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 Cours

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


  • 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