- Module code: MA231
- Module name: Vector Analysis
- Department: Mathematics Institute
- Credit: 12
Module content and teaching
This module aims to: 1. Teach a practical ability to work with functions of two or three variables and vector fields; 2. Present the theorems of Gauss and Stokes as generalisations of the fundamental theorem of calculus to higher dimensions;3. Establish Cauchy's theorem in complex analysis as a consequence of the Cauchy-Riemann equations and the divergence theorems; 4. Teach those rudiments of complex analysis which follow from Cauchy's theorem, namely, the Cauchy integral formula, Taylor expansions and residue calculus.
Principal learning outcomes
On successful completion of this module, a student should: 1. Be able to calculate line, surface and volume integrals in general curvilinear coordinates; 2. Be familiar with and use in a variety of contexts the fundamental results of vector calculus, namely, the divergence theorem and Stokes' theorem; 3. Understand the relation between the existence of a scalar or vector potential of a vector field and the vanishing of the curl or divergence of that vector field and be able to calculate the potential when it exists; 4. Be able to establish the Cauchy-Riemann equations for a complex differentiable function and establish Cauchy's theorem from the integral theorems of vector calculus; 5. Be able to prove Cauchy's integral formula from Cauchy's theorem, and to use the integral formula to establish differentiability and series properties of complex differentiable functions; 6. Be able to calculate Taylor expansions, residues and use them in the evaluation of definite integrals and summation of series.
Other essential notes
Prerequisites: MA127 3D Geometry and Motion or PX129 (Maths/Physics) Worksheets.
|Assessment group||Assessment name||Percentage|
|12 CATS (Module code: MA231-12)|
|D (Assessed/examined work)||Coursework||15%|
|2 hour examination (April)||85%|
This module is available on the following courses:
- Undergraduate Mathematics and Physics (BSc MMathPhys) (FG33) - Year 2
- Undergraduate Mathematics with Intercalated Year (G101) - Year 2
- Undergraduate Mathematics and Business Studies (with Intercalated Year) (G1N2) - Year 2
- Undergraduate Mathematics and Business Studies (G1NC) - Year 2
- Undergraduate Discrete Mathematics (G4G1) - Year 2
- Undergraduate Discrete Mathematics (G4G3) - Year 2
- Undergraduate Mathematics and Economics (GL11) - Year 2
- Undergraduate Mathematics and Economics (with Intercalated Year) (GL12) - Year 2
- Undergraduate Mathematics and Economics (with Intercalated Year) (GL12) - Year 4