## MAS241 Mathematics II (Electrical)

Semester 1, 2017/18 | 10 Credits | ||||

Lecturer: | Dr Fionntan Roukema | 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 | Blackwells | Amazon | |

B |
Robert Adams | Calculus: A Complete Course | Blackwells | Amazon |

(

**A**= essential,

**B**= recommended,

**C**= background.)

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