## Mathematics 1G1

 Unit code: MATH19731 Credit Rating: 10 Unit level: Level 1 Teaching period(s): Semester 1 Offered by School of Mathematics Available as a free choice unit?: N

Co-Requisite

#### Aims

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

#### Teaching and learning methods

Lectures, example classes, recommended textbooks, web resources, past exam papers, electronic supporting information (Blackboard), electronic assessment (STACK), peer-assisted study sessions (PASS)

#### Learning outcomes

Knowledge and understanding:

• Solve straightforward problems involving, functionselementary differentiation, integration and partial differentiation.
• Recognise how precision and uncertainty is represented.

Intellectual Skills :

• Show improved logical reasoning, problem solving and ability in applied mathematics.
• Calculate numerical answers to mathematical problems covered in lectures and tutorials.
• Carry out symbolic manipulations involving polynomials, exponentials, and logarithms. Integrate and differentiate functions that are common to materials science.
• Quantify the uncertainty of a value after mathematical manipulation.

Practical Skills:

• Express quantities using scientific and engineering notation, and interconvert between the two.
• Plot data graphically using histograms, scatter plots and line plots.
• Carry out ‘back of the envelope’/order-of-magnitude estimations mentally or on paper.

Transferable Skills and Personal Qualities:

• Apply the mathematical techniques covered in this unit to concurrent and subsequent materials science units.
• Convert between units.
• Work effectively in a group to solve problems.

#### Assessment methods

• Other - 30%
• Written exam - 70%

#### Assessment Further Information

2 Hour  Exam

Closed-book, unseen examination consisting of six compulsory questions (10 marks each) and a choice of two of three longer questions (20 marks each).

Coursework

Diagnostic Followup submitted around week 4. Four subsequent assignments – mixture of written tests (40 mins) and computerised work.

#### Syllabus

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 many variables, partial derivatives (6).
• Integral calculus:  definite and indefinite integrals, relation with differentiation, tables of  integrals, methods of integration. Error function (6).
• Application of differential calculus to functions: Taylor formula, approximate calculations, maxima / minima (4).

The tutorials cover typical mathematical problems faced in materials science and revolve around students attempting work in advance.

#### Recommended reading

“Mathematical techniques: An introduction for the engineering, physical and mathematical sciences” D.W. Jordan and P. Smith, 1997, 2ed, Oxford University Press: Oxford.

“Engineering mathematics” K.A. Stroud and D.J. Booth, 2007, 6th ed, Palgrave Macmillan: Basingstoke.

“Calculus made easy” S.P. Thompson, 1914, 2ed, MacMillan and Co.: London. (Available free at http://www.gutenberg.org/ebooks/33283)

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

#### Study hours

• Lectures - 22 hours
• Tutorials - 10 hours
• Independent study hours - 65 hours

#### Teaching staff

Carolyn Dean - Unit coordinator