This video quiz contains three questions on Maclaurin series followed by answers and, then, detailed solutions. Two of the questions contain ways to check your answer. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This screen capture video contains integrals for you to calculate using trigonometric changes of variables. Full solutions are provided. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This screen capture video contains integrals for you to calculate using partial fraction decompositions of the integrands. Full solutions are provided. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This screen capture video discusses the notation and interpretation of multiple integration. A simple example of a double integral is calculated to demonstrate the geometric interpretation of such integrals. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This screen contains two worked examples of the calculation of multiple (double) integrals.In one the order of integration is changed. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This screen capture video discusses the calculation of the complex roots of complex numbers and their location on the complex plane. It contains various worked examples. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This screen capture video contains a worked example of the calculation of an arc length by integration. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

From 2000BC, cryptography used substitution ciphers and relied on a key exchange. With Public Key Cryptography, Mathematics enabled exchange of a secret message without sharing a secret key. Now, through Physics, cryptography is literally awaiting a quantum leap: Can you transmit a key in the open without risk of eavesdropping? Prof. Kurt Langfeld explains concepts from Free Mason ciphers through to RSA, before explaining and illustrating Quantum Cryptography. [(CC) BY-NC-SA 2.0 UK]

This screen capture video discusses the integration of the inverse trigonometric functions. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

In this video two integrals are calculated: the cube of the secant function and the secant function raised to the fourth power. The reduction formula for the secant function raised to higher powers is also discussed. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This video shows how to integrate the secant function. It also hints at an extension exercise. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

It is often possible to predict whether a definite integral will be positive, negative or zero. This short video offers an example of the interpretation of a definite integral of a logarithm. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This video is really a series of exercises on partial differentiation which you can solve on paper and then fast forward through the solutions to see if you are right. If you get one wrong, you can play the relevant answer. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This video contains: the definition of a partial derivative; a worked example and some exercises (plus solutions) for you to work through. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

Repeated use of integration by parts requires care to avoid errors. Using reduction formulae is a way to automate this process and decrease the chance of making a mistake. This video contains a detailed example. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This video is an example of a sine substitution. The integrand contains the square root of 7 - 4 x^2 so that some care needs to be taken with the numbers. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This video shows how to integrate using an appropriate trigonometric substitution. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

In this video arctan((1+x)/(1-x)) is differentiated in two ways. The initially surprising result that its derivative is the same as that of arctan(x) is explained. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This video discusses integrals where the integrand contains factors of the square root of (1-x^2). It is argued why a sine substitution may be helpful and three different examples are worked through in detail. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This video contains two examples of how to integrate functions containing factors of the square root of 1+x^2. Emphasis is placed on the reason why a tangent substitution can help with such integrals. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This video contains 10 integrals. Nine may be performed using integration by substitution once the appropriate pattern has been spotted. In one case the integral does not fit the pattern and cannot be easily calculated. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This video introduces and derives the technique of integration by parts. An example is calculated and a rule for selecting the term to integrate and the term to differentiate is presented. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This screen capture video shows the calculation of a definite integral where the integrand is defined in a piece-wise fashion. In this video it is because the integrand involves a modulus. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

Brief outline of the canonical form of the exponential family, illustrated with the Poisson distribution. [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]

This briefly and roughly introduces the standard uniform distribution [Released under Creative Commons Attribution-NonCommercial-ShareAlike 2.0 UK: England & Wales licence.]