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Online course materials for MATH19731

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

Requisites

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

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