# Modiwl ICE-1212:Foundation Engineering Maths

### Ffeithiau’r Modiwl

Rhedir gan School of Computer Science and Electronic Engineering

20 Credyd neu 10 Credyd ECTS

Semester 1 a 2

Trefnydd: Mr Matthew Day

### Amcanion cyffredinol

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.

### Cynnwys cwrs

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

### Meini Prawf

#### trothwy

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.

#### da

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.

#### ardderchog

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.

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.

### Dulliau asesu

In-class Test 2 10
In-class Test 4 10
End of semester examination 35
In-class Test 3 10
GWAITH CWRS Problem Set

Practical problems completed by hand.

25
PRAWF DOSBARTH In-class Test 1

Class Tests x 4.

10

Oriau
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

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