Prerequisite: MATH 231, or equivalent, with grade C- or better
Course Topics:
- Vector algebra
- Vector functions
- Scalar and vector fields
- Gradient, divergence, curl
- Orthogonal curvilinear coordinates
- Tensor notation
- Line integrals, surface integrals, volume integrals
- Green's theorem, Stoke's theorem, Gauss' theorem
Course Learning Outcomes: By the end of this course students will be able to:
- Perform the algebra operations on vectors.
- Describe lines, planes, and surfaces in 3-space.
- Compute the tangent and normal vectors to space curves.
- Compute velocity, acceleration and curvature.
- Compute scalar and vector products.
- Use tensor notation to derive/verify vector identities
- Compute divergence and curl of vector fields
- Compute line integrals and test for independence of path
- Compute surface and volume integrals.
- State and use Green's, Stokes', Divergence Theorem.
Program Learning Outcomes and Mission Statement of the Department of Mathematics
Course Requirements
- Textbook (required): H. F. Davis and A. D. Snider, Introduction to Vector Analysis, 7th Edition, Brown Publishers, 1995
- Lecture Notes
- Goals and Objectives of the Course: The purpose of this course is to study the methods of vector analysis that have been introduced in MATH 231 (Calculus III) in more detail.
- Class Procedures: The majority of each class period will be lecture oriented. You are expected to: You are expected to: attend the lectures and to take your own lecture notes, read the textbook and work out problems from that section covered in class, do the homework problems.
- Attendance Requirements: It is important that you attend every class scheduled for this course. You are responsible for all announcements and material covered in this class as well as material from the textbook which is assigned but not covered in class.
- Computers: Any electronic devices such as laptops, tablets and cell phones cannot be used during the class. Please set your cell phones on vibrate. Calculators will be allowed on the tests, but you have to show your work in detail.
Grading
- Homework: There will be weekly homework assignments that will count for 25% of the grade.
- Tests: There will be two midterms tests and a final exam. Each test will count for 25% of the total grade.
- Make-ups: Make-up exams will be given only in cases of extremely properly documented emergencies. Late homework will not be accepted.
- Evaluation: Grades will be determined on a 100 point scale. Those point totals near cutoff will be individually considered for the next higher grade. I do reserve the right to add some extra points depending on the class participation and outstanding exam performance.
Changes: The course plan may be modified during the semester. Such modifications will be announced in advance during class periods. You are responsible for keeping abreast of such changes.
Remarks: This course is cumulative and it is assumed that all earlier parts covered are liable for any exam. It is strongly advised that you start working on this course from the very beginning. The course moves at a fast place, so it is very hard to catch up if you get behind.
Counseling and Disability Services. Reasonable Accommodations: New Mexico Tech is committed to protecting the rights of individuals with disabilities. Qualified individuals who require reasonable accommodations are invited to make their needs known to the Office of Counseling and Disability Services (OCDS) as soon as possible. In addition, New Mexico Tech offers mental health and substance abuse counseling through the Office of Counseling and Disability Services. The confidential services are provided free of charge by licensed professionals. To schedule an appointment, please call 835-6619.