Description

Maths 2 for Foundation

Description - summary of the module content

Module description

Now that you have completed Foundation Mathematics, you will be able to study techniques that are applied to current engineering problems. This module will introduce you to the techniques you will develop further in your engineering or mathematics degree: you will learn the basics of the mathematics used in the construction of machines, buildings or satellites; develop the skills in calculus needed for basic weather forecasting and climate studies; study the mechanics used for planning the movements of objects, such as car engines, trains pulling uphill or rockets launching into space; and the trigonometry used to design communications networks, aerials and medical treatments for diseases such as cancer.
If you study this module, you will also need to take INT0020 Maths 1

Module aims - intentions of the module

This module aims to provide a foundation in mathematics for students who intend to follow a degree programme in the areas of Mathematics, Engineering or related disciplines. It builds on the skills and knowledge developed in Foundation Mathematics. Students will be expected to manage their time successfully in order to complete a series of coursework and other tasks.

Intended Learning Outcomes (ILOs)

ILO: Module-specific skills

On successfully completing the module you will be able to...

• 1. Apply mathematical methods to solve problems requiring the use of algebraic and trigonometric formulae
• 2. Demonstrate recognition of and apply introductory techniques required in undergraduate mathematical courses
• 3. Demonstrate understanding of the basic principles of mathematics
• 4. Demonstrate understanding of the use of vectors in applications to geometry and mechanicsD
• 5. Apply techniques in calculus
• 6. Recognise when particular techniques are used in a variety of mathematical or engineering situations

ILO: Discipline-specific skills

On successfully completing the module you will be able to...

• 7. Demonstrate understanding of mathematical principles in Engineering and Mathematical disciplines
• 8. Construct models and solve problems which represent situations in science and engineering
• 9. Interpret answers to problems with appropriate accuracy

ILO: Personal and key skills

On successfully completing the module you will be able to...

• 10. Apply mathematical methods to address a well-defined problem
• 11. Communicate effectively in the written form

Syllabus plan

Syllabus plan

1. Vectors. The scalar product; Angle between two vectors. Cartesian co-ordinates of vector in 3 dimensions. The vector equation of a straight line. Resolving vectors into horizontal and vertical components.
2. Two-dimensional trigonometry. Solving trig equations for any angle in degrees in a given interval. Trigonometrical identities. Addition formula. Double angle formula. The sine and cosine rules. Solving equations of the form asinx +bcosx. Radian measure. Arc length and sector area.  Solving trig equations for any angle in radians for 0 < angle < 2π.
3. Polar co-ordinates. Converting between Cartesian and polar coordinates.
4. Introduction to complex numbers. Adding, subtracting, and multiplying. Complex conjugate.
5. Parametric equations. Drawing curves given by parametric equations.
6. Differentiation of sin x, cos x, tan x. Velocity and acceleration.  Differentiating functions given implicitly and parametrically. Simple Partial Differentiation (of 2 variables)
7. Integrations of trig functions. Use of trig identities to integrate functions such as cos²x. Application of integration to volumes of revolution.
8. Differential equations. Forming and solving simple differential equations. First order, variables separable differential equations. Numerical Solution of differential equations.
9. Mechanics. Variable Acceleration. Elastic collisions; Centre of mass; Simple harmonic motion.
10. Co-ordinate Geometry of Circles

Learning and teaching

Learning activities and teaching methods (given in hours of study time)

Details of learning activities and teaching methods

Assessment

Summative assessment (% of credit)

Details of summative assessment

Re-assessment

Details of re-assessment (where required by referral or deferral)

Re-assessment notes

The grade for the referred exam, and therefore the module grade, will be capped at 40%. Re-assessment grade will not include coursework marks. Deferred exams will not be capped and will include summative coursework marks in the final module grade.

Resources

Indicative learning resources - Web based and electronic resources

Berry, C., Hanrahan, V., Porkess, R. & Secker, P. (2004). MEI A2 Pure Mathematics C3-C4: MEI Structured Mathematics. London: Hodder and Murray.
Bryden, P. (2004). MEI Mechanics 1: MEI Structured Mathematics. London: Hodder and Murray.

Module has an active ELE page

Indicative learning resources - Other resources

Pledger, K., Attwood, G., MacPherson, A., Moran, B., Petran, J., Staley, G. & Wilkins, D. (2004). Core Mathematics 3: Heinemann Modular Mathematics. Oxford: Heinemann Educational.
Pledger, K., Attwood, G., MacPherson, A., Moran, B., Petran, J., Staley, G. & Wilkins, D. (2004). Core Mathematics 4: Heinemann Modular Mathematics. Oxford: Heinemann Educational.
Hebborn, J & Littlewood, J. (2004). Mechanics 1: Heinemann Modular Mathematics. Oxford: Heinemann Educational.

Key words search

Mathematics, Trigonometry, Mechanics; Differentiation; Integration