METRIC 'Taster' METRIC comprises a bank of online mathematical resources covering a variety of topic areas for GCSE, 1st and 2nd year undergraduate courses in science and engineering. The application, developed by Imperial College London, was originally designed as a standalone, internet resource; however, in order to increase its functionality and overall usefulness, the current version has been fully integrated into Imperial's Virtual Learning Environment. The METRIC application can be divided into 4 areas;
The following sections highlight the current topic areas within Metric with limited functionality within each topic area, so that you can get a feel for the type of content in Metric and how it is treated within the application. If you require any further information, please do not hesitate to contact the metric team : metric@imperial.ac.uk 

Algebra
Algebra. To factorise quadratics and solve quadratic equations, to simplify rational expressions and resolve into partial fractions, to calculate terms and sums of arithmetic and geometric series.

Complex Numbers
To add, subtract, multiply and divide complex numbers in the form x + i y. To solve polynomial equations with complex roots. To calculate the conjugate, modulus and argument of complex numbers. To use de Moivre's Theorem to calculate trigonometric identities, and the nth roots of complex numbers. To calculute exponential and logarithmic functions of complex numbers.

Coordinate Geometry
To relate the equation of a straight line to its gradient and intercept, to relate the equation of a circle to its centre and radius.

Differential Equations
To find general and particular solutions of first order differential equations that have separable variables, or are exact or linear. To find general and particular solutions of secondorder linear differential equations with constant coefficients. To find solutions of more general secondorder differential equations in series form. To locate and classify critical points of coupled systems.

Differentiation
To calculate, from first principles, derivatives and gradients at a point, to calculate derivatives of standard functions and their sums, products, quotients and composites, to use differentiation to locate and classify stationary points, and to locate points of inflexion, to calculate series expansions by repeated differentiation.

Fourier Theory
To calculate Fourier series, and sine and cosine halfrange series, of simple periodic functions.

Functions and Graphs
To express piecewise functions in terms of the Heaviside step function, to solve inequalities based on the modulus function, to compose and invert functions, to recognise odd and even functions, to perform calculations using exponential, logarithmic and hyperbolic functions.

Integration
To calculate integrals using the techniques of substitution and integration by parts, to integrate rational functions by resolving into partial fractions.

Laplace Transforms
To calculate the Laplace transforms of powers of t, as well as exponential and trigonometric functions. To use the Shift Theorems, together with known results, to calculate inverse Laplace transforms. To solve linear secondorder differential equations, with constant coefficients, using the method of Laplace transforms.

Limits
To calculate limits of functions as x tends to some finite value, or to plus or minus infinity, if necessary with the aid of l'Hopital's Rule.

Matrices
To calculate determininants and use them to solve equation systems; to invert square matrices using cofactors; to solve equation systems and invert square matrices by Gaussian elimination; to calculate eigenvalues and eigenvectors and thus diagonalise square matrices; to invert square matrices using the CayleyHamilton theorem.

Mechanics
To calculate speeds, distances and times under uniform acceleration; to analyse the motion of projectiles; to calculate motion relative to a moving frame of reference; to analyse the forces on a free particle or body; to resolve a force into its components; to calculate resultant forces; to predict the motion of systems of pulleys; to calculate the centre of mass of a compound body; to balance forces and moments on a rigid body in equilibrium.

Numbers and Arithmetic
To carry out prime factorisations, manipulate indices and surds and rearrange inequalities.

Numerical Methods
To use numerical algorithms to calculate integrals, including the use of the Richardson extrapolation. To solve algebraic equations by iteration, including Newton's method. To fit curves to data by regression or interpolation. To solve simple differential equations approximately using Euler's method.

Partial Differentiation
To calculate partial derivatives of simple functions. To use partial differentiation to calculate relative and absolute errors. To calculate higher partial derivatives. To use partial differentiation to locate and classify stationary points of functions of two variables.

Permutations and Combinations
Combinatorics. To calculate permutations and combinations, to use the Binomial Theorem, for integer exponents, to calculate expansions.

Statistics
To calculate the probabilities of oneoff events and combinations of events; to recognise and use mutual exclusion and independence; to calculate means and medians, and estimate them for grouped continuous data; to calculate standard deviations and interquartile ranges, and estimare them for grouped continuous data; to calculate probabilities based on the binomial and Poisson distributions; to use tables to perform calculations based on the Normal distribution; to set up null and alternative hypotheses in a range of scenarios; to test hypotheses at a range of significance levels.

Trigonometry
To express important angles in radians, and calculate their sines, cosines and tangents, to calculate the domain, range and period of trigonometric functions and their inverses, to calculate areas of plane figures, to use the pythagorea, addition, subtraction and doubleangle identities.

Vectors
To calculate the magnitude of a vector, and the scalar product of two. To calculate the unit vector parallel to a given vector. To calculate the vector equation of a line. To calculate the angle between two vectors or lines. To calculate the vector equation of a plane. To calculate distances among points, lines and planes. To calculate the scalar triple product of three vectors. To use mathematic...more


Explorations
Explore the underlying concepts in trigonometry, coordinate geometry, differentiation, integration, partial differentiation and numerical methods.

Toolbox
Plotting tools.
