## Mathematics 1G2

 Unit code: MATH19732 Credit Rating: 10 Unit level: Level 1 Teaching period(s): Semester 2 Offered by School of Mathematics Available as a free choice unit?:

Co-Requisite

#### Aims

Build on topics from semester 1 to develop 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), peer-assisted study sessions (PASS)

#### Learning outcomes

Knowledge and understanding:

• Solve straightforward problems involving vectors, complex numbers, matrices, elementary differentiation, integration and partial differentiation.
• Relate vector notation to directions in a multi-dimensional space.

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 trigonometric functions.
• Solve simple systems of first- and second-order partial differential equations.
• Manipulate vectors and matrices.
• Calculate the mean, variance and standard deviation for common distributions of values for a single variable.
• Measure and quantify the correlation between two variables.
• Quantify the uncertainty of a value after mathematical manipulation.

Practical skills:

• Construct Argand diagrams to represent complex numbers.
• Use vectors and matrices in real world settings.
• Model (relevant) scientific and engineering problems using differential equations.
• Apply core concepts from probability and statistics to (relevant) real world problems.

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

6 written or computerised assignments

#### 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:

• Vectors, matrices and their manipulations, including cross and dot products. (4)
• Trigonometry, including simple identities. (3)
• Complex numbers, including their addition and multiplication, their representation in Argand diagrams, and the relationship between complex exponential functions and trigonometric functions. (5)
• Common solutions to first- and second-order ordinary and partial differential equations. (6)
• Probability, standard distributions, variance, standard deviation, regression, correlation  (4)

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

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 - 24 hours
• Tutorials - 11 hours
• Independent study hours - 0 hours

#### Teaching staff

Carolyn Dean - Unit coordinator