Calculus of one & several variables / Robert T. Seeley.
Editor: Glenview, Ill. : Scott, Foresman, c1973Descripción: 903, A-127 p. : il. ; 25 cmISBN: 0673077799Otra clasificación: 26-01Part One. Calculus of One Variable Introduction A Thumbnail Sketch of the History of Calculus [1] The Plan of This Book [6] Chapter 0 Prerequisites The Real Numbers as Points on a Line [9] The Symbols => and <=> [15] Points in the Plane 16 Functions and Graphs [32] Summary [48] Review Problems [50] Chapter I An Introduction to Derivatives Forward [53] Limits [56] Derivatives [65] Reflection in a Parabolic Mirror [73] The Derivative as an Aid to Graphing [78] Maximum Problems [83] Newton’s Method for Square Roots (optional) [87] Appendix: The Accuracy of Newton’s Method for Square Roots (optional) [89] Velocity and Other Applications [93] Leibniz Notation [106] Chapter II Computation of Derivatives Forward [109] Derivatives of Sums and Products [111] The Derivative of a Quotient [120] Derivatives of the Trigonometric Functions [126] Appendix: The Trigonometric Functions [132] Composite Functions and the Chain Rule [142] Derivatives of Inverse Functions [152] The Natural Logarithm [159] Logs and Exponentials [170] Hyperbolic Functions (optional) [178] Summary of Derivative Formulas [181] Implicit Differentiation and Related Rates [185] Some Geometric Examples (optional) [191] Chapter III Applications of Derivatives Increasing and Decreasing Functions [198] Parallel Graphs [206] Exponential Growth and Decay [211] Second Derivatives [216] Periodic Motion (optional) [225] Chapter IV Theory of Maxima The Maximum Value Theorem [233] The Mean Value Theorem [249] Chapter V Introduction to Integrals The Definite Integral [257] A Problem of Existence [268] The Fundamental Theorem of Calculus [271] Some Applications of Integrals [282] Unbounded Intervals and Discontinuous Functions [301] Chapter VI Techniques of Integration Forward [309] 6.1 Linear Combinations [312] 6.2 Substitution [317] Appendix: Completing the Square [327] 6.3 Integration by Parts [329] 6.4 Rational Functions [337] 6.5 Special Trigonometric Integrals [354] 6.6 Trigonometric Substitution [361] 6.7 Separable Differential Equations [368] 6.8 First Order Linear Differential Equations [372] 6.9 Generalities on Differential Equations [379] Chapter VII Vectors and the Laws of Motion 7.1 Plane Vectors [383] 7.2 Length and Inner Product [387] 7.3 Vectors in Analytic Geometry [393] 7.4 Paths in the Plane [400] 7.5 Differentiation of Vector Functions; Velocity and Acceleration [404] 7.6 L’Hopital’s Rule [411] 7.7 Geometry of Parametric Curves (optional) [416] 7.8 Polar Coordinates [421] 7.9 Area and Arc Length in Polar Coordinates [427] 7.10 Vectors and Polar Coordinates [431] 7.11 Planetary Motion [435] Chapter VIII Complex Numbers Forward [441] 8.1 Definition and Elementary Algebraic Properties of the Complex Numbers [442] 8.2 Geometry of the Complex Numbers [446] 8.3 Multiplication of Complex Numbers [448] 8.4 Complex Functions of a Real Variable [454] 8.5 Linear Differential Equations with Constant Coefficients; The Homogeneous Second Order Case [460] 8.6 Linear Differential Equations with Constant Coefficients; The General Case [466] 8.7 The Fundamental Theorem of Algebra [474] Chapter IX Approximations Forward [479] Approximation by the Tangent Line [481] The Taylor Expansion [484] Newton’s Method [492] The Trapezoid Rule and Simpson’s Rule [495] Chapter X ZnyinUe Sequences Forward [505] Limit of a Sequence [506] The Algebra of Limits [513] Bounded and Monotone Sequences [525] Sequence Limits and Function Limits [530] The Bolzano-Weierstrass Theorem [536] Chapter XI Infinite Series Some Uses and Abuses of Infinite Series [543] The Sum of an Infinite Series [552] Positive Series [561] Appendix: Error Estimates (optional) [572] Absolute Convergence; Alternating Series [575] Power Series [581] Analytic Definition of Trigonometric and Exponential Functions [597] Grouping, Reordering, and Products of Series [602] Part Two. Calculus of Several Variables Chapter I Vectors Forward [611] The Vector Space E3 [612] The Cross Product [623] Spheres, Planes, and Lines [634] The Vector Space Rn [647] Linear Dependence and Bases [652] Chapter 11 Curves in Rn Definitions and Elementary Properties [669] Newton’s Law of Motion [679] The