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Calculus

Author: R L Jeffery
Publisher: Toronto] : University of Toronto Press, 1960.
Series: Heritage.
Edition/Format:   eBook : Document : English : Third editionView all editions and formats
Summary:
Since first publication in 1954, this text has been widely used in North American universities in introductory courses in science and engineering. It is a streamlined text, in which essential ideas are not buried in endless detail.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Jeffery, Ralph, L.
Calculus (Third Edition).
Toronto : University of Toronto Press, ©1960
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: R L Jeffery
ISBN: 1487599978 9781487599973
OCLC Number: 1005849085
Description: 1 online resource.
Contents: ""Cover""; ""Contents""; ""PREFACE""; ""PREFACE TO THE THIRD EDITION""; ""INTRODUCTION""; ""0.1 The real number system""; ""0.2 Decimal representation of rational numbers""; ""0.3 Decimals which are neither finite nor repeating""; ""0.4 Definition of real numbers in terms of rational numbers""; ""0.5 The number scale""; ""0.6 The rational points are dense on 1""; ""0.7 Points on the number scale not marked with rational points""; ""0.8 Real numbers and their properties""; ""0.9 Assumptions and working rules""; ""0.10 Functions and functional relations""; ""0.11 The double use of symbols"" ""0.12 The Greek alphabet""""I: SPEED AND LIMITS""; ""1.1 The idea of speed""; ""1.2 Speed at a point""; ""1.3 The idea of limit""; ""1.4 Properties of limits""; ""1.5 Improvements in notation""; ""II: THE DERIVATIVE OF A FUNCTION""; ""2.1 The derivative of a function""; ""2.2 The derivative as the slope of the tangent line to a curve""; ""2.3 The four step rule""; ""2.4 The limit of a ratio when both numerator and denominator tend to zero""; ""III: RULES AND FORMULAS FOR DIFFERENTIATION ""; ""3.1 Rules for differentiation""; ""3.2 Formulas for differentiation"" ""3.3 Proofs of formulas for differentiation""""3.4 The derivative of the square root of a function""; ""3.5 The derivatives of functions which are defined implicitly""; ""IV: DIFFERENTIALS, DIFFERENTIAL EQUATIONS AND ANTI-DIFFERENTIALS""; ""4.1 Definition and geometrical interpretation of a differential""; ""4.2 Relations between dy and Î#x94;y""; ""4.3 Functions with vanishing derivatives""; ""4.4 The fundamental theorem of the differential calculus""; ""4.5 Two theorems on differentials""; ""4.6 Some further applications of differentials""; ""4.7 Differential relations"" ""4.8 Rules for determining differentials""""4.9 Anti-differentials""; ""4.10 Formulas for anti-differentials""; ""V: THE DEFINITE INTEGRAL""; ""5.1 The definite integral""; ""5.2 Continuous function""; ""5.3 Definition of continuity""; ""5.4 Maximum and minimum values of a function""; ""5.5 Assumptions regarding the behaviour of continuous functions""; ""5.6 Sequences of numbers""; ""5.7 Notations for sums""; ""5.8 Areas and volumes""; ""5.9 A problem on area""; ""5.10 The definition of the definite integral""; ""5.11 The fundamental theorem of the integral calculus"" ""5.12 The solution of the area problem of  5.9 """"5.13 The symbol for the definite integral""; ""5.14 The double use of symbols""; ""5.15 The existence of the definite integral""; ""5.16 The definite integral of continuous functions""; ""5.17 Abbreviated methods""; ""5.18 Area as a function of the variable x and the double meaning of the symbol dA""; ""5.19 The existence of the definite integral of a continuous function""; ""5.20 The indefinite integral""; ""5.21 The fundamental theorem of the integral calculus""; ""VI: THE TRANSCENDENTAL FUNCTIONS""; ""6.1 Transcendental functions""
Series Title: Heritage.
Responsibility: R.L. Jeffery.
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Abstract:

Since first publication in 1954, this text has been widely used in North American universities in introductory courses in science and engineering. It is a streamlined text, in which essential ideas are not buried in endless detail.

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