Numerical Methods

For the equations that cannot be solved and the integrals that cannot be found — get a good enough answer anyway, and know how good it is.

• An Overview — the big idea, the three techniques, and the common mistakes

The specification statements

• NM1, NM3 · Change of Sign — locating a root, decimal search, bisection, and when the method fails
• NM2, NM3 · Iterative Methods — repeating a formula to close in on a root, convergence, and why a rearrangement can fail
• NM4–NM5 · Gradients from Chords — estimating a tangent’s gradient, and improving the estimate
• NM6–NM8 · Estimating Areas — rectangular strips, the trapezium rule, and over- or under-estimates
• NM9 · Numerical Methods in Context — applying these techniques to real data and real problems

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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.