Simon Fraser University Department of Mathematics
Spring 2004

MATH 252-3: Vector Calculus

Week 6

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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 5 due Friday, 20 February at the midterm (or by 4pm in the homework box)
      Problems: Sec.3.1 # 4, 5, 7, 10(a), 12, 17, 21, 23, 32, 34; Sec.3.2 # 3, 4; Sec.3.3 # 4, 6, 7, 8; Sec.3.4 # 4, 7, 9, 11; Sec.3.5 # 10; Sec.3.6 # 3 and additional problems
      .
    • Tutorial Sessions this Tuesday, 10 February
    • No class Monday the 16th or tutorials Tuesday the 17th: SFU mid-semester break; no office hours on Monday
    • Midterm exam next Friday, 20 February
    • Maple examples: fields (fields_nf with no figures: much smaller file)


Week 6:

  • Lecture 16: 9 February
    Flow Lines and Divergence:
    Computation of flow lines, relation with systems of first-order ordinary differential equations and their geometric interpretation; flux; the divergence of a vector field as flux per unit volume, derivation of formula for div
    F, examples
    Reading: D&S Ch.3 (3.2, 3.3)
  • Homework Set 5
  • Problems (HW Set 5): 3.2 - 3, 4; 3.3 - 4, 6, 7, 8
  • Suggested additional exercises for this lecture (optional):
    3.2 - 1, 2; 3.3 - 3, 5, 9, 12 (look at this result; see Notes)

  • Lecture 17: 11 February
    Conservation Laws and Curl:
    Flux and mass conservation, equation of continuity in fluid mechanics, general conservation laws; circulation; curl as circulation per unit area, derivation of formula for
    curl F, examples, angular velocity interpretation
    Reading: D&S Ch.3 (3.3, 3.4)
  • Homework Set 5
  • Problems (HW Set 5): 3.4 - 4, 7, 9, 11
  • Suggested additional exercises for this lecture (optional):
    3.4 - 6, 10, 12, 13

  • Lecture 18: 13 February
    Del Notation, the Laplacian, Vector Identities:
    Laplacian, the del operator and differential operators in Cartesian coordinates, tensor notation; vector identities: linearity, product rules, second derivaties;
    curl grad = 0, div curl = 0
    Reading: D&S Ch.3 (3.5, 3.6, 3.8, 3.9)
  • Homework Set 5
  • Problems (HW Set 5): 3.5 - 10; 3.6 - 3
  • Suggested additional exercises for this lecture (optional):
    3.5 - 4, 5, 6, 7, 8, 9; 3.6 - 2