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## Open Classes

*© 2022 Imperial College London. All rights reserved. These course materials have been added to Mobius to support students on Aeronautics Pre-sessional course.*

*Only these students may print and/or download a single copy for their personal, educational use. Further use and sharing of these materials by students or others is prohibited.*

This class covers the definition of the derivative from first principles, differentiation of key functions sums, products, quotients and composites, and using differentiation to sketch curves and solve problems. If you've done A-level Maths, this is mostly a revision module.

Learn, or revise, what complex numbers are, how to do calculations with them, how to use them to solve trig problems, how to define functions on them and how to represent shapes in the plane.

This class covers straight lines, circles, curves given by parametric equations and curves given by polar equations. The early topics are likely to be revision; you'll have met the later ones if you've done Further Maths or the equivalent.

Learn, or revise, solving first order differential equations by various methods, solving second order differential equations with constant coefficients, and classifying the critical points of systems.

Learn, or revise, differentiation from first principles, techniques of differentiation and using differentiation to sketch curves and solve problems.

Learn, or revise, Fourier series and sine and cosine half-range series.

Learn, or revise, composite and inverse functions; odd and even functions; the modulus function; exponential and logarithmic functions; hyperbolic functions.

Learn, or revise, techniques of integration (parts, substitution, partial fractions, reduction formulae) and applications to areas in the plane and volumes of revolution.

Learn, or revise, Laplace transforms and inverse Laplace transforms.

Learn, or revise, limits of sequences and functions, including special cases and L'Hopital's Rule.

Learn, or revise, determinants, matrix inverses, Gaussian elimination and eigenvalues/eigenvectors.

Learn, or revise, kinematics, forces, moments and circular motion.

This content has been developed by Imperial College to help develop core mathematics skills.

Learn, or revise, prime factorisation, laws of indices, surds and inequalities.

Learn, or revise, numerical integration, iterative solution of equations, fitting curves to data and numerical solution of differential equations.

Learn, or revise, the principles and techniques of partial differentiation.

Learn, or revise, permutations and combinations, an the binomial theorem.

Learn, or revise, basic stats, probability, hypothesis testing, estimation, regression and correlation.

Learn, or revise, trigonometrical functions (and their reciprocals and inverses) and trigonometrical identities.

Learn, or revise, vector quantities, the scalar product and the vector equations of lines and planes.