Day	Time	Location
Monday	13:00	W103
Thursday	12:00	W103
Friday	12.00	W103

Day	Time	Location
Friday	10:00	D110
Friday (technically SMB)	17:00	CG85

(Revision classes start on week 2 and are open to all, and particularly advised for those who got 18/35 or less on the SMA diagnostic test)

During the second week of term I will plan to revise trigonometry. This will involve the definition of trigonometric functions. Discussion of the addition formulae for sine and cosine function and then we will discuss also inverse trigonometric functions. In our lecture on Thursday (or on Friday) we will start discussing integration. We will mention the fundamental theorem of calculus and then introduce natural log and exponential functions.

During the third week of term I plan to continue our discussion of natural logarithms and exponential functions. Then I will discuss their properties and define hypergemetric functions and their inverses. I also plan to start the discussion of the methods of integration. We will mention various useful indefinite integrals and discuss integration by parts.

During the fourth week of term we will continue discussion of the use of integration by parts to calculate some indefinite integrals. We will also study some definitive integrals and in particular the gamma function. We will integrate by substitution and discuss partial fractions. This will be supplemented by many examples and we may discuss a little the 'cover-up' rule.

The first two lectures of week five will be given by Dr. Alexander Stasinski (as I am away). In these lectures he will discuss the integrations of powers of trigonometric functions and will also define and discuss line integrals. He will show how to calculate the arclength of a curve and will discuss also the work done by a force. I will be back to give Friday's lecture and in my Friday lecture we will start discussing complex numbers and some of their properties.

During the sixth week of the term we will continue our discussion of complex number started on Friday 13th November. In these lectures we will further discuss various properties of such numbers. We will emphasise the 2 dimensional nature of these numbers. Hence we will discuss their polar representation and talk about the geometry of their addition and multiplication. Then we will mention De Moivre's theorem and present many examples of its usefulness.

The first two lectures of week seven will be given by Dr. Alexander Stasinski (as I am away). In these lectures he will define complex functions and then start discussing some of them. In particular, he will talk about the complex exponential and trigonometric and hyperbolic functions. He will also talk about the derivative of e^{i \theta}. I will be back to give Friday's lecture and in my Friday lecture we will talk about equations in a complex variable. We will discuss transcendental equations and also some algebraic equations.

The meeting in Brussels that I was going to has just been cancelled. So all lectures next week will be given by me as originally planned.

During the eighth week of the term we will finish the discussion of Algebraic equations and then start the analysis of real numbers and real valued functions. We will talk a little about various types of real numbers and the irrationality of some of them. In particular we will discuss the irrationality of sqrt(2). We will also start to discuss limits of functions of a real variable.

During the nineth (penultimate) week of the term we will continue our discussion of limits of functions of a real variable. We will give many examples and also state various theorems (like the pinching theorem) which can help us in the calculation of limits. We will also discuss continuity of functions and start a discussion of the intermediate value theorem and its implications.

During the last week of the term we will continue our discussion of continuity of functions. We will discuss the differentiability of functions and present several examples of functions which are or are not differentiable at some points. We will also discuss some important theorems for differentiable functions, namely Rolle's and Mean Value theorems and finally discuss the l'Hopital's rule for calculating limits of some functions. The term will end with several examples on the use of the l'Hopital's rule.

Lecture notes for this term (in pdf form) are here: pdf.