Math 227 syllabus
Calculus III
Course Description:
This course is a continuation of MA 126. Topics include vectors and the geometry of
space; vector functions and functions of several variables; partial derivatives; local
linearity; directional derivative and gradient; differential of a function; chain
rule; higher order partial derivatives; quadratic approximation; optimization of functions
of several variables; parametric curves and surfaces; multiple integrals and their
applications; vector fields; line and surface integrals; vector calculus.
Core Course
Prerequisites: C or better in MA 126
Textbook: Joel Hass, Maurice D. Weir, and George B. Thomas, Jr.:
University Calculus – Early Transcendentals, Addison-Wesley, Boston, 2nd edition,
2012 (ISBN 978-0-321-71739-9).
Learning Objectives:
Upon successful completion of the course a student will be able to:
- Apply the algebra and geometry of vectors in 2- and 3-dimensional space;
- Analyze vector fields;
- Interpret the calculus of a single variable from a vector point of view;
- Apply the differential calculus of curves in 3-dimensional space and the calculus of path integrals;
- Check whether a vector field is conservative, and in the case it is, to find a potential function;
- State and use the fundamental theorem of line integrals;
- Analyze elementary functions of several variables, their graphs, and the standard quadratic surfaces;
- Compute and interpret partial and directional derivatives of multivariable functions and use these to compute local minima, local maxima, and tangent plane approximations;
- Compute double and triple integrals in various coordinate systems;
- State and use Green’s theorem;
- Compute and interpret line and surface integrals;
- State and use Stokes’ theorem and the divergence theorem.
Topics and Time Distribution:
By assuming the total of 13.5 weeks, the instructor is
given an extra week to use for tests, emphasis on certain topics, etc.
Chapter 11 - Vectors and the Geometry of Space (2 weeks)
Chapter 12 - Vector-Valued Functions and Motion in Space (1.5 weeks)
Chapter 13 - Partial Derivatives (3.5 weeks)
Chapter 14 - Multiple Integrals (3 weeks)
Chapter 15 - Integration in Vector Fields (3.5 weeks)
Last Updated February 4, 2014