*GENG0021 *Mathematics for Science & Engineering

## Module Overview

This module offers an introduction to the mathematics that supports science and engineering to students entering the Foundation Year with SPM or equivalent qualifications.

### Aims and Objectives

#### Module Aims

The aims of this module are to consolidate basic mathematical concepts and methods in the areas of number, algebra, trigonometry, graphical techniques and in an introduction to differentiation and integration. These are the foundation of mathematics for science and engineering. These concepts and methods will be applied to the solution of simple practical problems.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

- basic mathematical laws and concepts covered in the module;
- mathematical knowledge required to solve practical science and engineering problems;
- mathematical techniques are used in practical science and engineering problems.

##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

- select and apply appropriate mathematical methods to solve abstract and real-world problems;
- show confidence in manipulating mathematical expressions, setting up and solving equations.

##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

- manage your own learning;
- apply mathematical methods to solve problems;
- communicate mathematical ideas and concepts

### Syllabus

Number Revision of number systems. - Base 10 & 2. Simple binary addition & subtraction. Evaluation and simplification of numerical equations & numerical fractions including surds. Rationalise surds. Numbers raised to a power. Significant figures. - Evaluations should be mostly non--calculator based. Apply to areas & volumes of simple geometric shapes etc. Algebra Transposition of formulae. Will include the use of cross multiplication, multiplying brackets, common factors. - Use where possible of scientific and engineering formulae e.g. E = Q/(4πεor2) ; s = ½(u + v)t ; RT = R1R2/(R1+R2) Evaluation and simplification of algebraic fractions and indices. - Addition, subtraction, multiplication & division of algebraic fractions, but not ‘long’ division. Simple inequalities. Set up and solve linear simultaneous equations in two unknowns using substitution and elimination. - Apply to practical problems. E.g. currents in a circuit Set up and solve simple quadratic equations using factorisation and formula. - Apply to practical problems. E.g. s = ut + ½at2. Introduction to Boolean Algebra. AND, OR, NOT, EOR functions. Rules and simplification of Boolean expressions. Develop equations from written parameters. - Apply to practical problems Trigonometry Use 3 basic trigonometric functions for any angle (positive or negative). Graphs of sine & cosine functions of the form y = Asin(nx ±φ). Understand definition of a radian and be able to convert degrees radians. - Can be applied to problems such as simple harmonic motion, ac voltages & currents etc. The sine and cosine rules. Area of triangle = ½ bh = ½ absinC. - apply to practical problems. E.g. triangle of forces Solving simple trig equations in a given interval. Solutions may require use of basic trig Identities sin/cos=tan sin2+cos2=1 - Graphical methods as well as calculated solutions can be used Graphs Use rectangular coordinates to plot graphs of algebraic equations. Find gradients and equations of straight line graphs. Use graphs to solve pairs of simultaneous equations and roots of quadratic equations. - Use of Excel spreadsheets to plot graphs would be acceptable Plot experimental data. Obtain laws for linear relationships. Produce straight line graphs by plotting against x2, 1/x, ln(x) etc. - Use of Excel spreadsheets to plot graphs would be acceptable. Apply graphs of sine and cosine functions to add 2 waves of same or different frequencies. - Use of principle of superposition. Two sine waves of similar frequencies could be used to show principle of ‘beat frequency’ Introduction to Differentiation & Integration Basic differentiation by rule only. Obtain gradients of curves, stationary points, increasing or decreasing functions. Integration of simple functions by rule only. Determine areas under curves - Apply to simple practical examples e.g. acceleration and distance travelled from velocity time graphs Research a topic Students will work in small groups to produce a poster depicting one or more practical applications of mathematics in science and engineering. - Students may choose the application of mathematics in any branch of science or engineering.

### Learning and Teaching

#### Teaching and learning methods

Learning activities include individual work on exercises, supported by tutorial/workshop sessions with tutors. group presentation. lectures, supported by example sheets; tutorials/workshops; printed notes available through Blackboard and/or through your module lecturer. Teaching methods include: lectures, supported by example sheets; tutorials/workshops; printed notes available through Blackboard and/or through your module lecturer

Type | Hours |
---|---|

Teaching | 98 |

Independent Study | 77 |

Total study time | 175 |

#### Resources & Reading list

H. Neiland D. Quadling. Cambridge Advanced Mathematics Core 1 & 2.

Mark Rowland. Bridging GCSE & A Level Maths: Student Book.

### Assessment

#### Assessment Strategy

There is no pass/fail assessment in this semester. You will be expected to complete all assessment elements. You will be given extensive feedback on your performance to prepare you for the following semesters.

#### Summative

Method | Percentage contribution |
---|---|

Weekly exercises / tests and assignments | 100% |