# Mathematics AE2X ENG2042

• School: School of Engineering
• Credits: 10
• Level: Level 2 (SCQF level 8)
• Typically Offered: Semester 2
• Available to Visiting Students: Yes

#### Short Description

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.

#### Timetable

2 lecture hours per week
5 hours tutorials

#### Requirements of Entry

Mandatory Entry Requirements

None

Recommended Entry Requirements

None

None

None

#### Assessment

100% Examination

Main Assessment In: April/May

#### Course Aims

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.