The University of Southampton
Courses

# CHEM1047 Mathematical Methods in Chemistry I

## 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 mathematical methods for solving chemical theory and modelling problems.
• Basic types of 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.

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

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

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

### Assessment

#### Summative

MethodPercentage contribution
Exam  (120 minutes) 100%

#### Referral

MethodPercentage contribution
Exam  (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:

##### Anything else not covered elsewhere

Although multiples copies of the key texts are available in the Library, students should purchase 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.