The University of Southampton
Courses

CHEM2024 Mathematical Methods in Chemistry II

Module Overview

The module provides advanced mathematics training necessary for students planning to specialise in physical chemistry, computational chemistry, spectroscopy, data sicence 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 and applied training alone. In particular: - Basic linear algebra (spaces, operators, matrices) - Ordinary differential equations (uniform, non-uniform, 1st and 2nd order) - Basic pharmacokinetics modelling - Integration of functions of multiple variables - Polar, cylindrical and spherical coordinates - Algebraic foundations of quantum theory - Basic partial differential equations - Full solution of the Schrödinger equation for the hydrogen atom - Definition and applications of Fourier transform

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

Knowledge and Understanding

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

  • Advanced Mathematical methods for solving chemical theory and modelling problems.
  • Advanced types of chemical theory and modelling problems.
  • The use of Mathematical modelling methods in modern chemistry

Syllabus

Lecture 1. Chemical models: vector and matrix spaces I. Lecture 2. Chemical models: vector and matrix spaces II. Lecture 3. Chemical models: vector and matrix spaces III. Lecture 4. Chemical models: ordinary differential equations I. Lecture 5. Chemical models: ordinary differential equations II. Lecture 6. Chemical models: ordinary differential equations III. Lecture 7. Applications: pharmacokinetics of ethanol and THC. Lecture 8. Functions of multiple variables: integration I. Lecture 9. Integration in polar, cylindrical and spherical coordinates. Lecture 10. Functions of multiple variables: integration II. Lecture 11. Algebraic foundations of quantum theory I. Lecture 12. Algebraic foundations of quantum theory II. Lecture 13. Chemical models: partial differential equations I. Lecture 14. Chemical models: partial differential equations II. Lecture 15. Applications: solving Schrödinger’s equation for hydrogen atom. Lecture 16. Applications: solving Schrödinger’s equation for hydrogen atom. Lecture 17. Applications: Fourier transform. Lecture 18. Applications: Fick’s laws and the diffusion equation. Lecture 19. Applications: magnetic processes and spin. Lecture 20. Applications: molecular dynamics. Lecture 21. Applications: density functional theory. Lecture 22. Applications: magnetic resonance imaging models. Lecture 23. Applications: crystal structure prediction.

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.

TypeHours
Practical classes and workshops24
Lecture24
Revision20
Preparation for scheduled sessions24
Wider reading or practice10
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. 

Assessment

Summative

MethodPercentage contribution
Exam  (120 minutes) 100%

Referral

MethodPercentage contribution
Exam  (120 minutes) 100%

Repeat Information

Repeat type: Internal & External

Linked modules

Pre-requisites: CHEM1033 and CHEM1034 and (CHEM1047 or MATH1009 or MATH1056)

Costs

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:

Textbooks

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 www.calendar.soton.ac.uk.

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