Overview: Mathematical prerequisits for statistical mechanics

In this chapter you will revise the mathematics required to study statistical mechanics. This will include the elementary rules for differentiation; namely, the chain and product rules. In addition, you will need to know how to use the method of Lagrange multipliers. In order to revise this material more thoroughly you will learn about the ways that the interactions between atoms and molecules can be modelled mathematically.

Aims

• You should be able to use the chain and product rules to calculate derivatives of functions of functions and derivatives of products of functions.
• You should be able to use Lagrange's method of undetermined multipliers to determine solve constrained optimization problems.
• You should be able to describe the differences between the interactions between the atoms in ionic solids, covalent solids and metallic solids and give suitable functional forms to describe these different types of interaction.
• You should be able to discuss how the lattice energy of a molecular solid is partitioned between the inter and intra molecular components. You should then be able to discuss how these inter and intra molecular terms are further decomposed into bond terms, angle terms, torsional terms, electrostatic terms, short-range repulsive terms and dispersive interactions. You should be able to give suitable functional forms to describe all these various different types of interaction

Contact Details

School of Mathematics and Physics,
Queen's University Belfast,
Belfast,
BT7 1NN

Email: g.tribello@qub.ac.uk
Website: mywebsite