# Study-Unit Description

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CODE CHE1217

TITLE Additional Techniques of Chemical Calculations

LEVEL 01 - Year 1 in Modular Undergraduate Course

ECTS CREDITS 4

DEPARTMENT Chemistry

DESCRIPTION 1. Introduction and revision of basic concepts.

2. Determinants: Properties of determinants, reduction to triangular form, applications of determinants, Cramer’s rule and solutions of equations, alternating functions, differentiation of determinants.

3. Vectors: Vectors applied to mechanical and chemistry problems, scalar and vector fields, the gradient of a scalar field, divergence and curl of a vector field, vector spaces.

4. Matrices and the matrix eigenvalue problem: The eigenvalue problem, properties of the eigenvectors, matrix diagonalisation, quadratic forms, complex matrices.

5. Partial differential equations: Concepts, general solutions, separation of variables. Applications: wave functions, the particle in a rectangular box, the particle in a circular box, the hydrogen atom, The vibrating string, etc.

6. Introduction to tensor notation, Kronecker delta, alternating tensor, applications to chemical and materials science problems, e.g. crystalline properties, mechanical properties, the stress, strain, stiffness and compliance tensors, axis taransformations, etc.

7. Mathematics in Mechanics and Chemistry: Basic definitions, forces/moments, stresses, strains, etc.; Area properties, centre of gravity, second area moments, polar second area moment, dipole moments, forces and potential energy, torques, etc.

Study-unit Aims:

To equip chemistry students with an advanced set of mathematical tools which is required to enable them follow advanced chemistry and applied science courses with profit.

Learning Outcomes:

1. Knowledge & Understanding:
By the end of the study-unit the student will be able to:

a. Extract information from expressions that involve commonly encountered mathematical functions and also how to write such expressions;
b. Apply concepts involving linear algebra and calculus;
c. Interpret the fundamental forms of the SWE;
d. Apply advanced mathematical and computational techniques to solve complex chemistry and engineering problems.

2. Skills:
By the end of the study-unit the student will be able to:

a. Formulate / derive / solve equations encountered in advanced undergraduate chemistry and applied science courses which are based on mathematical models and calculations;
b. Organise information and solve problems in an appropriately structured manner.

Main Text/s and any supplementary readings:

Main Text:
- The Chemistry Maths Book (OUP) by Erich Steiner, 2nd Edition
- Course Notes on Tensors

Online Resources for The Chemistry Maths Book (available through the OUP website).

STUDY-UNIT TYPE Lecture and Tutorial

METHOD OF ASSESSMENT
 Assessment Component/s Assessment Due Resit Availability Weighting Examination (2 Hours) SEM2 Yes 100%

LECTURER/S Luke Collins

The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the description above applies to study-units available during the academic year 2021/2. It may be subject to change in subsequent years.

https://www.um.edu.mt/course/studyunit