

  • This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22.
  • 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 pre-requisite rules.
  • Find out more about these and other important University terms and conditions here.