# Videos

Choose from over 80 mathematical videos.

Our team of top teacher mathematicians have put together all the important topics and explain them with the types of examples that you would find in a normal textbook or exam.
• #### Integration using Algebraic Fractions Part 1

Integrating algebraic fractions (1). The integral of an algebraic fraction can often be found by first expressing the fraction as the sum of its partial fractions. To do this it is necessary to draw on a wide variety of other techniques. This unit considers the case where the denominator may be written as a product of linear factors.
Length: 44 minutes
• #### Integration using Algebraic Fractions Part 2

Integrating algebraic fractions (2). The integral of an algebraic fraction can often be found by first expressing the fraction as the sum of its partial fractions. Further techniques are available when the denominator involves an irreducible quadratic expression.
Length: 16 minutes
• #### Integration using Trigonometric Formulae

Integration using trigonometric formulae. Sometimes integrals involving trigonometric functions can be evaluated by using trigonometric identities. These allow the integrand to be written in an alternative form which may be more amenable to integration. Trigonometric formulae can also be used in substitutions to simplify complicated integrals.
Length: 39 minutes
• #### Introduction to functions

Introduction to functions. A function is a rule which operates on one number to give another number. However, not every rule describes a valid function. This unit also introduces some of the mathematical terms associated with functions.
Length: 32 minutes
• #### Introduction to vectors

Introduction to vectors. A vector is a quantity that has both a magnitude (or size) and a direction. Both of these properties must be given in order to specify a vector completely. Adding and subtracting vectors and using them in geometry is described.
Length: 33 minutes
• #### Inverse functions

Inverse functions. An inverse function is a second function which undoes the work of the first one. In this unit two methods for finding inverse functions are described, together with the possible need to restrict the domain of a function before an inverse function can exist.
Length: 18 minutes
• #### Limits of functions

Limits of functions. This unit explains what it means for a function to tend to infinity, to minus infinity, or to a real limit, as x tends to infinity or to minus infinity. A function which tends to a real limit as x tends to a given real number is also discussed.
Length: 17 minutes
• #### Limits of sequences

Limits of sequences. This unit introduces finite and infinite sequences, and explains what it means for two sequences to be the same and what is meant by the n-th term of a sequence. The divergence of an infinite sequence to plus or minus infinity, or its convergence to a real limit, is considered.
Length: 18 minutes
• #### Linear functions

Linear functions. Some of the most important functions are linear. This unit describes how to recognize a linear function and how to find the slope and the y-intercept of its graph.
Length: 19 minutes
• #### Logarithms

Before calculators logarithms were used to assist in multiplication and division. They still appear in a number of calculations in engineering, science, business and economics. This video looks at what a logarithm is, why use it and examples on how to use them.
Length: 32 minutes