Advanced Mathematical Modelling for Process Engineers

Code

MATH2052

School

School of Mathematical Sciences

Level

2

Credits

20

Semesters

Full year China

Summary

In this module, students learn to solve algebraic equations, ordinary differential equations and partial differential equations both analytically and numerically, using a variety of methods. Students also learn how to perform multiple integration and approximate periodic functions with Fourier series. Students learn how to write and use Python programs to perform numerical methods for the above topics (where appropriate). Then students apply the techniques learned to tackle chemical and environmental engineering problems. The syllabus comprises: 
• Solve algebraic equations by a variety of numerical methods (e.g. the bisection method).
• Derive and apply a variety of numerical methods and analytic methods to solve first-order and second order ordinary differential equations, including systems of equations.
• Analyse the numerical stability of a variety of numerical methods.
• Perform basic complex number arithmetic and manipulation, in particular Euler’s formula.
• Find Laplace transforms of basic functions and solve linear second-order ordinary differential equations using Laplace transforms.
• Perform multiple integration analytically and numerically.
• Compute the Fourier series of a periodic function.
• Solve important partial differential equations (e.g. the heat equation):
  o analytically using separation of variables;
  o numerically using the finite difference method.

Target Students

Students registered in the Department of Chemical and Environmental Engineering only.Requisites: That the module MATH1047 Mathematical Methods for Chemical and Environmental Engineering was taken and passed in year 2.

Classes

• One 2-hour workshop each week for 24 weeks
• One 1-hour lecture each week for 24 weeks
• One 1-hour computing each week for 24 weeks

Assessment

• 20% Coursework 1: Python (all numerical methods considered in Autumn semester)
• 20% Coursework 2: Python (all numerical methods considered in Autumn semester)
• 60% Exam 1 (3-hour): Mathematics (all analytical methods considered in full year)

Assessed by end of spring semester

Educational Aims

Learning Outcomes

A1.2.1 Have a knowledge and understanding of mathematics necessary for the analysis of and to support applications of key chemical engineering principles and processes. Assessed in both Python based courseworks and in the compulsory end of year written exam.

A1.2.6 Have a comprehensive knowledge and understanding of mathematics and scientific principles relevant to chemical engineering, demonstrated primarily through their ability to apply them to the solution of complex engineering problems. Assessed in both Python courseworks and in the compulsory end of year written exam.

A2.3.2 be competent in the use of numerical and computer methods, including commercial software for solving chemical engineering problems (detailed knowledge of computer coding is not required). Assessed in both Python courseworks.

A2.3.3 be able to select and adapt computational and analytical techniques to tackle complex problems. Assessed in both Python courseworks and in the compulsory end of year written exam.

A2.5.4 Be able to apply digital techniques to solving chemical engineering problems. Assessed in both courseworks.

A5.2.1 Have developed a wide range of problem-solving skills. Evidenced through completion of courseworks and the written examination.

A5.2.5 Be effective users of IT. Evidenced through completion of computer based courseworks.

A5.2.10 Have the ability to handle uncertainty and complexity. Evidenced through completion of courseworks and the written examination.

Conveners