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?:

Requisites

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.

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

Teaching staff

Carolyn Dean - Unit coordinator

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