Library

An advanced course on mastering the vector quantity that governs collisions, explosions and rocket propulsion: from the definition of p = m*v through to elastic collisions and Tsiolkovsky’s equation.

Find out why you can see yourself in a mirror and how light bounces off objects: a simple lesson, illustrated with everyday examples, to help you understand the laws of reflection.

Why does a straw look as if it’s broken when it’s in a glass of water? Discover Snell–Descartes’ laws, which explain how light changes direction when it passes from one medium to another.

Find out what electrical voltage is, how to measure it with a voltmeter, and how it behaves in a series or parallel circuit.

Find out why every action causes a reaction, and understand how this law explains walking, rockets and everyday collisions.

Find out how an electric charge affects its surroundings from a distance, and learn how to calculate, represent and analyse electric fields, whether uniform or non-uniform.

Find out how magnets, the Earth and electric currents create a magnetic field, and learn how to calculate its effects using Laplace’s force.

Find out how electricity flows through a torch or a string of Christmas lights, and learn how to draw and read simple electrical circuit diagrams.

Find out why an apple falls and why the Moon doesn’t fall to Earth: discover Newton’s law, weight and the orbits of satellites.

Learn to distinguish between the rate and progress of a reaction, identify the factors that accelerate a reaction, and understand how a chemical system reaches a dynamic equilibrium.

Learn how to distinguish between solute, solvent and solution, how to calculate concentration, and how to prepare a solution by dissolution or dilution without getting the volume wrong.

From Fermat's lemma to the mean value theorem: the proofs that finally justify the link between the sign of the derivative and the direction of variation.

Discover the natural logarithm and master its properties, its derivative and its limits to solve equations and inequalities.

Find out how to measure the instantaneous change in a function, from the rate of change to the derivative and on to the equation of the tangent line.

Discover the derivative, the key formulas for calculating it, and its applications to the study of tangents and variations.

Use the derivative to determine when a function is increasing, decreasing or reaching an extremum, and then draw up a complete table of variations.

Learn how to use the derivative to analyse a function, determine its extrema, draw tangents and solve optimisation problems.

Covers limits of functions, indeterminate forms and notable limits, with an introduction to the rigorous definition and the link to continuity.

Understand the continuity of a real-valued function and the Intermediate Value Theorem, including its applications to finding zeros and solving equations.

Build step by step the convergent subsequence of a bounded sequence: subsequences, nested intervals, bisection, and then the major theorems this result makes possible.

Understand uniform continuity, prove Heine's theorem on a closed interval, and use it for the integrability of continuous functions and the control of numerical errors.

Contraction mappings, iterated sequences and geometric convergence: the theorem that delivers existence, uniqueness and a computation algorithm all at once.

Discover the exponential function, which is equal to its own derivative, and learn how to work with its algebraic properties and its asymptotic behaviour.

Learn how to compare logarithms, powers and exponential functions in terms of their behaviour as they approach infinity, in order to resolve indeterminate forms.