Calculus (Third Edition) /

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.

Detalles Bibliográficos
Autor principal: Jeffery, R. L. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Toronto] : University of Toronto Press, 1960.
Edición:Third edition.
Colección:Book collections on Project MUSE.
Temas:
Calculus.
MATHEMATICS > Calculus.
calculus.
Calcul infinitesimal.
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 alphabetI: 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 differentiation3.4 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 differentials4.9 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

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