The University of Southampton

CHEM2024 Mathematical Models in Chemistry II

Module Overview

The module provides advanced mathematics training necessary for students planning to specialise in physical chemistry, computational chemistry, spectroscopy and quantitative finance. It also aims to provide training of rational reasoning skills in a subject-independent way: studying mathematical proofs and derivations introduces a more rigorous logical system than practical skills training alone.

Aims and Objectives

Module Aims

The aims of this option module are to provide an in-depth overview and to develop advanced practical skills of dealing with mathematical models and concepts in chemistry. At the end of this module, the students should be comfortable with advanced chemical theory and modelling problems.

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

  • Foundations of linear algebra
  • Ordinary differential equations
  • Numerical methods for ordinary differential equations
  • Multivariate calculus in chemistry
  • Multivariate chemical process optimisation
  • Foundations of partial differential equations and their applications in chemistry
  • Theoretical and computational modelling of real chemical systems


Week 18 Basic chemical models: vectors and matrices I Basic chemical models: vectors and matrices II Examples from coordinate transformations encountered in crystallography and quantum chemistry Week 19 Basic chemical models: introduction to differential equations Basic chemical models: ordinary differential equations I Examples from the reaction networks occurring in chemical kinetics and thermodynamics Week 20 Basic chemical models: ordinary differential equations II Basic chemical models: solving differential equations on a computer Week 21 Functions of multiple variables: differentiation Multivariate optimisation problems in chemistry Standard multivariate problem examples from laboratory practicals and optimisation problems encountered in chemical industry Week 22 Functions of multiple variables: integration Examples from thermodynamics, electronic structure theory, electrochemistry, materials chemistry and crystallography Polar, cylindrical and spherical coordinates Week 23 Advanced chemical models: function spaces Examples from electronic structure theory and magnetic resonance Quantum chemistry: algebraic foundations of quantum theory From function spaces to curly arrows: the connection between mathematics and quantum mechanics used in chemistry; Week 24 Modern chemical modelling: introduction to partial differential equations A qualitative introduction to equations describing diffusion, electrostatics, wave propagation, colloids, and electrochemistry Week 25 Revision Problem based learning 2: problem & revision A chemical problem making use of this semester’s material is formulated and advice is given on the possible approaches Weeks 26-29 Easter break and mock exam Week 30 Problem based learning 2: solution The possible solutions to the problem presented before the Easter break are presented and discussed Problem based learning of real chemical modelling: complete example 1 IK’s 3D protein tag distribution reconstruction + GD’s theoretical electrochemistry calculations Week 31 Problem based learning of real chemical modelling: complete example 2 Examples from inorganic chemistry and crystallography. Possible solutions to the problem Week 32 Problem based learning of real chemical modelling: complete example 3 Examples which introduce concepts of Laplace transform and its role in electrochemistry or Fourier Transforms Possible solutions to the problem Week 33 A serious “mathematics in chemistry” research talk The talk to combine absolutely everything from the entire course –localised nuclear singlet diffusion imaging. Revision lecture Weeks 34-36 Semester 2 examination

Learning and Teaching

Teaching and learning methods

Lectures and problem-solving workshops with group working and tutor support. Feedback is provided: - In workshops through assistance with the set work. - Through generic feedback following the examinations. - Upon request by viewing of marked examination scripts.

Preparation for scheduled sessions24
Wider reading or practice10
Practical classes and workshops24
Follow-up work48
Total study time150

Resources & Reading list

P. Monk, L.J. Munro (2010). Maths for Chemist. 

E. Steiner (2008). The Chemistry Maths Book. 



MethodPercentage contribution
Exam  (120 minutes) 100%


MethodPercentage contribution
Exam  (120 minutes) 100%

Linked modules

Pre-requisite: CHEM1047 or MATH1009 or MATH1056


Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:


Although multiple copies of the key texts are available in the Library; it is recommended they be purchased for personal use if at all possible.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at

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