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Master Syllabus

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Administrative Unit: Computer and Mathematical Sciences Department
Course Prefix and Number: MATH 300
Course Title: Multivariate Calculus
Number of:
Credit Hours 3
Lecture Hours 3
Lab Hours 0
Catalog Description:

Two and three dimensional vectors, partial derivatives, multiple integrals, line and surface integrals. Prerequisite: MATH 222 or MATH 235.

Prerequisite(s) / Corequisite(s):

MATH 222 or MATH 235.

Course Rotation for Day Program: Offered even Fall.
Text(s): Most current editions of the following:

By Finney, R. & G. Thomas (Addison-Wesley)
By Stewart (Brooks-Cole)
Course Objectives
  • To use calculus to formulate and solve problems and communicate solutions to others.
  • To use technology as an integral part of the process of formulation, solution, and communication.
  • To understand calculus from numerical, graphical, symbolic, and analytical perspectives.
  • To understand and appreciate the connections between mathematics and other disciplines.
    Measurable Learning
  • Use vectors in two and three dimensions to describe lines and planes in space.
  • Use vector functions to describe curves in space.
  • Use vector-valued functions to describe the motion of objects through space.
  • Apply basic ideas of differential calculus to functions of several variables.
  • Define double and triple integrals to extend the basic ideas of integral calculus to functions of two and three variables.
  • Apply double and triple integrals to find volumes, surface areas, masses, and centroids of solid regions.
  • Compute line and surface integrals and use these to solve applied problems in the sciences.
  • Establish connections between line and surface integrals and single, double, and triple integrals through the higher-dimensional versions of the Fundamental Theorem of Calculus: Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem.
    Topical Outline:
  • Vectors and the geometry of space
  • Vectors functions
  • Partial derivatives and their applications
  • Multiple integrals
  • Vector calculus

    Culminating Experience Statement:

    Material from this course may be tested on the Major Field Test (MFT) administered during the Culminating Experience course for the degree. 
    During this course the ETS Proficiency Profile may be administered.  This 40-minute standardized test measures learning in general education courses.  The results of the tests are used by faculty to improve the general education curriculum at the College.


    Recommended maximum class size for this course: 30

    Library Resources:

    Online databases are available at You may access them from off-campus using your CougarTrack login and password when prompted.

    Prepared by: Nataliya Latushkina Date: November 7, 2013
    NOTE: The intention of this master course syllabus is to provide an outline of the contents of this course, as specified by the faculty of Columbia College, regardless of who teaches the course, when it is taught, or where it is taught. Faculty members teaching this course for Columbia College are expected to facilitate learning pursuant to the course objectives and cover the subjects listed in the topical outline. However, instructors are also encouraged to cover additional topics of interest so long as those topics are relevant to the course's subject. The master syllabus is, therefore, prescriptive in nature but also allows for a diversity of individual approaches to course material.

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