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Class Details

Nick Collis (N.collis@imperial.ac.uk)

 

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

Algebra (Metric) Parent Class: Algebra 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.
Complex Numbers (Metric)
Parent Class: Complex Numbers 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.
Coordinate Geometry (Metric)
Parent Class: Coordinate geometry 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.
Differential Equations (Metric)
Parent Class: Differential Equations 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.
Differentiation (Metric)
Parent Class: Differentiation Learn, or revise, differentiation from first principles, techniques of differentiation and using differentiation to sketch curves and solve problems.
Fourier Theory (Metric)
Parent Class: Fourier Theory Learn, or revise, Fourier series and sine and cosine half-range series.
Functions and Graphs (Metric)
Parent Class: Functions and Graphs This class covers the idea of a function, composites and inverses, odd and even functions and specific functions including the modulus function, the exponential and logarithmic functions and the hyperbolic functions. Some of this is covered at A-level, and most of the rest is Further Maths.
Integration (Metric)
Parent Class: Integration Learn, or revise, techniques of integration (parts, substitution, partial fractions, reduction formulae) and applications to areas in the plane and volumes of revolution.
Laplace Tranforms (Metric)
Parent Class: Laplace Tranforms Learn, or revise, Laplace transforms and inverse Laplace transforms.
Limits (Metric) Parent Class: Limits Learn, or revise, limits of sequences and functions, including special cases and L'Hopital's Rule.
Matrices (Metric)
Parent Class: Matrices Learn, or revise, determinants, matrix inverses, Gaussian elimination and eigenvalues/eigenvectors.
Mechanics (Metric)
Parent Class: Mechanics Learn, or revise, kinematics, forces, moments and circular motion.
Numbers and Arithmetic (Metric)
Parent Class: Numbers and Arithmetic Learn, or revise, prime factorisation, laws of indices, surds and inequalities.
Numerical Methods (Metric)
Parent Class: Numerical Methods Learn, or revise, numerical integration, iterative solution of equations, fitting curves to data and numerical solution of differential equations.
Partial Differentiation (Metric)
Parent Class: Partial Differentiation Learn, or revise, the principles and techniques of partial differentiation.
Permutations and Combinations (Metric) Parent Class: Permutations and Combinations Learn, or revise, permutations and combinations, an the binomial theorem.
Statistics and Probability (Metric)
Parent Class: Statistics and Probability Learn, or revise, basic stats, probability, hypothesis testing, estimation, regression and correlation.
Trigonometry (Metric)
Parent Class: Trigonometry Learn, or revise, trigonometrical functions (and their reciprocals and inverses) and trigonometrical identities.
Vectors (Metric)
Parent Class: Vectors Learn, or revise, vector quantities, the scalar product and the vector equations of lines and planes.

Units

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