AMAT 11223: Vector Analysis

Course Code : AMAT 11223

Title : Vector analysis

Pre-requisites : A/L Combined Mathematics

Learning Outcomes :

At the end of the course the student will be able to

1. demonstrate knowledge of coplanarity of three vectors, orthogonal vectors, vector product.
2. calculate unit vectors, scalar and vector products, triple scalar & vector products, arc lengths, unit tangent and normal vectors.
3. define Gradient, Divergence, Curl Operators.
4. calculate derivatives of vector fields and normal and directional derivatives of surfaces.
5. identify conservative, solenoidal, rotational and irrotational vector fields.
6. apply Fundamental Theorem of Line Integrals to compute work.
7. establish the Divergence and Stoke’s theorems.

Course Content:

Vector Algebra:

- - Introduction to vectors, Condition for coplanarity of three vectors and collinearity of two vectors, Orthogonal triads of unit vectors, Scalar and vector products, Triple scalar and vector products, Solution of vector equations.

Vector Analysis:

- - Scalar and vector fields, Differentiation of vector functions, sketch curves defined by position vectors, arc length, unit tangent and unit normal vectors of curves, Gradient, Divergence and Curl operators and identities involving them, Surfaces and normal, Directional Derivative, Conservative, solenoidal, rotational & irrotational vector Fields, Sketching 3D objects, Line Integrals, Fundamental Theorem of Line Integrals, Area Integrals, Surface Integrals, Volume Integrals, Divergence and Stokes’ theorems.

Method of Teaching and Learning : A combination of lectures and tutorial discussions.

Assessment : Based on tutorials, tests and end of course examination.