Simon Fraser University Department of Mathematics
Spring 2005

MATH 252-3: Vector Calculus

Week 6 - Dyadics, Vector Identities

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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

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Week 6:

  • Lecture 16: 14 February
    Dyadics:
    Projection operator, dyadic, gradient of a vector field, matrix representation; interpretation of Laplacian

    Reading: D&S Ch.3 (3.6, 3.7)

  • Lecture 17: 16 February
    Tensor Notation and Vector Identities:
    Del notation, differential operators, tensor notation, vector product identies,
    curl grad f = 0
    Reading: D&S Ch.3 (3.8, 3.9)

  • Lecture 18: 18 February
    Cylindrical Coordinates:
    Proofs of vector identities, div
    curl F = 0, more complicated identities; definition of cylindrical coordinates, level surfaces, coordinate curves
    Reading: D&S Ch.3 (3.9, 3.10)