Course Description
Vector differentiation, vector integration, gradient, divergence, curl, Stokes' theorem, Green's theorem, and curvilinear coordinates will be used to solve classical problems in engineering, physics, astronomy, atmospheric sciences, and physical oceanography.
Athena Title
VECTOR ANALYSIS
Non-Traditional Format
The course is one of a set of one-credit modules. It is designed to be offered during the five weeks of fall semester.
Prerequisite
(MATH 2500 or MATH 2270) and (PHYS 1251 or PHYS 1211-1211L or PHYS 1311-1311L)
Pre or Corequisite
PHYS 1252 or PHYS 1212-1212L or PHYS 1312-1312L
Semester Course Offered
Offered every year.
Grading System
A - F (Traditional)
Course Objectives
Upon successful completion of this course, the student will be able to: 1. Evaluate line, surface, and volume integrals 2. Perform vector calculations in Cartesian, cylindrical polar, and spherical polar coordinates 3. Calculate the gradient, divergence, and curl 4. Apply the divergence and Stokes' theorem to common problems in engineering and physics 5. Apply vector calculus to classical problems in heat transfer, electromagnetism, solid mechanics, and fluid mechanics.
Topical Outline
Lecture 1: Dot product; Cross product; Scalar triple product; Vector triple product; Scalar and Vector fields Lecture 2: Line integrals; Surface integrals Lecture 3: Volume integrals Lecture 4: Gradient; Divergence Lecture 5: Curl; Kronecker delta; Alternating tensor notation Lecture 6: Applications of suffix notation (Kronecker delta and alternating tensor notation) Lecture 7: Green's Theorem Lecture 8: Stokes' Theorem Lecture 9: Cylindrical polar coordinates; Spherical polar coordinates Lecture 10: Surface and volume integrals using cylindrical and spherical polar coordinates Lecture 11: Applications to heat transfer Lecture 12: Applications to electromagnetism Lecture 13: Applications to continuum mechanics Lecture 14: Applications to solid mechanics Lecture 15: Applications to fluid mechanics
Syllabus