Calculus I / by Brian Knight, Roger Adams

Englisch

Boston, MA ; s.l. : Springer US ; Imprint: Springer, 1975

Online-Ressource : online resource

Erscheint auch als (Druck-Ausgabe) : ISBN 9780045170111

Erscheint auch als (Druck-Ausgabe) : ISBN 9781461565956

978-1-4615-6594-9

Weitere Ausgaben: 978-0-04-517011-1 (Druckausgabe)

DOI: 10.1007/978-1-4615-6594-9

*Science (General) ; Mathematical analysis. ; Social sciences. ; Humanities.

Klassifikation der Library of Congress: Q1-390

Dewey Dezimal-Klassifikation: 50; ; 515;

Book Industry Communication: PBK

bisacsh: MAT034000

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.

 

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