This module concerns the mathematical modelling of engineering problems and the tools and techniques required for there solution. Topics include: 1. Vector and Matrix Algebra 2. Linear Transformations 3. Matrix Inversion 4. System of Linear Equations (including under-constrained and over-constrained) 5. Gaussian Algorithm 6. Least Square solution of over-constrained systems and pseudo-inverse 7. Eigen values and Eigen vectors 8. Separable ODEs 9. Linear ODEs 10. Substitution techniques for solving non-linear first order ODEs (e.g. Bernoulli equation) 11. Second Order ODEs 12. System of Linear ODEs with constant coefficient 13. Mass and Volume balances applied to compartmental problems 14. Energy (heat) balance applied to compartmental problems and one-dimensional problems Applications, the course introduces the students to the following topics: 1. Discrete dynamical systems 2. Singular Value Decomposition 3. Markov chains and graphs 4. Buckling 5. Mass and spings systems 6. Delayed differential equations
Learning Outcomes
By the end of the module students should be able to:
Be able to understand and manipulate vector and matrices.
Demonstrate knowledge and understanding of mathematical principles necessary to underpin their education in engineering and to enable them to apply mathematical methods, tools and notations proficiently in the analysis and solution of engineering problems (UKSPEC US2).
Apply quantitative methods and computer software relevant to engineering, to solve engineering problems (UK SPECE3).
Be able to understand and use various techniques for solving first and second order Ordinary Differential
Be able to apply these techniques for solving typical modelling problems in Chemical Engineering
Assessment
41130-01 : Exam : Exam (Centrally Timetabled) - Written Unseen (80%)
41130-03 : Semester 1 Class Test : Class Test (10%)
41130-04 : Semester 2 Class Test : Class Test (10%)
Assessment Methods & Exceptions
Assessment
Class Test (20%)
3 hour closed book written unseen exam (80%)
