School of Mathematics and Statistics (SoMaS)

MAS248 Mathematics III (Chemical)

A Level 2 mathematics module for engineering students.

Prerequisites: MAS157 (Mathematics for Chemists)
No other modules have this module as a prerequisite.

Aims

• To consolidate previous mathematical knowledge;
• To develop new mathematical skills needed for Chemical Engineering.

Learning outcomes

• Find stationary points of functions f(x) or f(x,y), and use numerical algorithms for finding roots of f(x), i.e. solutions of f(x)=0;
• Recognise periodic, even and odd functions, and have a working knowledge of Fourier series;
• Understand the difference between scalar and vector fields;
• Differentiate and integrate these fields in space and/or time in simple cases;
• Understand the physical significance of these processes;

Teaching methods

Lectures, tutorials, independent study

Assessment

Provisional: 2 hour written exam, answer all 4 questions (which may contain sub-parts). (This may be subject to change due to Covid disruption.)

Full syllabus

• Revision of partial differentiation and chain rule.
• Finding maxima, mimina and roots of functions: stationary points; maxima, minima and saddle points; finding the roots of a function of one variable using bisection and Newton-Raphson methods.
• Fourier series: periodic functions; Fourier series; even and odd functions.
• Vector analysis: scalar and vector fields; grad, div and curl; vector identities; directional derivative; Laplacian; scalar and vector potentials.
• Partial differential equations: Laplace’s equation; diffusion equation; wave equation; d’Alembert’s solution; normal modes.
• Introduction to probability distributions.

Reading list