620-231 Vector Calculus: Semester 1, 2010
Topics covered in lectures.
Week 1. (2nd-4th March)
- Limits - several variables
- Limits - several variables, Sandwich rule, Continuity
- Differentiation, C^N
- Up to problem Q9
Week 2 (9nd-11th March)
- Chain rule for several variables, Matrix chain rule for several variables
- Chain rule cont., Taylor polynomials
- Extrema, Hessian matrix, Constrained extrema - elimination method, Lagrange multipliers
- Up to problem Q18
Week 3 (16th to 18th March)
- Lagrange multipliers
- Parametric paths, Differentiating paths, Arc Length
- Unit tangents Normal and bi-normal vectors, curvature, torsion,Vector fields
- Assignment One handed out - due Monday Week 5
- Up to problem Q29
Week 4 (22nd to 25 March)
- Flow lines
- Divergence, Curl, Laplacian
- Vector identities
- Up to problem Q38
Week 5 (30th March to 1st April)
- Vector identities completed
- Double integrals over general domains
- Double integrals over general domains, Triple integrals (First questionnaire)
- Assignment Two handed out - due Monday 19th April
- Up to problem Q50
Week 6 (13th - 15th April)
- Triple integrals cont.
- Curvilinear coordinates: Polar coords.
- Cylindrical and spherical coordinates
- Up to problem Q57
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Week 7 (20th - 22nd April)
- Change of variables for multiple integrals
- Change of variables for multiple integrals continued
- Applications of multiple integrals
- Assignment three handed out - due Monday 3rd May
- Up to problem Q63
Week 8 (27th - 29th April)
- Path Integrals, More Parameterising curves,
- Line integrals, Surfaces, Parameterising surfaces
- (Questionare report) Parameterised surfaces cont., Surface tangents, Surface normals
- Up to problem Q72
Week 9 (4th - 6th May)
- Tangent planes, Areas of surfaces, Integrals of scalar functions over surfaces
- Integrals of scalar functions over surfaces cont
- Integrals of vector fields over surfaces
- Assignment four handed out - due Monday 17th May
- Up to problem Q77
Week 10 (11th-13th May)
- Greens theorem
- divergence (Gausses) theorem in the plane
- Stokes theorem
- Up to problem Q86
Week 11 (18th-20th May)
- Stokes theorem, Conservative fields
- Conservative fields, divergence (Gausses) theorem
- Examples for integral theorems, Application - Continuity equation
- Application - Maxwells equations, curvilinear coordinates
- Up to problem Q93
Week 12 (25th-27th May)
- (Discuss final exam, Uni questionare) curvilinear coordinates cont.
- vector operators, volume element, surface element etc.
- Revision: Past Exam problems - end of course.
- all problems completed.