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.

Subject specific skills

TBC

Transferable skills

TBC