Geometry of Curves in R3 [687] Chapter III Differentiation of Functions of Two Variables 3.1 Definitions, Examples, and Elementary Theorems [699] 3.2 Polynomials of Degree One [711] Appendix: Two-Dimensional Linear Programming [717] 3.3 Partial Derivatives, the Gradient, and the Chain Rule [725] Computations with the Chain Rule [743] The Implicit Function Theorem [750] Derivatives of Higher Order [763] The Taylor Expansion [770] Maxima and Minima [775] Chapter IV Double Integrals, Vector Fields, and Line Integrals Forward [783] Double Integrals [784] Vector Fields [798] Line Integrals [805] Green’s Theorem [818] Change of Variable [832] Chapter V Functions of n Variables Forward [843] Continuity, Partial Derivatives, and Gradients [844] The Implicit Function Theorem [854] Taylor Expansions [860] Vector Fields and Line Integrals in R3 [863] Surface Integrals and Stokes’ Theorem [868] Triple Integrals [883] The Divergence Theorem [891] A Very Brief Introduction to Differential Forms [899] Appendix I Numbers Forward A-l Summation A-2 Mathematical Induction and the Natural Numbers A-6 Inequalities, and the Rational Numbers A-13 Ordered Fields A-18 The Least Upper Bound Axiom, and the Real Numbers A-26 The Integers as Real Numbers: Archimedean Property A-31 Appendix II How to Prove the Basic Propositions of Calculus Limits A-35 More Limits A-44 Derivatives and Tangents A-49 Continuous Functions A-51 Functions Continuous on a Closed Finite Interval A-54 Inverse Functions A-61 Uniform Continuity A-66 Integrals of Continuous Functions A-69 Arc Length A-83 L’Hopital’s Rule for the ∞ / ∞ Case A-90 Answers to Selected Problems Calculus of One Variable A-93 Calculus of Several Variables A-115
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 26 Se452 (Browse shelf) | Available | A-3829 |
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| 26 R916-2e Principios de análisis matemático / | 26 Sa161 Calculus : | 26 Sa271 What is calculus about? / | 26 Se452 Calculus of one & several variables / | 26 Sh553 Funciones hiperbólicas / | 26 Sh556 Análisis matemático en el campo de funciones racionales / | 26 Sh556m Mathematical analysis : |
"Combines the second edition of 'Calculus of one variable' with 'Calculus of several variables'."
Part One. Calculus of One Variable --
Introduction --
A Thumbnail Sketch of the History of Calculus [1] --
The Plan of This Book [6] --
Chapter 0 Prerequisites --
The Real Numbers as Points on a Line [9] --
The Symbols => and <=> [15] --
Points in the Plane 16 Functions and Graphs [32] --
Summary [48] --
Review Problems [50] --
Chapter I --
An Introduction to Derivatives Forward [53] --
Limits [56] --
Derivatives [65] --
Reflection in a Parabolic Mirror [73] --
The Derivative as an Aid to Graphing [78] --
Maximum Problems [83] --
Newton’s Method for Square Roots (optional) [87] --
Appendix: The Accuracy of Newton’s Method for Square Roots (optional) [89] --
Velocity and Other Applications [93] --
Leibniz Notation [106] --
Chapter II Computation of Derivatives Forward [109] --
Derivatives of Sums and Products [111] --
The Derivative of a Quotient [120] --
Derivatives of the Trigonometric Functions [126] --
Appendix: The Trigonometric Functions [132] --
Composite Functions and the Chain Rule [142] --
Derivatives of Inverse Functions [152] --
The Natural Logarithm [159] --
Logs and Exponentials [170] --
Hyperbolic Functions (optional) [178] --
Summary of Derivative Formulas [181] --
Implicit Differentiation and Related Rates [185] --
Some Geometric Examples (optional) [191] --
Chapter III Applications of Derivatives --
Increasing and Decreasing Functions [198] --
Parallel Graphs [206] --
Exponential Growth and Decay [211] --
Second Derivatives [216] --
Periodic Motion (optional) [225] --
Chapter IV Theory of Maxima --
The Maximum Value Theorem [233] --
The Mean Value Theorem [249] --
Chapter V Introduction to Integrals --
The Definite Integral [257] --
A Problem of Existence [268] --
The Fundamental Theorem of Calculus [271] --
Some Applications of Integrals [282] --
Unbounded Intervals and Discontinuous Functions [301] --
Chapter VI Techniques of Integration --
Forward [309] --
6.1 Linear Combinations [312] --
6.2 Substitution [317] --
Appendix: Completing the Square [327] --
6.3 Integration by Parts [329] --
6.4 Rational Functions [337] --
