VPAA__________________________
Date _________________________
Vice President/ Academic Affairs Office use only
STATE UNIVERSITY OF NEW YORK
College of Technology at Alfred
SCHOOL:
Arts and Sciences
DEPARTMENT:
Mathematics and Physics
COURSE NAME:
Multivariate and Vector Calculus
COURSE NUMBER: MATH 6104
SEMESTERS OFFERED: Fall and Spring
PREREQUISITE:
MATH 2094 or MATH 2074
COURSE FORMAT: ___4_____ (# of contact hours--lecture/week)
_________ (# of contact hours--laboratory/week)
COURSE EQUIVALENT: If there is an equivalent course, please list it here._MATH 3104 and
MATH 6014_____
COURSE LEVEL:
Upper
Date Approved by Faculty Senate: ___________________
COURSE DESCRIPTION
This course is designed as a continuation of MATH 2094. Topics will include: parametric equations,
polar, cylindrical and spherical coordinate systems, vectors and vector valued functions, functions of
several variables, partial derivatives and applications, multiple integrals, and vector analysis,
including Green’s theorem, Stokes’ theorem, and Gauss’ theorem. The course will include several
major projects outside of class.
STUDENT OBJECTIVES
At the end of the course the student will be able to do the following:
1. Analyze and evaluate multivariate and vector-valued functions using appropriate analytical
methods.
2. Analyze and evaluate multivariate and vector-valued functions using a computer algebra
system.
3. Perform basic vector operations (vector dot product, vector cross product), and development
of algorithms to determine equations for lines and planes in three-dimensional space.
4. Solve systems of linear equations using Gauss-Jordan elimination to reduced row-echelon
form or systems of nonlinear equations using appropriate methods.
5. Differentiate functions of multiple variables using appropriate analytical methods.
6. Solve multiple-variable optimization problems.
7. Perform multiple integrations.
8. Determine if a vector field is conservative.
9. Find a scalar potential function for conservative vector fields.
10. Perform a line integral or a surface integral.
TEXTS
Thomas, George B., et al. Calculus, Early Transcendentals. Addison Wesley, latest edition.
DIVISION OF SUBJECT MATTER
Topic
Total
Lecture
Hours
1. Vector Algebra
a. Vectors in two and three dimensions
b. Vector products
c. Vector geometry
d. New coordinate systems
2. Differentiation in Several Variables
a. Functions of several variables and graphing surfaces
b. Partial Derivatives
c. Directional derivative and the gradient
3. Vector-Valued Functions
a. Parametrized curves
b. Arclength and surface area
c. Vector fields, including the gradient, curl,
divergence, and the del operator
4. Applications of Partial Differentiation
a. Solution of systems of linear and nonlinear
equations by appropriate methods
b. Approximation by the total derivative
c. Extrema and saddle points of surfaces
d. Constrained optimization problems
5. Multiple Integration
a. Double and triple integrals
b. Areas, volumes, and other applications of
multiple integrals
6. Line integrals, surface integrals, and vector analysis
a. Conservative vector fields
b. Green’s theorem
c. Scalar and vector line integrals
d. Parametrized surfaces and surface integrals
e. Stokes’ and Gauss’ theorems
7. Evaluation
a. Tests
b. Three to four outside of class projects
Total hours
9
10
9
9
9
9
5
60
Total
Lab
Hours
BIBLIOGRAPHY
Latest edition instead of year and editions; use format below:
Colley, Susan Jane.Vector Calculus, Prentice Hall Publishing, latest edition.
Lial, Margaret L, Raymond N. Greenwell, and Nathan P. Ritchey, Calculus with Applications,
Addison Wesley Publishers, latest edition
O’Connor, Kevin M., Calculus Labs for MATLAB , Jones and Bartlett Publishers, latest edition
Keith, Sandra Z., Visualizing Linear Algebra with Maple, Prentice Hall Publishers, latest edition
Kleinfeld, Erwin and Margaret Kleinfeld, Understanding Linear Algebra using MATLAB,
Prentice Hall publishers, latest edition
Herman, Eugene A. and Michael D. Pepe, Visual Linear Algebra with Maple and Mathematica
Tutorials, John Wiley and Sons Publishers, latest edition
__________________________
Dean of School
__________________________
Department Chair
_________________________
Instructor of Course
__________________________
Date