## MAS241 Mathematics II (Electrical)

Note: Information for future academic years is provisional. Timetable information and teaching staff are especially likely to change, but other details may also be altered, some courses may not run at all, and other courses may be added.

Semester 1, 2022/23 | 10 Credits | ||||

Lecturer: | Prof Vladimir Bavula | Timetable | Reading List | ||

Aims | Outcomes | Assessment | Full Syllabus |

**Prerequisites:** MAS156 (Mathematics (Electrical and Aerospace))

The following modules have this module as a prerequisite:

MAS381 | Mathematics III (Electrical) |

## Aims

- To consolidate previous mathematical knowledge.
- To develop the mathematical techniques used in second year electrical and aeronautical engineering courses.
- To lay the foundations for the study of vector calculus.

## Learning outcomes

- Ability to understand complex valued functions, and functions of a complex variable.
- Ability to compute Laplace and Fourier transforms and apply the Laplace transform to solve differential equations.
- Ability to compute Fourier series, and Fourier sine and cosine series.
- Ability to find partial and directional derivatives.
- Ability to apply the chain rule to functions of multiple variables.
- Ability to find critical points of a function of two variables and determine their nature.
- Ability to compute double and triple integrals directly and/or by changing the order of integration/changing variables.
- Ability to compute the gradient of a scalar field, understand and apply its geometric interpretation.
- Ability to compute divergence and curl of a vector field.

22 lectures, 11 tutorials

## Assessment

One formal 2 hour written examination.

## Full syllabus

**Basics**- Review of complex numbers and complex valued functions
**Transforms**- Important real valued functions including the Heaviside, unit impluse and delta functions; complex Laplace transform and its properties; convolution; applications of the Laplace transform; the Fourier transform and its properties.
**Fourier series**- Periodic functions; Fourier series; even and odd functions; Fourier cosine and sine series; complex exponential Fourier series.
**Functions of several variables**- Review of partial derivatives; directional derivatives; chain rule; gradient vector and its geometric interpretation; higher order derivatives and equality of mixed derivatives; determining the nature of critical points for functions of two variables.
**Integration**- The definite integral; double and triple integrals, their geometric interpretations and properties; change of order of integration; change of variables; surface areas; cylindrical and spherical polar coordinates.
**Vector fields**- Vector and scalar fields; divergence and curl; elementary properties of divergence and curl.

## Reading list

Type | Author(s) | Title | Library | Blackwells | Amazon |
---|---|---|---|---|---|

B |
Dennis Zill, Warren Wright | Advanced Engineering Mathematics | |||

B |
Robert Adams | Calculus: A Complete Course |

(

**A**= essential,

**B**= recommended,

**C**= background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.