# Module ICE-1212:Foundation Engineering Maths

### Module Facts

Run by School of Computer Science and Electronic Engineering

20 Credits or 10 ECTS Credits

Semester 1 & 2

Organiser: Mr Matthew Day

### Overall aims and purpose

This module aims to provide:

• a grounding in engineering mathematics.
• an understanding of the fundamental mathematics underlying all engineering.
• experience dealing with the mathematical structures under-pinning engineering systems.
• a revision of and practice with elementary algebra.

### Course content

Indicative content includes:

Differentiation: Revision of notation for sets and functions. Revision of basic algebra techniques. The limit of a real function at a point. Derivative as gradient: tangent lines. Rules of differentiation. Polynomial, exponential, logarithmic, and inverse functions. Local maxima, minima, points of inflection. Using software to sketch graphs of functions. Parametric curves; polar coordinates. Solution of equations by iteration

Integration: Integration as anti-differentiation. The area under a curve. Integration by parts and by substitution. Methods of numerical integration. Mean and root-mean-square values. The method of partial fractions. Integrals of the form f’(x)/f(x) and f’(x).f(x). Distance, velocity and acceleration. Parametric curves: arc length and area. Maclaurin and Taylor series expansions. Arithmetic with Maclaurin series.

Number Systems: Integers, rationals and real numbers. Fractions ↔ infinite decimal expansions. j = √( -1), solving quadratic equations. Complex arithmetic; Argand diagram. Revision of trigonometric functions. Complex functions: bilinear; exp; log. exp(jθ) = cos(θ) + j.sin(θ). De Moivre’s theorem: n-th roots

Functions of two variables: Examples of real functions of two variables. Using software tools to sketch surfaces. Partial differentiation and tangent planes. Maxima, minima and saddle points. Solution of exact differential equations. Maclaurin series for f(x,y).

Probability and Statistics: Arrangement of data; histograms; mean; mode; and median. Dispersion; range; standard deviation. Normal distribution; standardized normal curve. ; Probability; Independence; Mutually exclusive events; Probability density functions; The binomial distribution; The Poisson distribution; The Gaussian distribution.

Matrices: Matrix definition; Operations on Matrices; Determinants; Matrix inversion; Solutions of linear equations using matrices;

Vectors and vector fields: Vector definition; Operations on vectors. Vectors in 2D and 3D; Representation of lines and planes using vectors; Scalar and vector products of two vectors; Angle between two vectors; Scalar fields; Vector fields; Gradient of a scalar field

### Assessment Criteria

#### threshold

Equivalent to 40%. Uses key areas of theory or knowledge to meet the Learning Outcomes of the module. Is able to formulate an appropriate solution to accurately solve tasks and questions. Can identify individual aspects, but lacks an awareness of links between them and the wider contexts. Outputs can be understood, but lack structure and/or coherence.

#### good

Equivalent to the range 60%-69%. Is able to analyse a task or problem to decide which aspects of theory and knowledge to apply. Solutions are of a workable quality, demonstrating understanding of underlying principles. Major themes can be linked appropriately but may not be able to extend this to individual aspects. Outputs are readily understood, with an appropriate structure but may lack sophistication.

#### excellent

Equivalent to the range 70%+. Assemble critically evaluated, relevent areas of knowledge and theory to constuct professional-level solutions to tasks and questions presented. Is able to cross-link themes and aspects to draw considered conclusions. Presents outputs in a cohesive, accurate, and efficient manner.

### Learning outcomes

1. Apply the basic rules and techniques of differential calculus and its application in engineering.

2. Apply the basic rules and techniques of integral calculus and its application in engineering.

3. Demonstrate the basics, rules and techniques of complex number algebra and its application in engineering.

4. Apply basic operations in vector algebra (Cartesian and geometric representations) to represent lines and planes, calculate the gradient of a scalar field using partial derivatives.

5. Use basic operations of matrix algebra, determinants and their application in solving systems of linear equations.

6. Demonstrate the basics, rules and techniques for partial differentiation.

7. Apply theory of probability and statistics to calculate averages, data spread and the probability of different events.

8. Use of software packages for statistical, probabilistic and matrix calculations.

### Assessment Methods

Type Name Description Weight
In-class Test 2 10
In-class Test 4 10
End of semester examination 35
In-class Test 3 10
COURSEWORK Problem Set

Practical problems completed by hand.

25
CLASS TEST In-class Test 1

Class Tests x 4.

10

### Teaching and Learning Strategy

Hours
Tutorial

Supporting tutorial (1 hr x 24 weeks)

24
Private study

Exercise questions and solutions are available to students for private study after each lecture.

80
Lecture

2 x 2 hours Lectures (lecturing+ student in-class practice style), over 24 weeks

96

### Transferable skills

• Literacy - Proficiency in reading and writing through a variety of media
• Numeracy - Proficiency in using numbers at appropriate levels of accuracy
• Computer Literacy - Proficiency in using a varied range of computer software
• Information retrieval - Able to access different and multiple sources of information
• Critical analysis & Problem Solving - Able to deconstruct and analyse problems or complex situations. To find solutions to problems through analyses and exploration of all possibilities using appropriate methods, rescources and creativity.

### Subject specific skills

• Apply underpinning concepts and ideas of engineering;
• Solve problems logically and systematically;
• Use both verbal and written communication skills to different target audiences;
• Analyse and display data using appropriate methods and mathematical techniques;
• Demonstrate familiarity with relevant subject specific and general computer software packages.