Advanced Mathematical Modelling for Process Engineers
| Code | School | Level | Credits | Semesters |
| MTHS2008 | Mathematical Sciences | 2 | 20 | Full Year UK |
- Code
- MTHS2008
- School
- Mathematical Sciences
- Level
- 2
- Credits
- 20
- Semesters
- Full Year UK
Summary
The module will cover the following topics:
- Analytical techniques for homogeneous and inhomogeneous second order linear ODEs;
- Numerical techniques for solving first and second order/linear ODEs, including:
- Forward/Backward Euler Method;
- Second order Taylor series methods;
- Runge-Kutta Methods;
- Shooting Methods;
- Finite Difference Methods;
- Stability of methods and the theory of errors;
- Complex Numbers;
- Calculating the Fourier series of periodic functions;
- Using Laplace transforms to solve linear ODEs;
- Multiple integrals using analytical and numerical techniques;
- Analytical solution of PDEs using separation of variables;
- Numerical solution of Poison and heat equations using finite difference methods;
- Writing and using numerical code to compute integrals and solve differential equations, with application to chemical engineering problems.
Target Students
Students registered in the Department of Chemical and Environmental Engineering only.
Classes
- One 1-hour workshop each week for 23 weeks
- One 2-hour lecture each week for 23 weeks
Assessment
- 20% Coursework 1: Coursework 1: Autumn Writing and using numerical code to compute integrals and solve differential equations
- 20% Coursework 2: Coursework 2: Spring Numerical solution of equations using finite difference methods.
- 60% Exam 1 (3-hour): Written Spring exam
Assessed by end of spring semester
Educational Aims
To provide the core mathematics, mathematical modelling and analysis skills that underpin studies in engineering through a blended learning and teaching programme of mathematics and coding:To integrate mathematical theories with chemical engineering practice.To emphasise the mathematical modelling and coding skills used in the design of chemical processes.Learning Outcomes
The broad objectives of this module are for students to:
- acquire the knowledge and understanding of the mathematics necessary to support the application of key engineering principles, and
- apply mathematical methods, tools and notations proficiently, in the analysis and solution of engineering problems.
More specific learning outcomes include:
L1 - Competency in the use of numerical and computer methods, including industry standard chemical engineering software, for solving chemical engineering problems; particularly those involving differential equations (detailed knowledge of computer coding is not required);
- This is achieved via computer workshops where selected programming languages and/or software are used to solve problems;
L2 - Be familiar with, and able to apply, a range of appropriate tools such as mathematical modelling;
L3 - Identify and use suitable numerical methods for a range of engineering problems;
L4 - Work with the concept of error and stability associated with approximate methods used for solving differential equations, and evaluate discretisation errors;
L5 - Evaluate multiple integrals both analytically and numerically;
L6 - Solve a range of second-order linear ordinary differential equations analytically;
L7 - Calculate the representation of a periodic function by a Fourier series;
L8 - Apply separation of variables to solve relevant partial differential equations;
L9 - Compute the Laplace transform of functions and use to solve linear ordinary differential equations.