The aim of this module is to introduce some of engineering mathematics to students of electronic engineering and telecommunications. The course will be illuminated by lectures, practical laboratory sessions and assignments in MATLAB.

Learning Outcomes

After completing this module, students will be expected to be able to:

1.Recognise, and perform routine calculations with a number of special functions, including trigonometric, logarithmic and exponential functions.

2. Define and explain the operations of differentiation and integration, and use appropriate rules to find derivatives and integrals.

3. Execute basic operations with vectors (including products of vectors) and matrices (+, -, x, determinants, inverse), and solve systems of linear equations via matrices.

4. Execute basic operations with complex numbers (+, -, x, /, *), and convert between Cartesian and polar forms. Find roots of polynomials (real and complex).

5. Find the Fourier series of a given periodic function, and explain the concept of the spectrum of a periodic function.

Outline Syllabus

1. Special Functions

Polynomial, trigonometric, logarithmic and exponential functions

Powers and Logatithms; The inverse operations; Rules of logarithms

Right-angle triangles,;The quadratic function; Symmetry of functions and their graphs

Visualisation with MATLAB

2. Differentiation

The derivative function

Some comon derivativesFinding the derivative of combinations of functionsApplications of differentiation

Visualisation with MATLAB

3. Integration

The integral as the area under a graph

Finding integralsApplications of integrationnumerical methods of integrationNumerical integration with MATLAB

4. Vectors and Matrices

Vectors and vector quantities;

Basic vectors; Products of vectors;

Vector calculation (addition, substraction and multiplication)

Matrix calculations (addition, subtraction and multiplication)

The matrix form of a set of linear equations

Determinants and inversion of 2x2 matrices

Visualisation with MATLAB

5. Complex Numbers

The square-root of negative numbers, and the number j

Cartesian representation of complex numbers: addition, subtraction, multiplication and division;

Complex numbers and operations

Polar representation: multiplication and division, conversion between forms

Applications to A.C. Linear circuits

Complex arithmetic with MATLAB

6. Fourier Series

Periodic functions obtained by adding sinusoids

Sine and cosine seriesThe Fourier series of symmetric periodic functionsAmplitude and phase representation of a Fourier seriesComputation and visualisation of Fourier series with MATLAB