Mathematics AE2X ENG2042
- Academic Session: 2018-19
- School: School of Engineering
- Credits: 10
- Level: Level 2 (SCQF level 8)
- Typically Offered: Semester 2
- Available to Visiting Students: Yes
This course covers techniques for evaluating line integrals in space, and the use of Green's theorem.
An introduction to vector calculus and vector fields is presented.
2 lecture hours per week
5 hours tutorials
Requirements of Entry
Mandatory Entry Requirements
Recommended Entry Requirements
Main Assessment In: April/May
The aims of this course are to:
■ introduce techniques for evaluating line integrals in space, and the use of Green's theorem
■ provide an introduction to vector calculus and vector fields, with particular interest in conservative and irrotational vector fields
■ application of the integral theorems to calculating surface integrals.
Intended Learning Outcomes of Course
By the end of this course students will be able to:
■ evaluate line integrals in 2 and 3 dimensions;
■ evaluate line integrals using Green's Theorem;
■ find a (unit) normal vector to a surface;
■ calculate the gradient of a scalar function;
■ calculate directional derivatives and find their maximum value;
■ state what a conservative vector field is, what a potential function is, and be able to calculate a potential function for a conservative vector field;
■ state when a vector field is solenoidal;
■ state Laplace's equation and define a harmonic function;
■ calculate the curl of a vector field;
■ solve simple identities involving gradient, divergence and curl;
■ state what an irrotational vector field is and the relationship between conservative and irrotational vector fields;
■ evaluate surface integrals using Gauss' Divergence Theorem.
Minimum Requirement for Award of Credits
Students must attend the degree examination and submit at least 75% by weight of the other components of the course's summative assessment.
Students should attend at least 75% of the timetabled classes of the course.
Note that these are minimum requirements: good students will achieve far higher participation/submission rates. Any student who misses an assessment or a significant number of classes because of illness or other good cause should report this by completing a MyCampus absence report.