BSc/MEng Materials Science with an Integrated Foundation Year

The Foundation Year Bursary  is available to UK students who are registered on an undergraduate foundation year here and who has had a full financial assessment carried out by Student Finance.

Details of country-specific funding available to international students can be found within our  International country profiles .

The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability, therefore, we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.

For information about scholarships please visit our  undergraduate student finance pages  and the Department funding pages that you intend to progress to after successfully completing the Foundation Year.

To provide an elementary second-semester course in calculus and algebra to students entering the university with no post-GCSE mathematics in the Foundation Year.

On completion of this unit successful students will be able to:

- define complex numbers and sketch them using the Argand Diagram

- perform arithmetic operations on complex numbers and compute their moduli, arguments and conjugates

- express complex numbers in their polar and exponential forms and perform computations using these expressions

- define arithmetic, geometric and binomial sequences, evaluate their sums and compute convergent series

- define binomial coefficients, write binomial formula and apply it in integration exercises

- write Taylor and Maclaurin Series and apply them to compute limits

- apply implicit, logarithmic and parametric differentiation in differentiation exercises

- write integration by parts and integration by substitution formulae and apply them in integration exercises

- compute examples of improper integrals

- express improper rational functions as proper rational functions

- find partial fraction coefficients for proper rational functions

- apply the algorithms of simplifying improper rational functions to compute their integrals

Complex Numbers (5 lectures) :

• Definition.
• Arithmetic operations in Cartesian form.
• Argand Diagram.
• Modulus, argument and conjugate.
• Polar and Exponential forms.

Sequences and Series (4 lectures)

• The notation of series
• Arithmetic and Geometric Series
• The role of convergence
• Binomial Series

Further Differentiation (4 lectures)

• Taylor and Maclaurin Series
• Implicit Differentiation
• Logarithmic Differentiation
• Parametric Differentiation

Further Integration (4-5 lectures)

• Reminder of basic integration
• Integration by parts
• Integration by substitution
• Improper integrals

Rational Functions and Partial Fractions (4-5 lectures)

• Simple Rational Functions (including distinction of proper / improper)
• Forms for Partial Fractions
• Techniques for finding partial fraction coefficients

Integration using partial fractions

Coursework 1 (week 4); Weighting within unit 10%

    Coursework 2 (week 10); Weighting within unit 10%

    End of semester 2 examination; Weighting within unit 80%

CROFT, A & DAVISON, R. 2010. Foundation Maths (5th ed.) Pearson Education, Harlow. (ISBN9780273730767)

This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  

Please see Blackboard / course unit related emails for any further updates