Mathematical Methods 3

 Unit code: CHEN30101 Credit Rating: 10 Unit level: Level 3 Teaching period(s): Semester 1 Offered by School of Chemical Engineering and Analytical Science Available as a free choice unit?: N

None

Aims

• Introduce the students to mathematical topics at a suitably advanced level.
• Teach students to carry out the relevant techniques but also have enough appreciation to apply the techniques in slightly different situations.
• Ensure that students have an appreciation of the application of such techniques in Chemical Engineering and related disciplines

Overview

1. Review of functions. Continuous and differentiable functions. Solving systems of nonlinear equations using Newton methods.
2. Optimisation of functions. Bisection and golden ratio methods for a function of one variable.  Graphical methods for minimising a linear function of two variables subject to constraints.
3. Numerical solution of systems of ODEs. Review of explicit and implicit Euler methods. Classical high-order Runge-Kutta methods.
4. Two-point boundary value problems. Finite difference approximations. Solution using Fourier series. Orthogonality. Series solutions of classical linear ODE problems. Legendre polynomials and Bessel functions.
5. Partial Differential Equations. Characterisation of second-order PDEs into elliptic, parabolic and hyperbolic type. Solution by separation of variables. Fourier series solutions.  Numerical solution of PDEs using finite difference approximations.

Teaching and learning methods

Two or three  hours of lectures every week for eight weeks.

Fortnightly example classes.

Optional computational assignments (using MATLAB).

Learning outcomes

 Category of outcome Students should/will (please delete as appropriate) be able to: Knowledge and understanding solve problems using appropriate mathematical techniques as mentioned in the syllabus. Intellectual skills have an appreciation of the basic methods and be able to adapt and generalise the underlying ideas Practical skills develop a working knowledge of associated computational algorithms Transferable skills and personal qualities develop an appreciation of the role of numerical methods in chemical engineering and associated subjects.

Knowledge and understanding

 Knowledge and understanding solve problems using appropriate mathematical techniques as mentioned in the syllabus.

Intellectual skills

 Intellectual skills have an appreciation of the basic methods and be able to adapt and generalise the underlying ideas

Practical skills

 Practical skills develop a working knowledge of associated computational algorithms

Transferable skills and personal qualities

 Transferable skills and personal qualities develop an appreciation of the role of numerical methods in chemical engineering and associated subjects.

Assessment Further Information

 Assessment task Length Weighting within unit (if relevant) Mid-semester test (week 7)End of semester examination 45 minutes90 minutes 20%80%

Erwin Kreyszig : Advanced Engineering Mathematics : Wiley  (2010, 10th Edition)

David Griffiths, John Dold, David Silvester : Essential Partial Differential Equations: Springer

Feedback methods

Two or three  hours of lectures every week for eight weeks.

Fortnightly example classes.

Optional computational assignments (using MATLAB).

Study hours

• Lectures - 18 hours
• Tutorials - 6 hours
• Independent study hours - 76 hours

Teaching staff

David Silvester - Unit coordinator