Foundation degrees

# Technology Mathematics

## Module summary

Module code: MATH1144
Level: 4
Credits: 30
School: Engineering and Science
Department: Engineering Science
Module Coordinator(s): Kaushika Hettiaratchi

## Specification

### Aims

The aim of this course is to consolidate and extend the students background knowledge so as to enable students to appreciate the use of mathematics as an engineering tool. A student’s level of knowledge and competence will be reinforced by applying basic mathematical methods to solve engineering problems and supported with an appropriate mathematical modelling and simulation tools. This course also aims to develop students understanding of the use and application of modelling and simulation tools to a range of engineering situations.

### Learning outcomes

On successful completion of this course a student will be able to:

1 Demonstrate an understanding of relevant mathematical concepts
2 Carry out relevant mathematical calculations by hand and with the use of software tools
3 Demonstrate an appreciation of simulation and modelling tools to support the application of mathematical techniques

### Indicative content

The topics listed under the indicative content below are the underpinning areas of knowledge and understanding that would be obtained from the course delivery (see: Learning and Teaching Activities). The content listed below is indicative
Foundations of Technology Mathematics

• Arithmetic: types of numbers, fractions, decimal numbers, powers, number systems, review of basic algebra, trigonometry, and logarithms;
• Introduction to Algebra: algebraic expressions, powers as related to logarithms, rules of logarithms, multiplication / division / factorisation of algebraic expressions;
• Expressions and Equations: evaluating expressions, independent variables, transposition of formulas, polynomial equations, remainder theorem, factorisation of quartic polynomials;
• Functions and Graphs: equations, cartesian and polar co-ordinates / axes, drawing a graph, use of a Excel / MATLAB for graph plotting;
• Linear Equations and Simultaneous Linear Equations: solution of simple (linear) equations , simultaneous linear equations with two unknowns (by substitution and by equating co-efficients);
• Differentiation: rates of change, critical values, basic concepts and operations, small increments and rates of change, partial differentiation;
• Integration: calculation of areas and volumes, multiple integration;
• Complex Numbers: Cartesian, polar and exponential forms, Argand diagrams;
• Matrices and Determinants: introducing matrices, matrix algebra, introducing determinants, value of a determinant, solving a stet of linear equations using matrices and determinants;
• Numerical Methods / Integration: roots of nonlinear equations: existence of solutions, bisection method, fixed-point iteration (simple iteration), convergence criteria, Newton - Raphson method and convergence of, the secant method, the trapezoidal rule, the multi-segment trapezoidal rule, Simpson's rule, the multiple-segment Simpson's rule;
• 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;

### Teaching and learning activity

Learning and teaching will be by a combination of lectures, tutorials and class sessions. The delivery of the course will be centred on a problem area that the students are expected to solve with the underpinning material supplied by lecture/tutorial delivery and the course page under the University’s Moodle system. Each topic will concentrate with the “problem of the week”: solve the particular problem by using the key mathematical topic(s). The listings in the indicative content for that week are examples of the concept(s) that needs to be covered in the problem posed to the student.

A typical contact week would be: Lecture / Tutorial (3hrs) and Practical / Laboratory Session (3hrs).

The first term will concentrate on fundamental mathematical principles so as to give 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. Each fundamental aspect of the topic for each week will be supported through mathematical software tools (Excel, MATLAB, or Mathcad). The results from a phase test (mock examination) in term 1 will indicate student’s current progress in the course.

The second term will concentrate on the application of mathematics from an engineering perspective. This can be achieved in a range of engineering subject contexts to help put the topic in a real-world perspective, for example, mechanics, structural analysis, the use of statistics in data analysis, numbers systems that are used in computer systems, communication and computer network systems, or the use of mathematics in business. The modelling assignment in this term will draw together the key concepts covered over the contact weeks in order to solve an engineering problem using appropriate mathematical software tools.

The examination after the end of term 2 will be the summative assessment of the course.

This course aims to meet the engineering benchmarking standards in the following areas:
IEng:
Underpinning Science and Mathematics, and Associated Disciplines: US2i
Engineering Analysis: EA1i, EA2i, EA3i, EA4i

### Assessment

Assignment - 40% weighting, 40% pass mark.
Learning outcome 3.
Outline Details - Modelling/simulator assignment using MATLAB / Excel

Examination - 60% weighting, 40% pass mark.
Learning outcomes 1 - 3.
Outline Details - 3 Hour paper.

In order to meet professional body requirements, students are expected to pass this course at 40% overall and with a minimum of 30% for each component.

Formative Assessment - Mock Examination (term 1).