MATH 252
Vector Calculus

Spring 2017

INSTRUCTOR: John Stockie
Office: K 10518
Phone: 778-782-3553
E-mail: stockie  [at]  math.sfu.ca
Course web page: http://www.sfu.ca/~jstockie/teaching/math252/
CLASS TIMES: MWF 8:30-9:20, WMC 3210
TUTORIAL: Thursday 12:30-13:20, AQ 2104 (D101)
Thursday 13:30-14:20, AQ 2104 (D102)
TA: Juan García (email: jggarcia  [at]  sfu.ca)
MY OFFICE HOURS: Wednesdays 12:30-14:30
PREREQUISITES: MATH 251; MATH 240 or 232. The course MATH 240 or 232 may be taken concurrently. Students with credit for MATH 254 may not take MATH 252 for further credit.
CALENDAR DESCRIPTION: Vector calculus, divergence, gradient and curl. Line, surface and volume integrals. Conservative fields, theorems of Gauss, Green and Stokes. General curvilinear coordinates and tensor notation. Introduction to orthogonality of functions, orthogonal polynomials and Fourier series. Quantitative.
TEXTBOOK: Introduction to Vector Analysis, 7th edition, by H. F. Davis and A. D. Snider (Hawkes Publishing, 2016).
HOMEWORK: There will be roughly N=10 homework assignments, handed out weekly and due on Fridays at 12:00 (noon). The homework portion of your final grade will be calculated based on your best N-1 assignment marks. The homework deadline is strict and late assignments will receive a mark of zero, with no exceptions. I encourage you to work together with your classmates on your assignment solutions; however, your written homework submission must be your own work. Plagiarism on homework assignments is a serious academic offense, and I will treat it as such.
DETAILED OUTLINE:   (references in parentheses indicate sections in the textbook)
  1. Vector algebra (mostly review) -- 1 week
    • Vector operations, equations of lines and planes (1.1-1.8, 1.10)
    • Vector products: dot, cross and triple-scalar product (1.9, 1.12-1.13)
    • Vector identities (1.14)
    • Index and tensor notation, Kronecker delta, permutation tensor (1.15)
  2. Vector functions of a single variable -- 1.5 weeks
    • Derivative of a vector function (2.1)
    • Space curves, velocity and acceleration, tangent and curvature (2.2-2.3)
    • Frenet frame (2.3-2.4)
  3. Scalar and vector fields -- 3 weeks
    • Surfaces, gradients, vector fields, flow lines (3.1-3.2)
    • Divergence, curl, Laplacian operators, vector identities (3.3-3.6, 3.8-3.9)
    • Cylindrical and spherical coordinates, general curvilinear coordinates (3.10-3.11)
  4. Integration -- 2 weeks
    • Line integrals (4.2-4.2)
    • Conservative, potential and irrotational fields (4.3-4.5)
    • Surface and volume integrals (4.6-4.8)
  5. Fundamental theorems -- 2.5 weeks
    • Divergence theorem (4.9, 5.1)
    • Laplace and Poisson equation, Green's theorem (5.2-5.4)
    • Stokes' theorem (5.5)
    • Transport theorems (5.6)
  6. Applications -- 2 weeks
    • Particle systems, rigid body motion (Appendix C)
    • Electromagnetism, Maxwell's equations (Appendix D)
    • Fluid dynamics, Euler and Navier-Stokes equations
MARKING SCHEME:
   Assignments (weekly):   20%
Midterm Test (tentatively Feb. 24, in class):   25%
Final Exam (Apr. 9): 55%

Last modified: Mon Apr 20 2020