MA231 Vector Analysis
Schedule:
Lecture
Monday, 3-4pm, MS.02
Tuesday, 3-4pm, MS.02
Thursday, 2-3pm, MS.02
Support class
Monday, 12-13 h, MA B3.02 week 2-9, and B2.01 (SciConc) in week 10 (support class
for Maths/Physics, first class week 2)
Prerequisites: MA134 Geometry and Motion or PX129 (Maths/Physics) worksheets.
Contents: The first part of the module provides an introduction to vector calculus which is
an essential toolkit for differential geometry and for mathematical modelling. After a brief
review of line and surface integrals, div, grad and curl are introduced and followed by the
two main results, namely, Gauss’ Divergence Theorem and Stokes’ Theorem. The usefulness
of these results in applications to flow problems and to the representation of vector fields
with special properties by means of potentials will be emphasised and will be illustrated with
many examples. This part will be finished in week 5. For maths students the first one or
two weeks might be some revision from Geometry and motion module.
The second part of the module introduces the rudiments of complex analysis leading up to
the calculus of residues. The link with the first part of the module is achieved by considering
a complex valued function of one complex variable as a vector field in the plane. Complex
differentiability leads to the Cauchy-Riemann equations which are interpreted as conditions
for the vector field to have both zero divergence and zero curl. Cauchy’s theorem for complex
differentiable functions is then established by means of the main integral theorems of vector
calculus.
Support Class: Support for the Maths students is given by the supervisors. For the
Maths/Physics students there will be a separate support class given by Sohail Iqbal (email
Assessment: One two-hour final examination counting for 85%. The remaining 15% will
be assessed through four assignments (weeks 4, 6, 8, and 10).
Lecture Notes: Printed lecture notes are available (end of this week) on the MathStuff
homepage or on my departmental homepage
http://www2.warwick.ac.uk/fac/sci/maths/people/staff/stefan adams/vectoranalysis 2010/
However, these notes will be updated on a regular basis during the whole term. An important
part in vector analysis are figures and pictures. These will not be contained in the notes.
For any figure which appears on the blackboard in my lectures, I leave some empty space
with a reference number which coincides with the number I am using in the lectures. You
can fill the diagrams and figures by yourself.
Stefan Adams
office B2.18
phone 23571
email [email protected]
office hours: Monday 4-5pm (or by appointment)