Module Title:   Mathematics 1b

Module Credit:   10

Module Code:   ENG5010M

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:   Professor A S Wood

Additional Tutor(s):   Associate college staff as appropriate

Prerequisite(s):   None

Corequisite(s):   None

Aims:
To provide a basis of knowledge and skills in introductory calculus required for the more advanced option units and to enable students to use techniques in fundamental calculus, statistics and probability 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.

 Study Hours: 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 calculus and statistical functions which underpin the numeric aspects of the programme.

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

apply the acquired the skills and techniques for problem-solving within standard engineering practice.

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

select and apply scientific method and implement systematic problem solving strategies.

 001. Assessment Type Duration Percentage Examination - closed book 2.00 100% Description 2.00 hour examination 900. Assessment Type Duration Percentage Examination - closed book 2.00 100% Description Supplementary assessment: 2 hour examination

Outline Syllabus:
Calculus
Differentiation: definition of derivative, standard functions, rate of change, product, quotient & chain rules; Integration: Area & inverse of differentiation, indefinite integral, constant of integration; standard integrals, algebraic & trig functions; definite integral & area under curves; Differentiation Techniques: Higher derivatives, logarithmic differentiation, implicit functions, inverse trigonometric & hyperbolic functions, partial differentiation; Integration Techniques: Substitution, partial fractions, integration by parts, reduction formulae; Applications: from maxima & minima, rates of change of temp, distance & time, elec capacitance, rms values, electric circuit analysis, electromagnetic field, velocity & acceleration, complex stress & strain, eng structures, simple harmonic motion, centroids, solids of revolution, second moments of area, moments of inertia, rules of Pappus, radius of gyration, thermodynamic work & heat energy; Eng Applications: torsion, motion, dynamic systems, oscillating systems, force systems, fluid flow, ac theory, electrical signals, information systems, transmission systems, electrical machines electronics.
Statistics
Data: Arrangement of data, histograms, central tendency, coding, average, dispersion, frequency polygons & curves; Probability: Empirical, laws, independent events, conditional, discrete distributions, permutations & combinations, binomial, Poisson, continuous distribution, normal curve; Regression, least squares regression, application to exp work, batch production, quality ctrl.

Version No:  2