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Numerical Methods (Metric)

Class Details

Tom Baker

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

Numerical Integration

Trapezium rule, Simpson's rule (A-level topics) and the Richardson extrapolation (not on lost A-level courses).

Estimating definite integrals using the ordinates \(y_0,\,y_1,\,y_2,\,\dots,y_n\).

Lesson

Getting an improved estimate by extrapolating.

Lesson

Iterative Solution of Equations

Fixed point iteration and Newton's method (on some A-level courses).

Solving the equation \(x=f(x)\) using the iteration \(x_{n+1}=f(x_n)\).

Lesson

Solving the equation \(g(x)=0\) using the iteration \(x_{n+1}=x_n-f(x_n)/f'(x_n)\).

Lesson

Data Fitting

Interpolation using polynomials; least-squares regression (mostly First Year university topics).

Fitting a polynomial exactly to a data set.

Lesson

The least-squares curve of best fit.

Lesson

Differential Equations

Euler's method for the approximate solution of differential equations.

Solving the differential equation \(dy/dx=f(x,\,y)\) approximately using the iteration \(y_{n+1}=y_n+h\,f(x_n,\,y_n)\).

Lesson
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