620-231 Vector Analysis
Topics covered in lectures.
Week 1.
- Mon: Limits - several variables
- Wed: Limits - several variables, Sandwich rule, Continuity
- Fri: Differentiation, C^N, Chain rule for several variables
Problems: Q1 to Q9
Week 2
- Matrix chain rule for several variables
- Chain rule cont., Taylor polynomials
- Extrema, Hessian matrix, Constrained extrema - elimination method,1
Problems: Q10 to Q15
Week 3
- Lagrange multipliers
- Parametric paths
- No lecture - University public holiday (Easter)
Problems: Q16 to Q23.
Week 4
- Differentiating paths, Arc Length, unit tangents
- Normal and bi-normal vectors, curvature, torsion,
- Vector fields, Flow lines, Divergence
Problems: Q24 to Q33.
Week 5
- Curl, Laplacian
- Vector identities
- (First questionnaire) Vector identities completed
Problems: Q34 to Q43.
Week 6
- Double integrals over rectangular domains, general domains
- Double integrals over general domains
- Triple integrals
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Problems: Q44 to Q52.
Week 7
- Triple integrals cont. Polar coords
- Mid-Semester test
- Anzac Day
Problems: Q53 to Q55.
Week 8
- Polar coords cont, Cylindrical Coords, Spherical coords, Change of variables for multiple integrals
- Change of variables for multiple integrals continued.
- Applications of multiple integrals (handout), Path Integrals, Line integrals
Problems: Q56 to Q66
Week 9
- Line integrals continued, Surfaces, Parameterised surfaces handout
- Parameterized surfaces, surface tangents, Surface normals,
- Tangent planes, Areas of surfaces
Problems: Q67 to Q73
Week 10
- Integrals of scalar functions over surfaces
- Integrals of vector fields over surfaces
- Greens theorem, areas with Greens theorem
Problems: Q74 to Q81
Week 11
- Divergence thm in plane, Stokes theorem
- Stokes theorem
- Conservative fields,divergence (Gausses) theorem
Problems: Q82 to Q93
Week 12
- divergence (Gausses) theorem cont