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The aims of this module are to consolidate and extend the students background knowledge to enable them to apply mathematics in engineering contexts. A student’s level of knowledge and competence will be reinforced by applying mathematical methods to solve mathematical and engineering problems.

On successful completion of this module a student will be able to:
1. Understand the mathematical concepts which are used to describe and analyse engineering systems.
2. Undertake mathematical calculations and use the Excel environment to complement and present numerical design proposals and solutions.
3. Demonstrate and apply statistics in engineering design, quality, and process control.
4. Apply mathematical principles to solve problems in engineering.

Arithmetic and algebra: Review of basic algebra, logarithms, algebraic expressions, powers as related to logarithms, rules of logarithms, multiplication / division / factorisation of algebraic expressions. Equations and Graphs: Evaluating expressions, independent variables, transposition of formulas, polynomial equations, remainder theorem, factorisation of quadratic polynomials. Equations, cartesian and polar co-ordinates / axes, drawing a graph, use of Excel. Trigonometry: Trigonometric equations, amplitudes, and phase angles. Functions: Polynomial functions, quadratic functions, cubic functions, and exponential functions. Differentiation: Rates of change, chain rule, product rule and quotient rule. Standard differentials. First and second derivatives. Integration: calculation of areas and volumes, multiple integration, mean value, and root mean square values. Complex Numbers: Cartesian, polar and exponential forms, Argand diagrams. Vectors, Matrices and Determinants: Vectors, scalar and cross product, direction cosines, angle between vectors. Matrices, matrix algebra, determinants, solving linear equations using matrices. Data Presentation: bar charts, pie charts, vertical line graphs, scatter diagrams, cumulative frequency; Statistics: the interpretation and use of the mean, mode, median, range, variance, standard deviation on sets of data, method of least squares. Correlation and Regression: calculation of correlation coefficient; Probability: empirical, classical, first- and second-order moments of a probability distribution; Probability Distributions: Normal (Gaussian), Gamma, Poisson, etc;

Lecture:
Learning and teaching will be a combination of lectures, tutorials and workshop style sessions. A typical contact week will be a 2-hour lecture and tutorial session. The module will focus on fundamental mathematical principles to provide students with a firm foundation in the core principles required for an understanding of various mathematic concepts, how to carry out appropriate mathematical calculations, use appropriate mathematical notation and terminology, and then be able to manipulate expressions and equations in a suitable manner. The mathematics will also show use in a range of engineering contexts to help put the topics in a real-world perspective.

Coursework 1: 40% weighting, 40% pass mark.
Outcomes assessed: 1, 4.
Outline details: Problem solving activity with questions based on first term’s topics.

Coursework 2 - 60% weighting, 40% pass mark.
Outcomes assessed: 2 - 4.
Outline details: Problem solving activity with questions based on second term’s topics.

Nature of FORMATIVE assessment/task supporting student learning:
In-class tutorial assignments will be used to help students to practice solving problems in the topics in the lecture programme. One to one feedback will also be given. Supporting solutions to tutorial problems will also be provided on moodle.