Simon Fraser University Department of Mathematics
Spring 2005

MATH 252-3: Vector Calculus

Week 4 - Motion in Polar Coordinates, Gradients

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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 3 due Wednesday, February 2
      Note: please hand in the extra problem and Maple output together with the problems from Davis and Snider
      Print out the homework cover page and hand it in with your homework; see the Tutorials web page for further information and instructions
      Some Notes on the homework set


Week 4:

  • Lecture 10: 31 January
    Planar Motion in Polar Coordinates:
    Binormal, curvature, torsion in terms of velocity, acceleration, jerk in any parametrization; polar coordinates in the plane, radial and angular unit vectors, velocity and acceleration

    Reading: D&S Ch.2 (2.3, 2.4)

  • Lecture 11: 2 February
    Scalar Fields, Directional Derivatives and Gradients:
    Scalar fields, isotimic (level) surfaces, directional derivatives, chain rule, gradients, properties of the gradient vector

    Reading: D&S Ch.3 (3.1)

  • Lecture 12: 4 February
    Vectors Fields and Flow Lines:
    Examples of level surfaces; vector fields, examples: gravitational, electrostatic, velocity fields; flow lines

    Reading: D&S Ch.3 (3.1, 3.2)