Preliminary calculus

Contents
Preface to the third edition
Preface to the second edition
Preface to the first edition
1
1.1
page xx
xxiii
xxv
Preliminary algebra
Simple functions and equations
1
1
Polynomial equations; factorisation; properties of roots
1.2
Trigonometric identities
10
Single angle; compound angles; double- and half-angle identities
1.3
1.4
Coordinate geometry
Partial fractions
15
18
Complications and special cases
1.5
1.6
1.7
Binomial expansion
Properties of binomial coefficients
Some particular methods of proof
25
27
30
Proof by induction; proof by contradiction; necessary and sufficient conditions
1.8
1.9
Exercises
Hints and answers
36
39
2
2.1
Preliminary calculus
Differentiation
41
41
Differentiation from first principles; products; the chain rule; quotients;
implicit differentiation; logarithmic differentiation; Leibnitz’ theorem; special
points of a function; curvature; theorems of differentiation
v