Produced by The Open University, a world leader in open and distance learning, all OpenLearn courses are free to study. We offer nearly 1000 free courses across 8 different subject areas. Our courses are available to start right away.

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Science, Maths & Technology

### Approaches to software development

This free course, Approaches to software development, presents an engineering approach to the development of software systems – a software engineering approach. The course pays particular attention to issues of software quality, in terms of both product (what is built) and process (how we build it).

Science, Maths & Technology

### An introduction to electronics

Electronics is fundamental to modern life. Using an interactive website, videos, and easy-to-use electronic circuit design and simulation software, this free course, An introduction to electronics, will show how electronic devices and systems pervade everything we do, and teach some of the basic ideas.

Science, Maths & Technology

### Can renewable energy sources power the world?

We ask the question ‘Can renewable energy sources power the world?’ as a response to the growing awareness that increased use of renewable energy technologies is making a major contribution to global efforts to limit anthropogenic climate change. The course begins by examining the environmental concerns that have caused a rise in interest in renewable energy, introducing the main sources and technologies, and describing global efforts to increase the share of renewables. The course then looks at each of the principal renewable energy technologies and the contributions they might make to global energy demand. Finally, several future energy scenarios are analysed to show how combinations of renewable energy sources and technologies could provide a major share of global energy needs.

Science, Maths & Technology

### Histology, microscopy, anatomy and disease

This free course, Histology, microscopy, anatomy and disease, will help you understand the basic principles of light microscopy, before introducing you to histology, concentrating on the structure, function and relationship of normal human tissues.

Science, Maths & Technology

### The science of nuclear energy

This free course, The science of nuclear energy, will delve into the science behind nuclear power and explain what happens inside a nuclear reactor and what it means for an element to be radioactive. It will explore some of the risks of producing nuclear power and examine the arguments for and against including it in future energy planning as well as looking at other potential future solutions.

Science, Maths & Technology

### Collisions and conservation laws

This free course, Collisions and conservation laws, begins by explaining elastic and inelastic collisions and then goes on to show how collisions may be quantified using the conservation of linear momentum and of kinetic energy. Interactive animations are used to illustrate this behaviour and video examples discuss collisions in the world around us. Finally, this course looks at how the understanding of collisions must be modified when the speeds involved are close to the speed of light, using special relativity.

Science, Maths & Technology

### Modelling events in time

This free course develops ideas about probability and random processes. Sections 1 and 2 introduce the fundamental ideas of random processes through a series of examples. Section 3 describes a model that is appropriate for events occurring ‘at random’ in such a way that their rate of occurrence remains constant. Section 4 derives the main results from Section 3. Section 5 introduces the multivariate Poisson process in which each event may be just one of several different types of event. Section 6 introduces the non-homogeneous Poisson process in which events occur at a rate that varies with time.

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 and 3 derive the stream functions for several simple two-dimensional ﬂow types (the uniform ﬂow, source, doublet and vortex), and suitable combinations of these are used to model more complicated ﬂows. Section 4 introduces the idea of diﬀerentiation following the motion, and Euler’s equation is developed in Section 5.

Science, Maths & Technology

### Linear programming – the basic ideas

This free course examines the formulation and solution of small linear programming problems. Section 1 deals with the formulation of linear programming models, describing how mathematical models of suitable real-world problems can be constructed. Section 2 looks at graphical representations of two-dimensional models, considers some theoretical implications and examines the graphical solution of such models. Section 3 introduces the simplex method for solving linear programming models and Section 4 uses matrix notation to formalize the simplex method.

Science, Maths & Technology

### Introduction to the calculus of variations

This free course concerns the calculus of variations. Section 1 introduces some key ingredients by solving a seemingly simple problem – finding the shortest distance between two points in a plane. The section also introduces the notions of a functional and of a stationary path. Section 2 describes basic problems that can be formulated in terms of functionals. Section 3 looks at partial and total derivatives. Section 4 contains a derivation of the Euler-Lagrange equation. In Section 5 the Euler-Lagrange equation is used to solve some of the earlier problems, as well as one arising from a new topic, Fermat’s principle.

Science, Maths & Technology

### Point estimation

This free course looks at point estimation, that is, the estimation of the value of the parameter of a statistical model by a single number, a point estimate for the parameter. Section 1 develops some aspects of maximum likelihood estimation. In particular, you will find out how to obtain the maximum likelihood estimator of an unknown parameter, using calculus. You will need to do lots of differentiation in this section. Section 2 introduces a number of important properties of point estimation.

Science, Maths & Technology

### Univariate continuous distribution theory

This free course looks at a number of the basic properties of statistical models. Section 1 is concerned with the distributions of continuous random variables which are described by their probability density functions (pdfs) and cumulative distribution functions (cdfs). Section 2 is concerned with moments and covers, the concept of expectation or expected value, the familiar notion of the mean, also known as the first moment, two general definitions of moments, variance, random variables linked by linear transformation and finally, how to deal with moments all in one go, using the moment generating function.