Mathematical Methods in Chemistry I | CHEM1047

Module overview

The module provides advanced mathematics training necessary for students planning to specialise in physical chemistry, computational chemistry, spectroscopy, data science 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 or applied skills training alone.

First year students should be aware that this module requires A-level mathematics. There are no pre-requisite modules for second and third year students.

Aims and Objectives

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

Basic types of chemical theory and modelling problems.
Basic mathematical methods for solving chemical theory and modelling problems.
Symbolic processing software: Mathematica

Syllabus

Lecture 1. Mathematical models in chemistry: an overview.

Lecture 2. Complex numbers and their applications in physical sciences.

Lecture 3. Limits and their applications in physical sciences.

Lecture 4. What is a continuous function and why are most functions in chemistry continuous?

Lecture 5. Formal definition of the derivative and its basic properties.

Lecture 6. Partial derivatives and their properties.

Lecture 7. Derivatives in chemistry: reaction rate equations.

Lecture 8. Derivatives in chemistry: process optimisation.

Lecture 9. Derivatives in chemistry: the linear least squares method.

Lecture 10. Derivatives in chemistry: the non-linear least squares method.

Lecture 11. Derivatives in chemistry: constrained optimisation.

Lecture 12. Derivatives in chemistry: constrained optimisation.

Lecture 13. Approximations in chemistry: basics.

Lecture 14. Approximations in chemistry: power series.

Lecture 15. Data processing: statistical analysis.

Lecture 16. Data processing: errors and probabilities.

Lecture 17. Formal definition of the integral.

Lecture 18. Integrals in chemistry: simple cases.

Lecture 19. Integrals in chemistry: complicated cases.

Lecture 20. Using Mathematica to differentiate, integrate and solve equations.

Lecture 21. Numerical differentiation and integration.

Lecture 22. Mathematical methods in chemistry: artificial neural networks.

Lecture 23. Mathematical methods in chemistry: data integrity assurance.

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.

Study time
Type	Hours
Follow-up work	48
Preparation for scheduled sessions	24
Practical classes and workshops	24
Revision	20
Wider reading or practice	10
Lecture	24
Total study time	150

Resources & Reading list

Textbooks

E. Steiner (2008). The Chemistry Maths Book. Oxford: OUP.

P.Monk, L.J. Munro (2010). Maths for Chemists. Oxford: OUP.

Assessment

Assessment strategy

A standard two-hour examination paper.

Summative

This is how we’ll formally assess what you have learned in this module.

Breakdown
Method	Percentage contribution
Continuous Assessment	100%

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Breakdown
Method	Percentage contribution
Continuous Assessment	100%

Repeat Information

Repeat type: Internal & External