6.5 Special Trigonometric Integrals [354] --
6.6 Trigonometric Substitution [361] --
6.7 Separable Differential Equations [368] --
6.8 First Order Linear Differential Equations [372] --
6.9 Generalities on Differential Equations [379] --
Chapter VII Vectors and the Laws of Motion --
7.1 Plane Vectors [383] --
7.2 Length and Inner Product [387] --
7.3 Vectors in Analytic Geometry [393] --
7.4 Paths in the Plane [400] --
7.5 Differentiation of Vector Functions; Velocity and Acceleration [404] --
7.6 L’Hopital’s Rule [411] --
7.7 Geometry of Parametric Curves (optional) [416] --
7.8 Polar Coordinates [421] --
7.9 Area and Arc Length in Polar Coordinates [427] --
7.10 Vectors and Polar Coordinates [431] --
7.11 Planetary Motion [435] --
Chapter VIII --
Complex Numbers --
Forward [441] --
8.1 Definition and Elementary Algebraic Properties of the Complex Numbers [442] --
8.2 Geometry of the Complex Numbers [446] --
8.3 Multiplication of Complex Numbers [448] --
8.4 Complex Functions of a Real Variable [454] --
8.5 Linear Differential Equations with Constant Coefficients; The Homogeneous Second Order Case [460] --
8.6 Linear Differential Equations with Constant Coefficients; The General Case [466] --
8.7 The Fundamental Theorem of Algebra [474] --
Chapter IX Approximations Forward [479] --
Approximation by the Tangent Line [481] --
The Taylor Expansion [484] --
Newton’s Method [492] --
The Trapezoid Rule and Simpson’s Rule [495] --
Chapter X ZnyinUe Sequences Forward [505] --
Limit of a Sequence [506] --
The Algebra of Limits [513] --
Bounded and Monotone Sequences [525] --
Sequence Limits and Function Limits [530] --
The Bolzano-Weierstrass Theorem [536] --
Chapter XI Infinite Series --
Some Uses and Abuses of Infinite Series [543] --
The Sum of an Infinite Series [552] --
Positive Series [561] --
Appendix: Error Estimates (optional) [572] --
Absolute Convergence; Alternating Series [575] --
Power Series [581] --
Analytic Definition of Trigonometric and Exponential Functions [597] --
Grouping, Reordering, and Products of Series [602] --
Part Two. Calculus of Several Variables --
Chapter I Vectors Forward [611] --
The Vector Space E3 [612] --
The Cross Product [623] --
Spheres, Planes, and Lines [634] --
The Vector Space Rn [647] --
Linear Dependence and Bases [652] --
Chapter 11 Curves in Rn --
Definitions and Elementary Properties [669] --
Newton’s Law of Motion [679] --
The Geometry of Curves in R3 [687] --
Chapter III Differentiation of Functions of Two Variables --
3.1 Definitions, Examples, and Elementary Theorems [699] --
3.2 Polynomials of Degree One [711] --
Appendix: Two-Dimensional Linear Programming [717] --
3.3 Partial Derivatives, the Gradient, and the Chain Rule [725] --
Computations with the Chain Rule [743] --
The Implicit Function Theorem [750] --
Derivatives of Higher Order [763] --
The Taylor Expansion [770] --
Maxima and Minima [775] --
Chapter IV Double Integrals, Vector Fields, and Line Integrals Forward [783] --
Double Integrals [784] --
Vector Fields [798] --
Line Integrals [805] --
Green’s Theorem [818] --
Change of Variable [832] --
Chapter V Functions of n Variables Forward [843] --
Continuity, Partial Derivatives, and Gradients [844] --
The Implicit Function Theorem [854] --
Taylor Expansions [860] --
Vector Fields and Line Integrals in R3 [863] --
Surface Integrals and Stokes’ Theorem [868] --
Triple Integrals [883] --
The Divergence Theorem [891] --
A Very Brief Introduction to Differential Forms [899] --
Appendix I Numbers Forward A-l --
Summation A-2 --
Mathematical Induction and the Natural Numbers A-6 --
Inequalities, and the Rational Numbers A-13 --
Ordered Fields A-18 --
The Least Upper Bound Axiom, and the Real Numbers A-26 --
The Integers as Real Numbers: Archimedean Property A-31 --
Appendix II How to Prove the Basic Propositions of Calculus --
Limits A-35 --
More Limits A-44 --
Derivatives and Tangents A-49 --
Continuous Functions A-51 --
Functions Continuous on a Closed Finite Interval A-54 --
Inverse Functions A-61 --
Uniform Continuity A-66 --
Integrals of Continuous Functions A-69 --
Arc Length A-83 --
L’Hopital’s Rule for the ∞ / ∞ Case A-90 --
Answers to Selected Problems --
Calculus of One Variable A-93 --
Calculus of Several Variables A-115 --
MR, REVIEW #
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