Dr. Joseph N. Grima
Department of Chemistry
University of Malta, Msida, MSD 06, MALTA

• Tutorial Sheet 1 - Indices and Logarithms
• Tutorial Sheet 2 - Functions
• Tutorial Sheet 3 - Differentiation
• Tutorial Sheet 4 - Integration

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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 co-ordinate geometry
• Complex numbers
• 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.
1. The use of integration to calculate p-V work (i.e. to find the area under p-V graphs).
2. Integration as a means to obtain a 'measurable' change in a quantity, Dx, from infinitesimally small changes, dx.
3. Partial differentiation and state functions.
4. 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. 
5. The role of differential equations in:
• Chemical kinetics; 
• Quantum mechanics.

4. Matrices and determinants:
• Matrix notation
• Elementary matrix operations and properties
• Determinants
• Inverse matrices
• Eigenvalues and eigenvectors

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.

Method of assessment: