Each chapter in this book deals with a single mathematical topic,
which ideally should form the basis of a single lecture. The
chapter has been designed as a mixture of the following
ingredients: -(i) Illustrative examples and notes for the student's
pre-lecture reading. (ii) Class discussion exercises for study in a
lecture or seminar. (iii) Graded problems for assignment work.
Contents 1 Sets, functions page 11 2 Limits and continuity 17 3 The
exponential and related functions 25 4 Inverse functions 30 5
Differentiation 35 6 Differentiation of implicit functions 44 7
Maxima and minima 50 8 Curve sketching 54 9 Expansion in series 61
10 Newton's method 67 11 Area and integration 72 12 Standard
integrals 80 13 Applications of the fundamental theorem 87 14
Substitution in integrals 94 15 Use of partial fractions 100 16
Integration by parts 106 Answers to problems 110 Index 116 1 Sets,
Functions A set is a collection of distinct objects. The objects be
longing to a set are the elements (or members) of the set. Although
the definition of a set given here refers to objects, we shall in
fact take objects to be numbers throughout this book, i.e. we are
concerned with sets of numbers. Illustrative Example 1: Set
Notation We give straight away some examples of sets in set
notation and explain the meaning in each case.
General
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