## MATH 342 - Vector Calculus

Vector Calculus  - MATH 342

Class Meeting: Wednesday 0800 - 0930
Monday 1200 - 1330

Catalog Description:

Vector fields, differentiation of vector functions, the derivation as a linear transform, gradient of scalar function, inverse and implicit function theorem, directional derivative, divergence, curl, differential forms, linear integrals, Stokes theorem and Green’s Theorem with applications, orthogonal curvilinear coordinate systems, cylindrical, spherical and elliptic coordinate systems.

Course Objectives:

The aim is to provide the student with basic topics in Vector Analysis, where the focus on the notion of the Gradient, the Curl, and the Divergence of vectors. Study important theorems in Physics and applied Mathematics such as Gauss divergence theorem and its applications, Stocks theorem, Green’s theorems, and Green theorem in the plane. The course is ended by studying the curvilinear coordinate systems.
Intended Learning Outcomes (ILO’s)

Knowledge and understanding:

K1-Identify basic theorems and concepts of vector calculus.

K2-Classify mathematical problems and discuss them with appropriate theorems and concepts in problem solving.

K3-Define vector derivatives and vector field integration.

Intellectual abilities:

I1-Formulate problems using tools of Stokes and Green theorems.

I2-Evaluate integrals using different methods and techniques.

I3-Apply techniques of vector derivatives and vector integration to physical and mathematical problems.

I4-Apply theorems and rules of calculus to physical and mathematical problems.

Professional and Practical competencies:

P1-Solve many physical problems using tools of vector calculus manually.

P2-Operate and practice with problems in mathematics and physics using available techniques of vectors.

P3-Solve problems using skills, and tools of modern mathematics.

General and Transferable Skills:

S1-Communicate ideas effectively in graphical, oral, and written media

S2-Functioning in multi-disciplinary teams.

S3-Deal with Scientific material in English