Related Course/s:

Aims & Objectives:

This unit aims:

• To introduce students to the computer package Mathematica.
• To provide students with the mathematical knowledge and skills to support their engineering studies.

Teaching Methods:

Lectures (36 Hours), Laboratory (Mathematica) (12 hours), Tutorials (12 hours)

Assessment:

Examinations (50%), Tests (30%), Mathematica Assignment (20%)

Generic Skills Outcomes:

• Ability to apply knowledge of basic science and engineering fundamentals
• Ability to communicate effectively, not only with engineers but also with the community at large
• Ability to undertake problem identification, formulation and solution

Content:

• Introduction to Mathematica (8%)
• Fourier Series (24%): Fourier series expansion, functions defined over a finite interval, differentiation and integration of Fourier series, complex form of Fourier series, engineering application.
• Fourier Transforms (16%): The Fourier transform, properties of the Fourier transform, the frequency response, transforms of the step and impulse functions, engineering application.
• Laplace Transforms (20%): The Laplace transform, properties of the Laplace transform, solution of differential equations, step and impulse functions, transfer-functions, engineering application.
• Vector Calculus (32%): Derivatives of a scalar point function, derivatives of a vector point function, line integrals, double integrals, surface integrals, volume integrals, Green's theorem in a plane, Gauss's divergence theorem, Stokes' theorem, engineering application.

Reading Materials:

James, G et al., Advanced Engineering Mathematics, 2nd edn, Addison-Wesley, 2000.