Module Title:   Mathematics 1a

Module Credit:   10

Module Code:   ENG5001M

Academic Year:   2015/6

Teaching Period:   Semester 1

Module Occurrence:   A

Module Level:   FHEQ Level 4

Module Type:   Standard module

Provider:   Engineering

Related Department/Subject Area:   Engineering: Mathematics and Computing (not in use)

Principal Co-ordinator:   Dr A Wood

Additional Tutor(s):   Associated college staff as appropriate

Prerequisite(s):   None

Corequisite(s):   None

Aims:
To develop a basis of knowledge and skills for the further study of analytical methods and mathematics needed for the more advanced option units by enabling students to use fundamental algebra and trigonometry for the analysis, modelling and solution of (realistic) engineering problems.

Learning Teaching & Assessment Strategy:
Mathematical principles and calculation strategies will be developed and analysed in lectures and then applied, practised and discussed in tutorial and PC lab sessions. Practical skills are developed in lab sessions where assessment of this material also takes place. The wider Learning Outcomes of the modules are assessed in a final written examination.

Lectures:   24.00          Directed Study:   50.50           
Seminars/Tutorials:   12.00          Other:   0.00           
Laboratory/Practical:   12.00          Formal Exams:   1.50          Total:   100.00

On successful completion of this module you will be able to...

understand and explain algebraic and trigonometric functions that underpin numerical aspects of the degree programme.

On successful completion of this module you will be able to...

select and apply a range of mathematical principles to describe, model and analyse engineering problems.

On successful completion of this module you will be able to...

apply scientific method and systematic problem solving strategies.

  Examination - closed book 2.00 100%
 
  2 hour examination
  Examination - closed book 2.00 100%
 
  Supplementary assessment: 2 hour examination

Outline Syllabus:
Algebra
Polynomials: Polynomial algebra (Precis), partial fractions.
Functions: algebraic functions, exponential & logarithmic functions, reduction of exponential laws to linear form, solution of exponential hyperbolic & logarithmic equations, trigonometric & hyperbolic identities.
Sequences/series: notation, arithmetic & geometric sequences, limit of a sequence, sigma notation, sum of a series, arithmetic & geometric series, binomial theorem.
Standard power series, Maclaurin`s series, binomial series, L`Hopital`s rule.

Trigonometric functions
Functions: Review trigonometric ratios, Cartesian & polar co-ordinate systems, properties of the circle, radian measure, sinusoidal functions.
Applications: angular acceleration, centripetal force, angular velocity and frequency, amplitude & phase, complex waveforms using sinusoidal graphical synthesis, AC waveforms & phase shift.
Identities: Trigonometric & hyperbolic identities, double & compound angle formulae, converting products to sums & differences, trigonometric equations, simplifying complex expressions.

Version No:  3