234 - Calculus -- Functions of Several Variables

Prerequisites: 

Math 222. Closed to students with credit for Math 223.

Frequency: 
Fall (I), Spring (II), Summer (SS)
Student Body: 

This course is intended for students in the sciences, mathematics, computer science and engineering, or for other students who want preparation for higher level math courses or courses in allied fields

Credits: 
4. (N-I)
Recent Texts: 

Thomas' Calculus W/Second Order Differential Equations (special Wisconsin printing) Weir, Hass, Giordano

Course Coordinator: 
Sigurd Angenent
Background and Goals: 

This course is the last course in the standard Calculus series at the UW, Math 221-222-234. This series is designed for students with majors in the Sciences or Engineering. Honors student interested in a theoretical approach should consider our sequence 275-276-375-376 instead of 221-222-234. Full credit is not allowed for both 234 and 223.

Alternatives: 
Some majors in the school of business require Math 211-213 instead of Math 221-222-234. Math 213 has some content overlap with Math 234 and full credit cannot be received for both Math 234 and Math 213.
Subsequent Courses: 
n/a
Course Content: 
  • Vector functions and space curves, velocity and acceleration
  • Arc length and curvature, normal and binormal
  • Motion in space, planetary motion
  • Partial derivatives
  • Tangent planes and normals
  • Linear approximation
  • gradient and total differential
  • Local and absolute extrema
  • Lagrange multipliers
  • Higher derivatives, exact differentials
  • Double and iterated integrals, including polar coordinates
  • Applications of double integrals
  • Triple and iterated integrals, including cylindrical and spherical coordinates
  • Applications of triple integrals, volume and surface areas.
  • Vector fields, surface integrals and line integrals
  • Flux, Green's theorem
  • Divergence Theorem, Stokes' theorem