Topics for Mathematics 234

The textbook

• Weir, Hass & Giordano: Thomas' Calculus 11^th Edition, Addison Wesley
  Non-ET version, including differential equations.
  ISBN: Old style, 0-321-49069-X; New style, 9780321490698.

List of topics

Vector Valued Functions
13.1. Vector functions and space curves, parametrizations, velocity and acceleration (this is partially review).
13.3 Arclength and the unit tangent vector
13.4 Curvature and the unit normal vector
13.5 Torsion and the unit binormal vector
13.6 Applications (if time permits): Motion in space, planetary motion

Partial derivatives
14.1. Functions of several variables
14.2. Limits & continuity
14.3. Partial derivatives
14.4. The Chain Rule, implicit derivatives
14.5. Directional derivatives and the gradient
14.6. Tangent planes and the differential
14.7. Extreme values and saddle points
14.8. Lagrange multipliers
14.10. Taylor's formula in two variables

Multiple integrals
15.1. Double integrals
15.1. Double integrals over non rectangular domains
15.2. Areas, moments and centers of mass
15.3. Double integrals in polar coordinates
15.4. Triple and iterated integrals
15.5. Masses and Moments in three dimensions
15.6. Triple integrals in spherical and cylindrical coordinates
15.7. Substitution in multiple integrals.

Vector Analysis
16.1. Line integrals
16.2. Vector Fields, Work, Flux and Circulation
16.3. Path independence, Potential Functions and Conservative Fields
16.4. Green's theorem in the plane
16.5. Surface area and surface integrals
16.6. Parametrized surfaces
16.7. Stokes' theorem
16.8. The divergence theorem