| Preface to the second edition Preface to the first edition 1 Preliminary algebra 1.1 Simple functions and equations Polynomial equations; factorisation; properties of roots 1.2 Trigonometric identities Single angle; compound-angles; double- and half-angle identities 1.3 Coordinate geometry 1.4 Partial fractions Complications and special cases 1.5 Binomial expansion 1.6 Properties of binomial coefficients 1.7 Some particular methods of proof Proof by induction; proof by contradiction; necessary and sufficient conditions 1.8 Exercises 1.9 Hints and answers 2 Preliminary calculus 2. 1 Differentiation Differentiation from first principles: products; the chain rule; quotients; implicit differentiation; logarithmic differentiation; Leibnitz'' theorem; special points of a function: curvature: theorems of differentiation 2.2 Integration Integration from first principles; the inverse of differentiation; by inspection; sinusoidal Jhnctions; logarithmic integratio |
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