*CHEM1047 *Mathematical Models in Chemistry

## 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. In particular: - Complex numbers - Limits, differentiation and integration - Reaction kinetics modelling - Chemical process optimisation - Linear and non-linear least squares - Modelling thermodynamic and electrochemical systems - Approximation techniques - Statistical analysis - Symbolic processing software - Numerical methods in chemistry

#### Learning Outcomes

##### Knowledge and Understanding

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

- At the end of this module, the students should be comfortable with basic chemical theory and modelling problems.

### Syllabus

Week 1 Mathematical models in chemistry: an overview An overview of application areas, modelling and supercomputing in chemistry with an explanation of what kind of mathematics is required in chemical modelling. Introduction to complex numbers and their applications in physical sciences This is a relatively simple topic that would allow the students to adjust to a university teaching style. Week 2 Introduction to limits and their applications in physical sciences. What is a continuous function and why are most functions in chemistry continuous? This is necessary because the definition of a derivative involves a limit, and to introduce basic proof techniques. Week 3 Basic definition of a function derivative and basic explanation of where differentiation rules coming from. Partial differentiation Necessary background to the subsequent usage of derivatives in a chemical context. Week 4 Derivatives in chemistry: reaction rate equations Derivatives in chemistry: process optimisation Real-world examples, differentiation skills, minima and maxima Week 5 Derivatives in chemistry: the linear least squares method Derivatives in chemistry: the non-linear least squares method Real-world examples, differentiation skills, data analysis, linearisation, using their lab scripts as examples Week 6 Tools for tackling more complex equations in thermodynamics and electrochemistry Systems of equations in thermodynamics and chemical kinetics Real-world examples, equation solving skills, transcendental equations Week 7 Approximations in chemistry: approximation techniques Approximations in chemistry: power series approximations Taylor series, estimates with examples from chemistry Week 8 Data processing in chemistry: introduction to statistical analysis I Data processing in chemistry: introduction to statistical analysis II Using their lab scripts as examples, possibly connecting to thermodynamics Week 9 Definition of a function integral Integrals in chemistry: simple cases Integration, with physical and chemical examples Week 10 Integrals in chemistry: complicated cases Integration techniques and examples of chemical problems leading to complicated integrals Using symbolic processing software to differentiate, integrate and solve equations Mathematica and its applications to chemical problem solving; introduction to using computers in chemistry Week 11 Numerical differentiation and integration on finite grids Problem based learning 1: problem Problem 1: a real chemical problem that uses many of the maths concepts learned during the semester Weeks 12-14 Christmas break and mock exam Week 15 Problem based learning 1: solution The possible solutions to the problem presented before the Christmas break are presented and discussed Revision lecture and mock examination paper Weeks 16-17 Term I examinations

### 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.

Type | Hours |
---|---|

Practical classes and workshops | 24 |

Preparation for scheduled sessions | 24 |

Wider reading or practice | 10 |

Revision | 20 |

Lecture | 24 |

Follow-up work | 48 |

Total study time | 150 |

#### Resources & Reading list

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

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

### Assessment

#### Summative

Method | Percentage contribution |
---|---|

Exam (120 minutes) | 100% |

#### Referral

Method | Percentage contribution |
---|---|

Exam (120 minutes) | 100% |

### Linked modules

Pre-requisite: A-level mathematics or equivalent OR module(s) listed under pre-requisites

#### Pre-requisites

To study this module, you will need to have studied the following module(s):

Code | Module |
---|---|

CHEM1034 | Fundamentals of Physical Chemistry II |

MATH1004 | Introductory Mathematics for Chemists and Oceanographers |

### 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.