# Mechanical Engineering with Aeronautics BEng/MEng

## Mathematics AE2X ENG2042

**Academic Session:**2020-21**School:**School of Engineering**Credits:**10**Level:**Level 2 (SCQF level 8)**Typically Offered:**Semester 2**Available to Visiting Students:**No**Available to Erasmus Students:**No

### 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

### Excluded Courses

None

### Co-requisites

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.