MATH 3335 - Vector Analysis - University of Houston
Skip to main content

# MATH 3335 - Vector Analysis

***This is a course guideline.  Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***

Prerequisites: MATH 2433.

Course Description: Algebra and calculus of vectors, vector differential operators, Green’s and Stokes’ theorems, curvilinear coordinates, tensors.

Recommended Text: “Introduction to Vector Analysis”, 7th Ed., by H. F. Davis and A. D. Snider, Wm. C. Brown, Publ., 1998.

Another good text is “Vector Calculus” by P. C. Matthews, Springer-Verlag, 1998 (It may be useful for the instructor to look at the text “Div, Grad, Curl and All That” by H. M. Shey, W. W. Norton & Co., 1973, to see a physicist's view of the material)

This course is an introduction to the theory of vector fields in 2 and 3 dimensions and some associated differential geometry. It is primarily a service course for students majoring in physics and engineering. The hope is that the course will cover the mathematical background required for classical continuum theories and electromagnetic field theory.

The prerequisite for the course is Math 2433 and the course may be regarded as a natural continuation of Math 2433. The emphasis is not on complete proofs, but rather on intuition and/or plausibility.

Suggested Syllabus

This syllabus is based on the recommended text by Davis and Snider.

1. Introduction to vectors in the plane and in space; scalar and vector products, parametric equations of lines and planes, length, area and volume of boxes and tetrahedra.

2. Vector-valued functions of a scalar variable and the analysis of curves in space. Tangents, normals and curvature.

3. Vector fields in Cartesian coordinates, their field lines, gradients and vector differential operators, (div, grad, curl and Dv = matrix derivative of the field v). The scalar and vector Laplacian.

4. Spherical and cylindrical polar coordinate systems, unit vector fields (moving frames) and vector differential operators in these systems.

5. Line, surface and volume integrals, characterization of irrotational fields.

6. The Divergence Theorem and Stokes' Theorem in 3 dimensions and associated theorems.

CSD Accommodations:

Academic Adjustments/Auxiliary Aids: The University of Houston System complies with Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990, pertaining to the provision of reasonable academic adjustments/auxiliary aids for students who have a disability. In accordance with Section 504 and ADA guidelines, University of Houston strives to provide reasonable academic adjustments/auxiliary aids to students who request and require them. If you believe that you have a disability requiring an academic adjustments/auxiliary aid, please visit The Center for Students with DisABILITIES (CSD) website at http://www.uh.edu/csd/ for more information.

Accommodation Forms: Students seeking academic adjustments/auxiliary aids must, in a timely manner (usually at the beginning of the semester), provide their instructor with a current Student Accommodation Form (SAF) (paper copy or online version, as appropriate) from the CSD office before an approved accommodation can be implemented.

Details of this policy, and the corresponding responsibilities of the student are outlined in The Student Academic Adjustments/Auxiliary Aids Policy (01.D.09) document under [STEP 4: Student Submission (5.4.1 & 5.4.2), Page 6]. For more information please visit the Center for Students with Disabilities Student Resources page.

Additionally, if a student is requesting a (CSD approved) testing accommodation, then the student will also complete a Request for Individualized Testing Accommodations (RITA) paper form to arrange for tests to be administered at the CSD office. CSD suggests that the student meet with their instructor during office hours and/or make an appointment to complete the RITA form to ensure confidentiality.

*Note: RITA forms must be completed at least 48 hours in advance of the original test date. Please consult your counselor ahead of time to ensure that your tests are scheduled in a timely manner. Please keep in mind that if you run over the agreed upon time limit for your exam, you will be penalized in proportion to the amount of extra time taken.

UH CAPS

Counseling and Psychological Services (CAPS) can help students who are having difficulties managing stress, adjusting to college, or feeling sad and hopeless. You can reach (CAPS) by calling 713-743-5454 during and after business hours for routine appointments or if you or someone you know is in crisis. No appointment is necessary for the "Let's Talk" program, a drop-in consultation service at convenient locations and hours around campus.