MATHEMATICS 252-3
VECTOR CALCULUS
Spring 1999
DAY COURSE
Instructor: Dr. John Hebron
Office: K 10529
Office Hours: Monday, Wednesday, Friday, 9:30 AM - 10:30 AM
Phone: 291-3636
Fax: 291-4947
E-mail: Click here for info.
Class E-mail List: math252-d1@sfu.ca
(Restricted to members only!)
Class Web Site (containing this page):
http://www.math.sfu.ca/~hebron/math252/
Class Web Conference:
http://caucus.sfu.ca/caucus/math252_d1
Lectures:
Mondays, Wednesdays, and Fridays, 8:30 AM - 9:20 AM, in room AQ 3159.
Tutorials:
- Tutorial 01: Tuesdays 8:30 AM - 9:20 AM, in room AQ 5009.
- Tutorial 02: Tuesdays 9:30 AM - 10:20 AM, in room AQ 5050.
- Tutorial 03: Thursdays 9:30 AM - 10:20 AM, in room AQ 5038.
- Tutorial 04: Thursdays 8:30 AM - 9:20 AM, in room AQ 5050.
- Your Teaching Assistant is Y.L. (Alex) Zhao.
Prerequisites:
MATH 232 and
MATH 251.
Students with credit for MATH 312
may not take MATH 252 for further credit.
Textbook:
Introduction to Vector Analysis (Seventh Edition),
by H.F. Davis and A.D. Snider, Wm C. Brown Publishers.
Calendar Description:
Vector functions of a single variable, space curves, scalar and vector
fields, conservative fields,
surface and volume integrals, and theorems of Gauss, Green and Stokes.
Outline:
Note: This outline may be subject to change as the semester
progresses, but you can take it to be at least 80% accurate.
- Introductory Material and Chapter 1 of the textbook -- 6 lectures from
Monday, January 4th 1999 to Friday, January 15th 1999.
- Historical background.
- Definitions (Salars, Vectors, Dot Product, Scalar Fields, Vector Fields, etc.)
- Vectors and Geometry, Lines and Planes in 3-space.
- Vector Products, Triple Scalar Products
- Vector Identities, Tensor Notation
- Chapter 2 of the textbook -- 4 lectures from Monday, January 18th to
Monday, January 25th 1999.
- Differentiation of Vector Functions
- Space Curves: Velocities, Tangents, Acceleration, Curvature
- Frenet Formulas
- Planar Motion in Polar Coordinates
- Chapter 3, sections 3.1 to 3.10 of the textbook -- 9 lectures from
Wednesday, January 27th 1999 to Monday, February 15th, 1999.
- Scalar Fields and Gradients
- Vector Fields, Divergence, Curl
- Laplacian
- Dyadics
- More Vector Identities
- More Tensor Notation
- Cylindrical and Spherical Coordinates
- Mid-Term Exam -- 8:30 AM Wednesday, February 17th 1999, in class.
Fifty-minute closed-book exam. No calculators.
- Chapter 3, section 3.11 of the textbook -- one lecture on Friday,
February 19th, 1999.
- Orthogonal Curvilinear Coordinates
- Chapter 4 of the textbook -- 9 lectures from Monday, February 22nd to
Friday, November 12th 1999.
- Line Integrals
- Conservative Vector Fields, Potential Function, Irrotational Fields
- Vector Potentials and Solenoidal Fields
- Oriented Surfaces
- Surface Integrals
- Volume Integrals
- Intro to Divergence Theorem and Stokes' Theorem
- Intro to Transport Theorems
- Chapter 5 of the textbook -- 8 lectures from Monday, March 15th to
Wednesday March 31st 1999
- Divergence Theorem
- Green's Formulas: Laplace's and Poisson's Equations
- Fundamental Theorem of Vector Analysis
- Green's Theorem
- Stoke's Theorem
- Transport Theorems
- Matrix Techniques
- Linear Orthogonal Transformations
- Final Exam -- 8:30 AM Tuesday, April 6th 1999. Three-hour closed-book
exam. No calculators. Location t.b.a.
Lecture Notes:
A summary of each lecture will be posted on the Class Web Site, along
with scanned-in colour transparancies which were used in the lectures.
Homework Assignments:
Weekly homework assignments will be given in each Friday's class,
and will be due in class the following Friday at 8:30 AM.
The homework assignments will also be posted on the Class Web Site,
along with solutions (after the assignment is due).
Reference Books:
- Advanced Calculus by M.R. Spiegel, Schaum Series, Chapters 6 - 10.
- Vector Analysis by M.R. Spiegel, Schaum Series.
- Advanced Engineering Mathematics by D.G. Zill and M.R. Cullen,
PWS-Kent Publishing Company, Chapter 8.
Computers and Math 252:
- Click here for information on using computers
in Math 252.
Grading:
Midterm - 30%
Assignments - 20%
Final Exam - 50%
Students should be aware that they have certain rights to confidentiality
concerning the return of course papers and the posting of marks.
Click here for more info.
SFU /
Math & Stats /
~hebron /
math252 /
outline.html
Revised January 1999 by
John Hebron.