Calculus with applications and computing / Peter Lax, Samuel Burstein, Anneli Lax.
Series Undergraduate texts in mathematicsEditor: New York : Springer-Verlag, 1976-Descripción: <1> v. : il. ; 24 cmISBN: 0387901795Tema(s): CalculusOtra clasificación: 26-01Preface Chapter [1] Real numbers 1.1 The algebra of numbers; a review [1] 1.2 The number line [4] 1.3 Infinite decimals [7] 1.4 Convergent sequences [11] 1.5* Infinite sums [20] 1.6 The least upper bound [30] Appendix 1.1 Irrationality of √2 and e [36] Appendix 1.2 Floating point representation [37] Chapter [2] Functions 2.1 The notion of a function [39] 2.2 Functions of several variables [44] 2.3 Composite functions [46] 2.4 Sums, products, and quotients of functions [51] 2.5 Graphs of functions [54] 2.6 Linear functions [60] 2.7 Continuous functions [63] 2.8 Convergent sequences of functions [74] 2.9 Algorithms [79] Appendix 2.1 Partial fraction expansion [84] Chapter [3] Differentiation 3.1 The derivative [87] 3.2 Rules of differentiation [92] 3.3 Increasing and decreasing functions [102] 3.4 The geometric meaning of derivative [107] 3.5 Maxima and minima [113] 3.6 One-dimensional mechanics [126] 3.7 Higher derviatives [131] 3.8 Mean value theorems [134] 3.9* Taylor’s theorem [144] 3.10* Newton’s method for finding zeros of a function [150] 3.11 Economics and the derivative [158] Chapter [4] Integration 4.1 Examples of integrals [161] 4.2 The integral [166] 4.3* Existence of the integral [179] 4.4 The fundamental theorem of calculus [184] 4.5 Rules of integration and how to use them [189] 4.6 The approximation of integrals [202] 4.7* Improper integrals [211] Chapter [5] Growth and decay 5.1 The exponential function [224] 5.2 The logarithm [234] 5.3 The computation of logarithms and exponentials [245] Chapter [6] Probability and its applications 6.1 Discrete probability [259] 6.2 Information theory or how interesting is interesting [266] 6.3 Continuous probability [271] 6.4 Law of errors [289] 6.5 Diffusion [298] Chapter [7] Rotation and the trigonometric functions 7.1 Rotation [316] 7.2 Properties of cosine, sine, arcsine, and arctan [325] 7.3 The computation of cosine, sine, and arctan [338] 7.4 Complex numbers [348] 7.5 Isometries of the complex plane [360] 7.6 Complex functions [365] 7.7 Polar coordinates [380] 7.8 Two-dimensional mechanics [388] Chapter [8] Vibrations 8.1 The differential equation governing vibrations of a simple mechanical system [400] 8.2 Dissipation and conservation of energy [404] 8.3 Vibration without friction [408] 8.4 Linear vibrations without friction [410] 8.5 Linear vibrations with friction [415] 8.6 Linear systems driven by an external force [422] 8.7 An example of nonlinear vibration [430] 8.8 Electrical systems [438] Chapter [9] Population dynamics and chemical reactions 9.1 The differential equation [442] 9.2 Growth and fluctuation of population [448] 9.3 Mathematical theory of chemical reactions [468] FORTRAN programs and instructions for their use P. 1 The bisection method for finding a zero of a function [485] P.2 A program to locate the maximum of a unimodal function [487] P.3 Newton’s method for finding a zero of a function [490] P.4 Simpson’s rule [493] P.5 Evaluation of log x by integration [495] P.6 Evaluation of ex using the Taylor series [496] P.7 Evaluation of sin x and cos x using the Taylor series [498]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 26 L425 (Browse shelf) | Vol. 1 | Available | A-4581 |
