Course Details in

Module Title	Modelling Concepts and Tools
School	Chemical Engineering
Department	Chemical Engineering
Module Code	04 21830
Module Lead	Dr Alessio Alexiadis
Level	Certificate Level
Credits	20
Semester	Full Term
Pre-requisites
Co-requisites
Restrictions	None
Contact Hours	Lecture-22 hours Tutorial-66 hours Guided independent study-112 hours Total: 200 hours
Exclusions
Description	This module concerns the mathematical modelling of engineering problems, and introduces students to the mathematical methods (e.g. Linear Algebra and Ordinary Differentia Equations) and software tools (MATLAB) they will require for such modelling. Concerning Linear Algebra, the course introduces the students to the following topics: 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 Concerning Ordinary Differential Equations (ODEs), the course introduces the students to the following topics: 1. Separable ODEs 2. Linear ODEs 3. Substitution techniques for solving non-linear first order ODEs (e.g. Bernulli equation) 4. Second Order ODEs 5. System of Linear ODEs with constant coefficient Concerning the use of ODEs in modelling applications, the course introduces the students to the following topics: 1. Mass and Volume balances applied to compartmental problems 2. Energy (heat) balance applied to compartmental problems and one-dimensional problems
Learning Outcomes	By the end of the module students should be able to: Be able to understand, apply and manipulate vector and matrices and use this knowledge to solve linear algebra problems Be able to understand, apply various techniques for solving Ordinary Differential and use this knowledge to solve typical modelling problems in Chemical Engineering 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).
Assessment	21830-02 : Examination : Exam (Centrally Timetabled) - Written Unseen (80%) 21830-07 : Test 1 Linear algebra : Class Test (10%) 21830-09 : Test 2 Differential equations : Class Test (10%)
Assessment Methods & Exceptions	Assessment: 2 h written examination (80%) 1.5 h MapleTA Tests on Linear Algebra (10%) 1.5 h MapleTA Tests on Ordinary Differential Equations (10%) (MapleTA Tests themselves are 30 minutes each but an hour extra specified for each for system set-up and preparation) Reassessment: 3h written examination only
Other	None
Reading List	Croft and Davidson, Mathematics for Engineers; Basmadjian, Mathematical Modelling of Physical Systems; Moore, MATLAB for Engineers;