Related Course/s:

Aims & Objectives:

This unit aims to:

• To provide students with mathematical knowledge and skills needed to support their concurrent and subsequent engineering studies
• To provide students with a thorough grounding in mathematics
• To lay a foundation for further studies in engineering mathematics

Teaching Methods:

Lecture/tutorials (48 hours), seminars (12 hours)

Assessment:

Assignments (10-15%), Tests (25-35%) and closed book exam (50-60%).

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:

• Vectors: Basic operations in 2D, introduction to 3D space, basic vectors in 3D, products, projections, angular velocity, torque; application to lines and planes in 3D.
• Algebra: Equations in one variable: algebra, graphical solution, numerical solution; inequations in one variable: algebra, graphical solution; transformation of equations and formulae.
• Functions and Graphs: Review of functions and graphs, including polynomials, rational functions and a review of trigonometry, problems of domain, limits, asymptotes, partial fractions, inverse trigonometric functions, hyperbolic and inverse hyperbolic functions.
• Differentiation: Definition and interpretation, standard derivatives, rules, implicit and logarithmic differentiation, optimisation, detailed graphing including inflection, rates, approximations, error analysis, Taylor polynomials, indeterminate forms, limits, Newton-Raphson method.
• Integration: Anti-differentiation, substitution, parts, general techniques, use of extensive tables, areas, centroids, volumes, arc lengths, surface areas, numerical integration.

Reading Materials:

Course notes will be available.
Graphical calculator.