MA20223: Vector calculus and partial differential equations
Academic Year:  2020/1 
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:  EX 100% 
Supplementary Assessment: 

Requisites: 
Before or while taking this module you must take MA20219 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 2020 
MA20223 is Compulsory on the following programmes:Department of Mathematical Sciences
MA20223 is Optional on the following programmes:Department of Mathematical Sciences

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