Numerical Methods

What to do when an equation cannot be solved exactly or an integral cannot be found by algebra. DfE content area I · locating roots, iteration, the Newton–Raphson method and the trapezium rule.

• An Overview — the four tools, the language, a combined worked example and the common mistakes

The content statements

• Locating Roots — change of sign, roots to a given accuracy, and when the method fails
• Iteration — x_n+1 = g(x_n), staircase and cobweb diagrams, convergence and divergence
• The Newton-Raphson Method — the formula from the tangent, worked iterations and failure near stationary points
• The Trapezium Rule — estimating integrals, over- and underestimates from concavity, and use in context

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Each page has step-by-step notes, several worked examples, a quick-reference grid and ten practice questions with fully worked solutions.