This module covers the classical theory of vector calculus. Topics covered include gradient, divergence and curl, areas of surfaces and integrals over surfaces. Three central theorems of the subject, Green's Theorem, the Divergence Theorem, and Stokes' theorem, are developed and various examples are given including applications to electromagnetism and Maxwell's equations. A more detailed syllabus is as follows:
Brief review of Vectors, including scalar and cross products.
Definition of gradient, divergence and curl. Examples.
Brief review of double integrals (including change of variables), triple integrals.
Path and line integrals.
Areas of surfaces, integrals over surfaces.
Green's Theorem (sketch proof included but not examinable).
Divergence Theorem.
Stokes Theorem.
Applications and examples.
Maxwell’s equations.
Brief review of Vectors, including scalar and cross products.
Definition of gradient, divergence and curl. Examples.
Brief review of double integrals (including change of variables), triple integrals.
Path and line integrals.
Areas of surfaces, integrals over surfaces.
Green's Theorem (sketch proof included but not examinable).
Divergence Theorem.
Stokes Theorem.
Applications and examples.
Maxwell’s equations.
- Module Supervisor: Georgi Grahovski