This module covers the classical theory of vector calculus, building on knowledge in MA206 and MA114. Topics covered include gradient, divergence and curl, areas of surfaces and integrals over surfaces. Two central theorems of the subject, due to Green and Stokes, are developed, the proofs are outlined and various applications and examples are given. The last one-third or so of the module is devoted to s sutained application of the ideas, in (e.g.) fluid dynamics. 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).
Stokes Theorem (sketch proof included but not examinable).
Applications and examples.
Applications in an area of the lecturer's choosing (e.g. fluid dynamics or electrodynamics).
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).
Stokes Theorem (sketch proof included but not examinable).
Applications and examples.
Applications in an area of the lecturer's choosing (e.g. fluid dynamics or electrodynamics).