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| 26 L253f Foundations of analysis : | 26 L269 Calculus of several variables / | 26 L334c1-9 Cálculo 1 : | 26 L425 Calculus with applications and computing / | 26 L466-8 Éléments de calcul différentiel et de calcul intégral / | 26 L732 Análise no espaço Rn / | 26 L743 Einführung in die höhere Analysis : |
Preface --
Chapter [1] --
Real numbers --
1.1 The algebra of numbers; a review [1] --
1.2 The number line [4] --
1.3 Infinite decimals [7] --
1.4 Convergent sequences [11] --
1.5* Infinite sums [20] --
1.6 The least upper bound [30] --
Appendix 1.1 Irrationality of √2 and e [36] --
Appendix 1.2 Floating point representation [37] --
Chapter [2] --
Functions --
2.1 The notion of a function [39] --
2.2 Functions of several variables [44] --
2.3 Composite functions [46] --
2.4 Sums, products, and quotients of functions [51] --
2.5 Graphs of functions [54] --
2.6 Linear functions [60] --
2.7 Continuous functions [63] --
2.8 Convergent sequences of functions [74] --
2.9 Algorithms [79] --
Appendix 2.1 Partial fraction expansion [84] --
Chapter [3] --
Differentiation --
3.1 The derivative [87] --
3.2 Rules of differentiation [92] --
3.3 Increasing and decreasing functions [102] --
3.4 The geometric meaning of derivative [107] --
3.5 Maxima and minima [113] --
3.6 One-dimensional mechanics [126] --
3.7 Higher derviatives [131] --
3.8 Mean value theorems [134] --
3.9* Taylor’s theorem [144] --
3.10* Newton’s method for finding zeros of a function [150] --
3.11 Economics and the derivative [158] --
Chapter [4] --
Integration --
4.1 Examples of integrals [161] --
4.2 The integral [166] --
4.3* Existence of the integral [179] --
4.4 The fundamental theorem of calculus [184] --
4.5 Rules of integration and how to use them [189] --
4.6 The approximation of integrals [202] --
4.7* Improper integrals [211] --
Chapter [5] --
Growth and decay --
5.1 The exponential function [224] --
5.2 The logarithm [234] --
5.3 The computation of logarithms and exponentials [245] --
Chapter [6] --
Probability and its applications --
6.1 Discrete probability [259] --
6.2 Information theory or how interesting is interesting [266] --
6.3 Continuous probability [271] --
6.4 Law of errors [289] --
6.5 Diffusion [298] --
Chapter [7] --
Rotation and the trigonometric functions --
7.1 Rotation [316] --
7.2 Properties of cosine, sine, arcsine, and arctan [325] --
7.3 The computation of cosine, sine, and arctan [338] --
7.4 Complex numbers [348] --
7.5 Isometries of the complex plane [360] --
7.6 Complex functions [365] --
7.7 Polar coordinates [380] --
7.8 Two-dimensional mechanics [388] --
Chapter [8] --
Vibrations --
8.1 The differential equation governing vibrations of a simple mechanical system [400] --
8.2 Dissipation and conservation of energy [404] --
8.3 Vibration without friction [408] --
8.4 Linear vibrations without friction [410] --
8.5 Linear vibrations with friction [415] --
8.6 Linear systems driven by an external force [422] --
8.7 An example of nonlinear vibration [430] --
8.8 Electrical systems [438] --
Chapter [9] --
Population dynamics and chemical reactions --
9.1 The differential equation [442] --
9.2 Growth and fluctuation of population [448] --
9.3 Mathematical theory of chemical reactions [468] --
FORTRAN programs and instructions for their use --
P. 1 The bisection method for finding a zero of a function [485] --
P.2 A program to locate the maximum of a unimodal function [487] --
P.3 Newton’s method for finding a zero of a function [490] --
P.4 Simpson’s rule [493] --
P.5 Evaluation of log x by integration [495] --
P.6 Evaluation of ex using the Taylor series [496] --
P.7 Evaluation of sin x and cos x using the Taylor series [498] --
MR, 50 #7428
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