Vector Calculus
| Code | School | Level | Credits | Semesters |
| MATH2032 | School of Mathematical Sciences | 2 | 10 | Autumn China |
- Code
- MATH2032
- School
- School of Mathematical Sciences
- Level
- 2
- Credits
- 10
- Semesters
- Autumn China
Summary
This module provides a grounding in vector calculus methods that are widely used in Applied Mathematics and Mathematical Physics. The module introduces the vector differentiation operations of gradient, divergence and curl, develops integration methods of scalar and vector quantities over paths, surfaces and volumes, and relates these operations to each other via the integral theorems of Green, Stokes and Gauss. The methods are then applied to the solution of Laplace's equation under simple boundary conditions by separation of variables. This module covers material fundamental to applied mathematics modules at levels 2, 3 and 4.
Target Students
Single Honours students from the School of Mathematical Sciences.
Classes
- One 1-hour seminar each week for 12 weeks
- One 2-hour lecture each week for 12 weeks
Activities may take place every teaching week of the Semester or only in certain weeks.
Assessment
- 10% Inclass Exam 1 (Written): Inclass test
- 90% Exam 1 (2-hour): 2-hour written examination
Assessed by end of autumn semester
Educational Aims
Thismodule aims to give students a sound grounding in the application of both differential and integral calculus to vectors, and to apply vector calculus methods and separation of variables to the solution of partial differential equations. Themodule is an important pre-requisite for a wide range of othercourses in Applied Mathematics.Learning Outcomes
A student who completes this course successfully will be able to:
L1 - evaluate and apply mathematical operations involving the gradient, divergence and curl, in Cartesian and other coordinate systems;
L2 - evaluate line, surface and volume integrals, in Cartesian and other coordinate systems;
L3 - state and apply Stokes' theorem, the divergence theorem and Green's identities;
L4 - solve Laplace's equation using separation of variables.
Conveners
- Dr Vladimir Toussaint