Quick Links:
Instructor:
Ralf Wittenberg
K-10536, 291-4792
ralf@sfu.ca |
Lectures:
M, W, F 8:30-9:20am
in K 9500 |
Text:
Davis & Snider,
Introduction to Vector Analysis
Wm.C. Brown |
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Announcements:
- Lecture 24: 1 March
Orthogonal Curvilinear Coordinates:
Orthogonal curvilinear coordinates, level surfaces, coordinate curves and basis vectors; scale factor, arc length, volume element; gradient, divergence, Laplacian and curl in general curvilinear coordinate systems
Reading: D&S Ch.3 (3.11) - Homework Set 7
- Problems (HW Set 8): 3.11 - 3, 7, 9, 11, 12, 13, 14
- Suggested additional exercises for this lecture (optional):
3.11 - 1, 5, 6, 10
- Lecture 25: 3 March
Dyadics, Linear Approximation:
Projection operator, dyadic, gradient of a vector field; linear approximation, differentiability in one and two dimensions, tangent line and plane
Reading: D&S Ch.3 (3.7) (and see Marsden and Tromba or another book on reserve, for information on differentiability in higher dimensions)
- Homework Set 7Suggested additional exercises for this lecture (optional):
3.11 - 5, 6, 10
- Lecture 26: 5 March
Differentiability, Quadratic Approximation, Taylor Polynomials:
Derivative of vector fields; Taylor polynomials, quadratic approximation, Hessian; extrema, criterion for maxima; local average property of Laplacian
Reading: D&S Ch.3 (3.7)
- Homework Set 8
- Problems (HW Set 8): 3.7 - 2, 3, 5, 7 and additional problems
- Suggested additional exercises for this lecture (optional):
3.7 - 1, 6
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