Exam topics:

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.