
Tutorial Sheets:
Credit Value: 
4 ECTS 
No. of Lectures: 
28 
No. of Tutorials/Labs: 
28 
Year: 
1 
Semester: 
1 & 2 
Prerequisite: 
OLevel Maths 
Syllabus:
[TOP]
1. Elementary
algebra:

Evaluation of expressions: Introduction
to the f(x) notation, brackets, factorising, solving quadratic
equations, solving simultaneous equations, partial fractions, inequalities,
sigma and pi notation

Functions: trigonometric, exponential, logarithmic,
inverse functions,

Essential coordinate geometry

Complex numbers

Series
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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.
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3. Calculus
(Applications):

Application of differentiation to locate and identify turning points.

The role of calculus in thermodynamics.

The use of integration to calculate pV work (i.e. to find the area under
pV graphs).

Integration as a means to obtain a 'measurable' change in a quantity, Dx,
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.
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4. Matrices
and determinants:

Matrix notation

Elementary matrix operations and properties

Determinants

Inverse matrices

Eigenvalues and eigenvectors
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5. Probability
and statistics:

Permutations and combinations

Introduction to statistics

Regression analysis

Applications
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6. Mathematics
through computers:

Plotting of curves, data analysis, etc.
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Method of assessment:
Course work 25%
End of year test 