## All content

Hundreds of educational interactives, games, quizzes, videos and podcasts, plus 1000s of articles written by academic experts and guest contributors.

Science, Maths & Technology

### Introduction to linear equations and matrices

In this free course, matrices are used as a concise way of representing systems of linear equations which occur frequently in mathematics. Section 1 looks at simultaneous linear equations in two and three unknowns and then generalises the ideas to systems of linear equations. Section 2 develops a strategy for solving systems of linear equations....

Science, Maths & Technology

### Introduction to analysis

This free course is an introduction to analysis which looks at real numbers and their properties, with a particular emphasis on inequalities. Section 1 starts by revising rational numbers and their decimal representations. Then, real numbers are introduced as infinite decimals. Section 2 looks at rules for manipulating inequalities and finding ...

Science, Maths & Technology

### Second-order differential equations

This free course is concerned with second-order differential equations. Section 1 introduces some basic principles and terminology. Sections 2 and 3 give methods for finding the general solutions to one broad class of differential equations, that is, linear constant-coefficient second-order differential equations. Section 2 covers homogeneous ...

Science, Maths & Technology

### Dynamics

This free course is concerned with moving objects, that is, dynamics. Section 1 introduces concepts like position, velocity and acceleration, which describe the way an object moves. Section 2 discusses Newton’s laws of motion, which predict the motion of an object when the forces acting on it are known. Section 3 shows how Newton’s second law of...

Science, Maths & Technology

### Medical statistics

This free course is concerned with some of the statistical methods used in epidemiology and more widely in medical statistics. Section 1 introduces cohort studies in which individuals are classified according to their exposure and followed forward in time to evaluate disease outcomes. Section 2 looks at models for cohort studies. Section 3 ...

Science, Maths & Technology

### Bayesian statistics

This free course is an introduction to Bayesian statistics. Section 1 discusses several ways of estimating probabilities. Section 2 reviews ideas of conditional probabilities and introduces Bayes’ theorem and its use in updating beliefs about a proposition, when data are observed, or information becomes available. Section 3 introduces the main ...

Science, Maths & Technology

### Modelling and estimation

This free course is concerned with modelling and estimation and looks in particular at the binomial distribution. Section 1 starts by defining probability, introduces relevant notation and briefly discusses basic properties of probabilities. The section concludes by considering some of the general features of and ideas about modelling discrete ...

Health, Sports & Psychology

### The science of nutrition and healthy eating

This free course, The science of nutrition and healthy eating, looks at the science behind nutrition, covering aspects of biology, chemistry and physics as well as giving some insight into healthier eating. Reading food labels, choosing healthier foods, hydrating appropriately and understanding how we taste food will allow you to be more ...

Science, Maths & Technology

### Discovering chemistry

Chemistry lies at the centre of our modern life, playing a part in areas as diverse as the development of new drugs and materials, analysing our environment through to more mundane activities such as washing your clothes and making your tea. But to truly understand the role chemistry plays you need to have a sound grasp of a number of ...

Science, Maths & Technology

### Scales in space and time

Scale – dealing with the miniscule to the massive, over milliseconds to millennia – is central to all the sciences. In this free course, Scales in space and time, you’ll go to the absolute limits of what can be measured – all through a study of an oak tree! By studying it you will be introduced to concepts in physics, chemistry, biology and ...

Science, Maths & Technology

### Exploring the relationship between anxiety and depression

This free advanced level course, Exploring the relationship between anxiety and depression, serves as an introduction to masters level study in neurosciences and mental health. Focusing on anxiety and depression, you will consider key issues concerning diagnosis, causes and interventions, exploring how these conditions relate to each other. You ...

Science, Maths & Technology

### Kinematics of fluids

This free course examines the basic kinematics of two-dimensional fluid flows. Section 1 introduces the diﬀerential equations for pathlines and streamlines. Section 2 introduces a scalar ﬁeld, called the stream function, which for an incompressible ﬂuid provides an alternative method of modelling the ﬂow and ﬁnding the streamlines. Sections 2 ...