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

#### 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: Vector and matrix spaces I Lecture 2: Vector and matrix spaces II Lecture 3: Vector and matrix spaces III Lecture 4: Vector and matrix spaces IV Lecture 5: Ordinary differential equations I Lecture 6: Ordinary differential equations II Lecture 7: Ordinary differential equations III Lecture 8: Ordinary differential equations IV Lecture 9: Functions of multiple variables: integration I Lecture 10: Functions of multiple variables: integration II Lecture 11: Functions of multiple variables: integration III Lecture 12: Functions of multiple variables: integration IV Lecture 13: Algebraic foundations of quantum theory I Lecture 14: Algebraic foundations of quantum theory II Lecture 15: Partial differential equations I Lecture 16: Partial differential equations II Lecture 17: Schrödinger’s equation for hydrogen atom I Lecture 18: Schrödinger’s equation for hydrogen atom II Lecture 19: Fourier transform Lecture 20: Applications: molecular dynamics Lecture 21: Applications: density functional theory Lecture 22: Applications: magnetic resonance imaging Lecture 23: Applications: crystal structure prediction Lecture 24: Revision

### 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
Lecture24
Follow-up work48
Preparation for scheduled sessions24
Practical classes and workshops24
Revision20
Total study time150

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

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

### Assessment

#### Summative

MethodPercentage contribution
Final Assessment   (120 minutes) 100%

#### Referral

MethodPercentage contribution
Final Assessment   (120 minutes) 100%

#### Repeat Information

Repeat type: Internal & External

### 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.