Simon Fraser University Department of Mathematics
Spring 2005

MATH 252-3: Vector Calculus

Week 8 - Curvilinear Coordinates, Line Integrals

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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:

    • Homework Set 6 due Wednesday, March 2
      Notes on differentiating electric and magnetic fields E and B
      (This problem was on HW 7 in Spring 2004)


Week 8:

  • Lecture 22: 28 February
    Curvilinear Coordinates:
    Spherical and orthogonal curvilinear coordinates, level surfaces, coordinate curves, scale factors, gradient

    Reading: D&S Ch.3 (3.10, 3.11)

  • Lecture 23: 2 March
    Path Integrals:
    Divergence, Laplacian, curl in general curvilinear coordinate systems; path integral of scalar fields, element of arc length

    Reading: D&S Ch.3&4 (3.10, 3.11, 4.1)

  • Lecture 24: 4 March
    Line Integrals and Domains:
    Parametrization, line integral of vector fields, examples; neighbourhoods, interior, boundary and exterior points, open and closed sets; connected sets, domains, simply connected sets, star-shaped domains

    Reading: D&S Ch.4 (4.1, 4.2)