Study-Unit Description

Study-Unit Description


TITLE Methods of Chemical Calculations

LEVEL 01 - Year 1 in Modular Undergraduate Course



DESCRIPTION 1. Algebra and coordinate geometry:
Elementary algebra - Evaluation of expressions: brackets, factorising, solving quadratic equations, solving simultaneous equations, partial fractions, inequalities, sigma and pi notation; Functions: trigonometric, exponential, logarithmic, inverse functions; Real and Complex numbers; Essential co-ordinate geometry; series.

2. Calculus (Theory):
Differentiation: Differentiation of basic functions, product rule, quotient rule, minima and maxima, function of a function, chain rule, curve sketching and essential coordinate geometry, complex numbers, Maclaurin and Taylor Series.
Integration: Integration of basic functions. Integration by substitution, integration by parts, finite integration, numerical integration.
Functions of several variables and partial differentiation. Differential equations: First and second order differential equation, boundary conditions.

3. Calculus (Applications):
Application of differentiation to locate and identify turning points.
The role of calculus in thermodynamics.
The use of integration to calculate p-V work (i.e. to find the area under p-V graphs).
Integration as a means to obtain a 'measurable' change in a quantity, Delta_x, from infinitesimally small changes, dx.
Partial differentiation and state functions.
The use of partial derivatives to differentiate expressions of the sort G = H - TS, and then use these to find how, for example, G varies with T at constant p. The role of differential equations in: Chemical kinetics; Quantum mechanics.

4. Vectors, Matrices and determinants:
Notation, vectors and scalars, basic vector and matrix algebra, vectors, elementary matrix operations and properties, determinants, the matrix inverse, transformations, eigenvalues and eigenvectors. Applications.

5. Mathematics through computers:
Plotting of curves, data analysis, etc

Study-unit Aims:

To equip chemistry students with the calculations and mathematical toolkit required to enable them follow mainstream chemistry courses with profit.

Learning Outcomes:

1. Knowledge & Understanding:

a. Understand how to extract information from expressions that involve commonly encountered mathematical functions;
b. Differentiate functions of single and several variables;
c. Integrate equations that are normally encountered in chemical problems, in particular the SWE in a 1D box and rate laws.

2. Skills:

a. Successfully tackle most types of calculations and derivations that are normally encountered in undergraduate chemistry courses.

Main Text/s:

Essential Mathematics for Chemists, Pearson Education Ltd., by J. Gormally
Maths for Chemists Vol. 1 & 2 (RSC Tutorial Chemistry Texts) by Martin C.R. Cockett and Graham Doggett
Mathematics: The Core Course for A-Level by L. Bostock and S. Chandler

Supplementary readings:

The Chemistry Maths Book (OUP) by Eric Steiner
Atkins P.W., Physical Chemistry

STUDY-UNIT TYPE Lecture and Tutorial

Assessment Component/s Assessment Due Resit Availability Weighting
Examination (3 Hours) SEM2 Yes 100%

LECTURER/S Joseph Noel Grima

The availability of optional units may be subject to timetabling constraints.