Numerical Methods in A-Level Mathematics
Numerical Methods
When we cannot solve an equation, for example, using the normal analytical techniques we often use Numerical Methods. This usually requires the use of computers but at A-Level Maths we learn the fundamentals of these processes by doing the calculations by hand (or with a calculator). Recall that we first saw numerical methods in GCSE Maths when using iteration.
We do not study Numerical Methods in AS-Maths. However, in Year 2, we take a look at various numerical methods for finding roots. We also explore ways of estimating the area beneath graphs which up until now we have found using definite integrals.
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- (not covered in AS Maths)
Other Topic Areas in AS-Maths
- PROOF – proof by deduction, proof by exhaustion, disproof by counterexample
- ALGEBRA & FUNCTIONS – completing the square, cubics, curve sketching, discriminant, indices, inequalities, polynomials, quadratics, simultaneous equations, surds, transformations
- COORDINATE GEOMETRY – straight lines, equation of a circle
- SEQUENCES & SERIES – binomial expansion
- TRIGONOMETRY – non-right-angled triangles, trigonometric equations, trigonometric graphs, trigonometric identities
- EXPONENTIALS & LOGS – exponential & logarithmic graphs, logs, their rules and solving log equations, growth & decay, differentiating e to the kx
- DIFFERENTIATION – differentiation from first principles and differentiating polynomials, increasing & decreasing functions, stationary points, tangents & normals, differentiating e to the kx
- INTEGRATION – fundamental theorem of calculus and integrating powers of x, definite integrals
- VECTORS – two-dimensional vectors, vector arithmetic, vectors in context
Other Topic Areas in A2-Maths
- PROOF – proof by contradiction
- ALGEBRA & FUNCTIONS – modulus of a function, partial fractions, inverse and composite functions, compound transformations
- COORDINATE GEOMETRY – parametric equations
- SEQUENCES & SERIES – arithmetic series (and sigma notation), geometric series, sequences, binomial expansion
- TRIGONOMETRY – radians, arc length & area of a sector, small angle approximations, reciprocal trigonometric functions, inverse trigonometric functions, double & compound angle formulae
- EXPONENTIALS & LOGARITHMS – compound transformations
- DIFFERENTIATION – concavity, convexity & inflection points, derivatives of trigonometric functions, product, quotient & chain rule, parametric & implicit differentiation, differentiating exp/log functions, differential equations & rates
- INTEGRATION – further integration, integration using trigonometric identities, integration by substitution, integration by parts, integration using partial fractions, solving differential equations,
- VECTORS – 3D vectors