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Calculus I

  • Book
  • © 1975

Overview

Authors:
  1. Brian Knight

    1. Goldsmiths’ College, London, UK

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    You can also search for this author in PubMed   Google Scholar

  2. Roger Adams

    1. Thames Polytechnic, London, UK

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (16 chapters)

  1. Front Matter

    Pages N2-9
    Download chapter PDF

  2. Sets, Functions

    • Brian Knight, Roger Adams
    Pages 11-16

  3. Limits and Continuity

    • Brian Knight, Roger Adams
    Pages 17-24

  4. The Exponential and Related Functions

    • Brian Knight, Roger Adams
    Pages 25-29

  5. Inverse Functions

    • Brian Knight, Roger Adams
    Pages 30-34

  6. Differentiation

    • Brian Knight, Roger Adams
    Pages 35-43

  7. Differentiation of Implicit Functions

    • Brian Knight, Roger Adams
    Pages 44-49

  8. Maxima and Minima

    • Brian Knight, Roger Adams
    Pages 50-53

  9. Curve Sketching

    • Brian Knight, Roger Adams
    Pages 54-60

  10. Expansion in Series

    • Brian Knight, Roger Adams
    Pages 61-66

  11. Newton’s Method

    • Brian Knight, Roger Adams
    Pages 67-71

  12. Area and Integration

    • Brian Knight, Roger Adams
    Pages 72-79

  13. Standard Integrals

    • Brian Knight, Roger Adams
    Pages 80-85

  14. Applications of the Fundamental Theorem

    • Brian Knight, Roger Adams
    Pages 87-93

  15. Substitution in Integrals

    • Brian Knight, Roger Adams
    Pages 94-99

  16. Use of Partial Fractions

    • Brian Knight, Roger Adams
    Pages 100-105

  17. Integration by Parts

    • Brian Knight, Roger Adams
    Pages 106-109

  18. Back Matter

    Pages 110-118
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Keywords

About this book

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.

Authors and Affiliations

  • Goldsmiths’ College, London, UK

    Brian Knight

  • Thames Polytechnic, London, UK

    Roger Adams

Bibliographic Information

  • Book Title: Calculus I

  • Authors: Brian Knight, Roger Adams

  • DOI: https://doi.org/10.1007/978-1-4615-6594-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1975

  • Softcover ISBN: 978-0-04-517011-1Published: 31 December 1975

  • eBook ISBN: 978-1-4615-6594-9Published: 19 December 2013

  • Edition Number: 1

  • Number of Pages: 118

  • Number of Illustrations: 23 b/w illustrations

  • Topics: Analysis, Science, Humanities and Social Sciences, multidisciplinary

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