Exam topics:
The final exam will cover Sections 14.1 - 14.4 and 17.1-17.9 of the textbook. Specific topics
are as follows:
Chapter 14:
- Vector-valued functions, curves (includes graphing curves)
- Differentiating and integrating vector-valued curves
- Tangent vectors, tangent lines
- Arclength, arclength parametrization
- Curvature
- Principal normal and binormal vectors, normal and osculating planes
- Velocity, speed, acceleration, tangential and normal components of acceleration
- Skip "Kepler's laws", Section 14.4
Chapter 17:
- Vector fields
- Line integrals (with respect to arclength, dx, dy, dz)
- Line integrals of vector fields
- Conservative (gradient) vector fields
- Fundamental Theorem of Calculus for line integrals
- Skip "Conservation of energy", Section 17.3
- Green's Theorem
- Curl and divergence
- Parametric surfaces (You will need to use polar, spherical and cylindrical coordinates. If you don't remember
this material well, please review Sections 16.4, 16.7 and 16.8.)
- Surface area
- Scalar and vector surface integrals (omit centroids and centers of mass)
- Stokes' Theorem
- The divergence theorem
Resources:
- Old midterms and practice midterms are available
from the MATH 317, Fall 2008, webpage
(Prof. K. Behrend)
- UBC Math Club,
located in Math Annex 1119, sells
math exam packages (old exams together with solution sets)
for a nominal price before each final exam session.
[Mathematics Department]
[University of British Columbia]