MA2VCNU-Vector Calculus

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:5
Semesters in which taught: Semester 1 module
Pre-requisites: MA1LANU Linear Algebra MA1DE1NU Differential Equations I or MA1CANU Calculus
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Current from: 2023/4

Module Convenor: Dr Peter Chamberlain
Email: p.g.chamberlain@reading.ac.uk

NUIST Module Lead: Vahid Darvish
Email: vdarvish@gmail.com

Type of module:

Summary module description:

The module involves differentiation of scalar and vector fields by the gradient, Laplacian, divergence and curl differential operators. A number of identities for the differential operators are derived and demonstrated. The module also involves line, surface and volume integrals. Various relationships between differential operators and integration (e.g. Green’s theorem in the place, the divergence and Stokes’ theorems) are derived and demonstrated.

NUIST Module leads:Ìý

Yanmei Xue (Atmospheric Science students)Ìý002433@nuist.edu.cn

Vahid DarvishÌý(Maths students)Ìývdarvish@gmail.comÌý

Aims:

To introduce and develop the ideas and methods of vector calculus.

Assessable learning outcomes:

By the end of the course, students are expected to be able:

• Demonstrate problem solving skills;


• Understand and apply the concepts of vector calculus;


• Derive and apply differential identities and integral theorems of vector calculus.

Additional outcomes:

Students will develop a thorough knowledge of mathematical notation, and an improved ability to interpret mathematical expressions. They will be able to manipulate different mathematical objects, such as scalar and vector quantities.

Outline content:

Vector Fields and vector differential operators. Scalar fields, vector fields, vector functions (curves). Vector differential operators: partial derivatives, gradient, Jacobian matrix, Laplacian, divergence, curl. Vector differential identities. Solenoidal, irrotational and conservative fields, scalar and vector potentials.

Vector integration. Line integrals of scalar and vector fields. Independence of path, line integrals for conservative fields and fundamental theorem of vector calculus. Double and triple integrals, change of variables. Surface integrals, unit normal fields, orientations and flux integrals. Special coordinate systems: polar, cylindrical and spherical coordinates.

Green's theorem in the plane, divergence and Stokes’ theorems and their applications.

Brief description of teaching and learning methods:

Lectures enhanced by self-study and peer-group learning.