Mathematical Modelling with Professional Skills - PHY00024C

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  • Department: Physics
  • Module co-ordinator: Prof. Irene D'Amico
  • Credit value: 20 credits
  • Credit level: C
  • Academic year of delivery: 2019-20

Related modules

Pre-requisite modules

  • None

Co-requisite modules

  • None

Module will run

Occurrence Teaching cycle
A Autumn Term 2019-20 to Summer Term 2019-20

Module aims

The aim of this module is to illustrate the general principles in constructing models by simple examples, and practice. The level of mathematics used will be modest, and some new simple mathematical techniques will be introduced to extend the range of models that can be studied. Some of the ideas will be implemented using spreadsheets but no computer programming is required. The examples will be drawn mainly from physics. Problems encountered in the real- world will also be discussed. Also it includes a general introduction to the subject, basic IT skills, report writing, use of information resources, experimental techniques, problem solving and computer programming. This will be achieved through a mix of activities, including laboratories, workshops, lectures, programming classes and small group teaching.

Introductory Python Programming (term 2)

This course introduces problem solving using computers, using Python as the programming language. The most difficult aspect of programming is designing a step-by- step recipe (algorithm) to solve a given problem. This kind of logical problem solving is a useful skill which is highly valued in research and in the commercial world, and which all physicists should learn through practice. Once an algorithm has been designed, it must be implemented in a programming language, which for this course is Python. Python is a modern language which is freely available for Windows, Linux/Unix and Mac OS with extensive documentation, tutorials and extensions available online. It is easy to learn but very powerful, and is increasingly being used commercially and in scientific research. Students will learn how to create programs in the Python language to solve physics problems and then visualise the results in 2D and 3D. The emphasis is on problem solving, and teaching skills which students can then apply to other areas of their study.

Module learning outcomes

  • Explain the basic philosophy of mathematical modelling
  • Use dimensional analysis to propose a simple mathematical form for a model
  • Use the results of experiments to provide values for parameters in the model
  • Optimise the parameter values in the model
  • Create a model using network analysis
  • Derive a mathematical form and solve using calculus-based methods

Module content

Mathematical Modelling Syllabus

  • Modelling Principles
  • Dimensional analysis and Dimensional similarity
  • Fitting and Interpolation
  • Optimisation
  • Networks
  • Difference equations and differential equations
  • Numerical Integration
  • Stochastic methods

Professional Skills Syllabus

  • Induction Activities (weeks 1 and 2, term 1): Introduction to communication skills, study skills, career planning, personal development planning (3 hour lecture). Library: tour of the JB Morrell library (1 hour) and information retrieval exercises. A basic introduction to IT (web, e-mail, etc) and use of Office applications for scientific presentation (3 hours of computer sessions).
  • Statistics (weeks 4-7, term 1): Five lectures on basic concepts in probability and statistics, with weekly coursework problems. Covers the notion of probability and binomial, Poisson, and normal probability distributions.

Introduction to Experimental Laboratory

  • (weeks 2-3, term 1): Three short workshops on experimental measurement techniques, plotting scientific data, and recording data and analysing errors.
  • (weeks 4-5, term 1): A core experiment to be presented in a formal report (see First Year Laboratory Handbook for full details).
  • Scientific report writing (week 6, term 1): An introduction to writing scientific reports (1-hour workshop).
  • Problem solving skills (fortnightly, term 1): Small group discussions with your supervisor, to help develop “thinking-like- a-physicist” skills such as order of magnitude estimations, dimensional analysis, applying differential equations, and curve sketching and interpretation (5 x 1-hour tutorials).

Introductory Python Programming (term 2) Syllabus

  • Problem solving strategies and algorithm development
  • Computer programming fundamentals and Python
  • Looping with for..in and while loops
  • Control using if, elif and else
  • Getting input from the user, and printing results
  • Debugging and testing methods
  • Pythons module system and importing libraries
  • Defining functions and using built-in mathematical functions
  • Using Visual Python to produce animations of mechanics simulations

Assessment

Task Length % of module mark
Essay/coursework
Induction and laboratory activities
N/A 5
Essay/coursework
Laboratory reports
N/A 10
Essay/coursework
Marking of lab books
N/A 5
Essay/coursework
Physics Practice Questions (Mathematical Modelling)
N/A 7
Essay/coursework
Physics Practice Questions (Statistics)
N/A 10
Essay/coursework
Python: assignments totalling
N/A 20
University - closed examination
Mathematical Modelling
1.5 hours 43

Special assessment rules

None

Reassessment

Task Length % of module mark
Essay/coursework
Induction and laboratory activities
N/A 5
Essay/coursework
Laboratory reports
N/A 10
Essay/coursework
Marking of lab books
N/A 5
Essay/coursework
Python: assignments totalling
N/A 20
University - closed examination
Mathematical Modelling
1.5 hours 43

Module feedback

Physics Practice Questions (PPQs) - You will receive the marked scripts via your pigeon holes. Feedback solutions will be provided on the VLE or by other equivalent means from your lecturer. As feedback solutions are provided, normally detailed comments will not be written on your returned work, although markers will indicate where you have lost marks or made mistakes. You should use your returned scripts in conjunction with the feedback solutions.

Exams - You will receive the marks for the individual exams from eVision. Detailed model answers will be provided on the intranet. You should discuss your performance with your supervisor.

Advice on academic progress - Individual meetings with supervisor will take place where you can discuss your academic progress in detail.

Indicative reading

First course in mathematical modelling (3rd ed) by F P Giordano, D Weir and W P Fox. (Brooks- Cole, 2002)***



The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.