Simon Fraser University Department of Mathematics
Spring 2005

MATH 252-3: Vector Calculus

Week 9 - Conservative and Solenoidal Fields

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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 7, due March 9
      (Update, March 4: This link now works; please contact me by e-mail concerning any broken links!)


Week 9:

  • Lecture 25: 7 March
    Conservative Fields and Potentials:
    Conservative fields, scalar potential function, fundamental theorem of calculus for gradients, path-independence for conservative fields; irrotational fields

    Reading: D&S Ch.4 (4.3, 4.4)

  • Lecture 26: 9 March
    Conservative, Irrotational and Solenoidal Fields:
    Irrotational fields are conservative in simply connected domains, examples of conservative fields, computing the scalar potential, example of non-conservative irrotational field in punctured domain; solenoidal fields, vector potential

    Reading: D&S Ch.4 (4.3, 4.4, 4.5)

  • Lecture 27: 11 March
    Vector Potentials, Oriented Surfaces:
    Solenoidal vector fields have vector potential in simply connected domains, interpretation of scalar and vector potential; surfaces, normal vector, orientation, nonorientable surfaces

    Reading: D&S Ch.4 (4.4, 4.5, 4.6)