# Calculus I

• Brian Knight
Book

1. Front Matter
Pages N2-9
Pages 11-16
Pages 17-24
Pages 25-29
Pages 30-34
Pages 35-43
Pages 44-49
Pages 50-53
Pages 54-60
Pages 61-66
Pages 67-71
Pages 72-79
Pages 80-85
Pages 87-93
Pages 94-99
Pages 100-105
Pages 106-109
18. Back Matter
Pages 110-118

### Introduction

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.

### Keywords

curve sketching differential equation integral integration maximum minimum

#### Authors and affiliations

• Brian Knight
• 1
• 2
1. 1.Goldsmiths’ CollegeLondonUK
2. 2.Thames PolytechnicLondonUK

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4615-6594-9
• Copyright Information Springer-Verlag US 1975
• Publisher Name Springer, Boston, MA
• eBook Packages
• Print ISBN 978-0-04-517011-1
• Online ISBN 978-1-4615-6594-9
• Buy this book on publisher's site
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