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.
Recommended Reading :
- Spiegel, M. & S. Lipschutz. Vector Analysis, (2e) McGraw-Hill Education, 2009.
- Chatterjee, D. Vector Analysis, PHI Learning private limited, India, 2009.
- Davis, H.F. & Snider, A.D. An Introduction to Vector Analysis, C. Brown, New York, 1992.