BSc Materials Science and Engineering

This unit covers the topics in applied mathematics required to provide the necessary tools to study materials science at an undergraduate level.

 

The lectures cover:

 

Elementary functions:  linear functions, powers, polynomials, fractions, exponentials, logarithms,

 

Basic differential calculus:  differentials and derivatives, main properties, differentiation of elementary functions. Chain, Product and Quotient Rules. Differentiation of functions of several variables, partial derivatives  

 

Integral calculus:  definite and indefinite integrals, relation with differentiation, tables of integrals, methods of integration. Error function.

 

Application of differential calculus to functions: Taylor formula, approximate calculations, maxima / minima. 

To introduce the mathematical tools for symbolic and numerical manipulation and analysis required to study materials science at an undergraduate level. 

Differentiate (find differentials and derivatives of) all elementary functions and apply properties of differentiation to differentiate their arbitrary combinations; find differentials and partial derivatives for functions of several variables, including higher partial derivatives; apply differentials to approximate calculations and estimation of errors;

Use properties of elementary functions, solve simple equations, use the binomial formula, and express an arbitrary rational function as the sum of its whole part and partial fractions;

Recognize standard indefinite integrals; express definite integrals using the fundamental theorem of calculus, in particular, calculate areas under graphs; find antiderivatives satisfying initial value condition;

Apply integration methods such as integration by parts and substitution; solve integrals of rational functions by using partial fraction decomposition;

State the Taylor formula for the standard list of functions; find Taylor expansion with a small number of terms for a given function; apply Taylor expansions to finding limits and approximate calculations.

 

This unit covers the topics in applied mathematics required to provide the necessary tools to study materials science at an undergraduate level.

The lectures cover:

Elementary functions: linear functions, powers, polynomials, fractions, exponentials, logarithms,

Basic differential calculus: differentials and derivatives, main properties, differentiation of elementary functions. Chain, Product and Quotient Rules. Differentiation of functions of several variables, partial derivatives  

Integral calculus: definite and indefinite integrals, relation with differentiation, tables of integrals, methods of integration. Error function.

Application of differential calculus to functions: Taylor formula, approximate calculations, maxima / minima. 

Assessment - Coursework - 3 hours

Assessment - Exam - 2 hours

Lecture - 11 hours

Tutorial - 11 hours

Independent Study - 47 hours

 Assessment - Revision/preperation - 26 hours

Written exam - 70%

3 online tests each worth 10%

“Mathematical techniques: An introduction for the engineering, physical and mathematical sciences” D.W. Jordan and P. Smith, 2008, 4th ed, Oxford University Press: Oxford.

 “Engineering mathematics” K.A. Stroud and D.J. Booth, 2013, 7th ed, Palgrave Macmillan: Basingstoke. (available as an e-book from the library)

HELM (Helping Engineers Learn Mathematics), available at http://www.maths.manchester.ac.uk/study/undergraduate/information-for-current-students/service-teaching/helm/ 

Tuition fees for home students commencing their studies in September 2027 will be £10,050 per annum. Tuition fees for international students will be £41,900 per annum.

For general information please see the undergraduate finance pages.

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

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

For information about scholarships and bursaries please visit our undergraduate student finance pages and our the Department funding pages.