MATH 256 Syllabus

Calculus III

Revised: January 2015

Course Description

Plane curves, polar coordinates, vectors and solid analytic geometry, vector-valued functions, partial differentiation, multiple integrals. Prerequisite: MATH 255. Four semester hours.

Student Learning Objectives

By the end of the course students should be able to:

  • work with and visualize graphs of functions of several variables;
  • Geometrically and algebraically describe vectors and vector operations;
  • Differentiate and integrate vector valued functions, and using these operations appropriately in applications;
  • Differentiate multivariate functions and determine when partial differentiation or ordinary differentiation is needed;
  • Use differentiation, directional derivatives, and the gradient in solving applied problems;
  • Solve constrained and unconstrained optimization problems with several independent variables;
  • Setup and evaluate double and triple integrals in Cartesian, polar, cylindrical, and spherical coordinates; and
  • Work with parametric curves, equations, and vector fields.


Steward, James. Calculus: Early Transcendentals, 6th edition , Thomson Brooks/Cole, 2008.

Grading Procedure

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Course Outline

  • CHAPTER 12 -Vectors and Geometry of Space (8 days)

All sections are to be covered Functions: Three-dimensional coordinate systems, vectors, the dot product, the cross product, equations of lines and planes, cylinders and quadric surfaces.

  • CHAPTER 13 - Vector Functions (6 days)

All sections are to be covered: vector functions and space curves, derivatives and integrals of vector functions, arc length and curvature, motion in space with velocity and acceleration.

  • CHAPTER 14 - Partial Derivatives (10 days)

All sections are to be covered: functions of several variables, limits and continuity, partial derivatives, tangent planes and linear approximations, the chain rule, directional derivatives and the gradient vector, maximum and minimum values, lagrange multipliers.

  • CHAPTER 15 - Multiple Integrals (11 days)

All sections are to be covered: double integrals over rectangles, iterated integrals, double integrals over general regions, double integrals in polar coordinates, applications of double integrals, triple integrals, triple integrals in cylindrical coordinates, triple integrals in spherical coordinates, change of variables in multiple integrals

  • CHAPTER 16 - Vector Calculus (as time allows)

As time allows: vector fields, linea integrals, the fundamental theorem for line integrals, Green’s Theorem, curl and divergence, parametric surfaces and their areas, surface integrals, Stokes’ Theorem

Plus selected topics from Chapter 17 and Chapter 18 as time allows.

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