Mathematics

90 Episodes

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Maclaurin series quiz

2016-08-0126:10

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.]

Trigonometric change of variable quiz

2016-03-1736:01

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.]

$Partial fraction integral quiz$

Partial fraction integral quiz

2016-03-0734:57

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.]

Multiple integrals

2016-02-2516:19

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.]

Multiple integral example

2016-02-1513:33

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.]

Complex roots of complex numbers

2016-02-0825:54

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.]

Arc Length Example

2016-01-2712:59

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.]

Quantum Cryptography

2016-01-0454:53

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]

Integrating inverse trigonometric functions

2013-06-0512:02

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.]

Integrals of powers of the secant function

2013-05-1322:59

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.]

Integral of secant function

2013-05-0720:19

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.]

Definite integral of a logarithm interpretation

2013-04-1503:55

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.]

partial derivatives quiz

2013-03-2740:48

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.]

Partial differentiation introduction

2013-03-1206:28

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.]

Reduction formula example and check

2013-03-0719:11

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.]

A sine substitution with numbers

2013-02-2308:55

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.]

Trigonometric substitution example

2013-02-1812:55

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

Implicit differentiation example

2013-02-1117:27

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.]

Integrals with root of (1-x^2)

2013-02-0427:01

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.]

Change of variables_ tangent substitutions

2013-01-2925:16

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.]

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Alifiya Tahir