Engineering Mathematics 1


Unit code: CHEN10011
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

None

Aims

The unit aims to: 

Provide the background mathematical skills required for subsequent chemical engineering courses in mathematically oriented topics.  Engineering applications are to be introduced where relevant.

 

Overview

Calculus:

Brief review of differentiation (single variable)

Integration (single variable):  exact, numerical, applications

Taylor series (single variable)

Vectors algebra (includes scalar and vector products).

Partial differentiation:  tangent planes, change of variables, stationary points.

Complex numbers.

 

Statistics:

Nature of errors

Summarising data:

-     Measures of central tendency – mean, median, mode

-     Measures of dispersion – variance, standard deviation, median absolute deviation

Combination and propagation of errors

Regression and correlation

Correlation coefficient

Least squares fitting

Software packages:

-     Excel/Openoffice Calc

Teaching and learning methods

The course will consist of lectures and tutorials on both calculus and statistics.

 

Learning outcomes

 

Category of outcome

Students should be able to:

Knowledge and understanding

Understand the different types of variable and the different types of error.

Understand the basic concepts of calculus.

Understand the basic concepts of statistics.

 

Intellectual skills

Understand where it is appropriate to use calculus and statistics.

 

Practical skills

Differentiate functions of one or more variables

Expand functions in series form

Manipulate partial derivatives

Manipulate vectors

Manipulate complex numbers

Obtain numerical solutions to problems in some important engineering subject areas

 

Transferable skills and personal qualities

Apply mathematical skills to solve relevant engineering problems.

 

 

Knowledge and understanding

Knowledge and Understanding

  • Understand the different types of variable and the different types of error (systematic and indeterminate)
     
  • Understand how errors combine and propagate
     
  • Understand the basic concepts of calculus

Intellectual skills

Intellectual Skills

  • Understand where it is appropriate to use calculus and statistics

Practical skills

Practical Skills

  • Differentiate functions of one or more variables
     
  • Differentiate functions of one or more variables
     
  • Expand functions in series form
     
  • Manipulate partial derivatives
     
  • Manipulate vectors
     
  • Manipulate complex numbers
     
  • Obtain numerical solutions to problems in important engineering subject areas.

Transferable skills and personal qualities

Transferable Skills and Personal Qualities

  • Apply mathematical skills to solve relevant engineering problems

Assessment Further Information

 

 

Assessment task

Length

Weighting within unit (if relevant)

Coursework (Diagnostic follow-up and online assessment)

 

Examination

---------------

 

 

1.5 hours

20%

 

 

80%

 

 

Recommended reading

Stroud KA, Engineering Mathematics, 5th Edition, Palgrave, 2001. ISBN: 0333919394, Joule Library 510/STR (or optionally any more recent edition).

James G, Modern Engineering Mathematics, 3rd Edition, Addison-Wesley, 2001.  ISBN: 0130183199, Joule Library 510/JAM (or optionally any more recent edition).

Online Resources: http://www.maths.manchester.ac.uk/study/undergraduate/information-for-current-students/service-teaching/resources/

 

Study hours

  • Lectures - 16 hours
  • Tutorials - 8 hours
  • Independent study hours - 76 hours

Teaching staff

Colin Steele - Unit coordinator

Thomas House - Unit coordinator

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