Content and teaching | Assessment | Availability

Module content and teaching

Principal aims

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.

Departmental link

http://go.warwick.ac.uk/MA231/

Other essential notes

Prerequisites: MA127 3D Geometry and Motion or PX129 (Maths/Physics) Worksheets.

Module assessment

Assessment group	Assessment name	Percentage
12 CATS (Module code: MA231-12)
D (Assessed/examined work)	Coursework	15%
	2 hour examination (April)	85%

Module availability

This module is available on the following courses:

Core

• 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

Optional Core

N/A

Optional

• 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