Introductory description

ES4C3-15 Mathematical and Computer Modelling

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Introduction to Modelling and Problem Solving Techniques
o Computers and Software. Approximations and errors
o Linear versus nonlinear systems: Linear and Non-linear resonance, Self-oscillations, Bifurcations

• Data driven models
  o Interpolation and Extrapolation
  o Least-squares regression
  o Curve fitting
• Roots of nonlinear equation
  o Bracketing methods
  o Open methods
• Computational differentiation and integration
  o Finite-difference approximation of derivatives
  o Computation of derivatives via interpolation and extrapolation
  o Newton-Cotes versus Gauss quadrature
• Numerical solution of ordinary differential equations
  o Initial value problem
  o Boundary value problem
• Partial-Differential Equations
  o Classification, initial and boundary conditions
  o Finite-difference methods
  o Iterative methods for solution of linear matrix equation and their application for solving partial differential equations
  o Finite-element approach

Each topic includes illustrative examples and templates of Matlab scripts for relevant modelling and computational techniques.

Learning outcomes

By the end of the module, students should be able to:

• 1. Built or select mathematical models over a wide range of application areas in engineering.
• 2. Intelligently select and use suitable computational methods and software systems for engineering tasks.
• 3. Evaluate the principles, purpose, and limitations of models and computational methods used in engineering software.
• 4. Implement, evaluate and use key computational methods in Matlab environment.

Indicative reading list

1. Jaan Kiusalaas, “Numerical methods in engineering with MATLAB”, Cambridge Press, 2010, e-book format.
2. A. Gialt and V. Subramaniam, “Numerical methods for engineers and scientists: An introduction with Applications using MATLAB”, New York : Wiley, 2008.
3. S.S. Rao, Applied Numerical Methods for Engineers and Scientists, Prentice Hall, 2002.
4. Won Young Yang and others, Applied numerical methods using MATLAB, Willey, 2005, e-book format.
5. Steven H. Strogatz, Nonlinear dynamics and chaos : with applications to physics, biology, chemistry, and engineering, Westview Press, 2015, e-book format.
6. Douglas Thorby, Structural dynamics and vibration in practice : an engineering handbook, Elsevier, 2008, e-book format.

Research element

Providing an overview of new development in engineering modelling. Using research project and research outcome as examples in the teaching to show how research contributes in engineering development.

Subject specific skills

Ability to integrate analytical, mathematical and programming skills for analysing, developing and critically evaluating mathematical engineering models.
Ability to be pragmatic, taking a systematic approach and the logical and practical steps necessary for complex concepts to become a reality.
Ability to apply the knowledge of specific software package for engineering modelling.
Ability to understand typical simple nonlinear models and their place in engineering design.
Appreciation of the global dimensions of engineering modelling and its connections to the Industry 4 revolution.

Transferable skills

Ability to overcome difficulties by employing skills, knowledge and understanding in a flexible manner.
Ability to apply mathematical and computational methods to communicate parameters, model and optimise solutions.
Ability to apply problem-solving skills, information retrieval, and the effective use of specific software packages and general IT facilities.
Ability to plan self-learning and improve performance as the foundation for lifelong learning and continuous professional development.