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. 

The unit aims to:

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

On the successful completion of the course, students will be able to:  

ILO 1

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;

ILO 2

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;

ILO 3

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;

ILO 4

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

ILO 5

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.

1 review session and 1 tutorial per week, 4 hours of private study including watching the videos, reading the notes and doing the quizzes in the VLE. 

Coursework - 1-2 hours, 30% weighting

Final exam - 2 hours, 70% weighting

“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/