Simon Fraser University Department of Mathematics
Spring 2004

MATH 252-3: Vector Calculus

Week 9

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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

Announcements:


Week 9:

  • 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