Calculus : one and several variables, with analytic geometry / S. L. Salas, Einar Hille, John T. Anderson.
Editor: New York : Wiley, c1986Edición: 5th edDescripción: 2 v. : il. (algunas col) ; 25 cmISBN: 0471831034 (pt. 1)Tema(s): CalculusOtra clasificación: 26-01Contents Chapter 12 SEQUENCES; INDETERMINATE FORMS; IMPROPER INTEGRALS [593] Sequences of Real Numbers [593] The Limit of a Sequence [599] Some Important Limits [611] Limits as x→±∞ [615] The Indeterminate Form (0/0) [619] Infinite Limits; The Indeterminate Form (∞/∞) [625] Improper Integrals [632] 12.8 Additional Exercises [638] 12.9 Chapter Summary Chapter [639] 13 INFINITE SERIES [643] 13.1 Sigma Notation [643] 13.2 Infinite Series [646] 13.3 The Integral Test; Comparison Theorems [656] 13.4 The Root Test; The Ratio Test [664] 13.5 Absolute and Conditional Convergence; Alternating Series [669] 13.6 Taylor Polynomials in x; Taylor Series in x [675] 13.7 Taylor Polynomials in x - a\ Taylor Series in x — a [687] 13.8 Power Series [691] 13.9 Differentiation and Integration of Power Series [697] 13.10 The Binomial Series [709] 13.11 Series Solutions of Differential Equations [711] 13.12 Additional Exercises [715] 13.13 Chapter Summary [718] Chapter .14 VECTORS [721] 14.1 Cartesian Space Coordinates [721] 14.2 Displacements and Forces [725] 14.3 Vectors [729] 14.4 The Dot Product [738] 14.5 Lines [748] 14.6 Planes [758] 14.7 The Cross Product [766] 14.8 Some Geometry by Vector Methods [774] 14.9 Additional Exercises [776] 14.10 Chapter Summary [779] Chapter 15 VECTOR CALCULUS [781] 15.1 Vector Functions [781] 15.2 Differentiation Formulas [789] 15.3 Curves [793] 15.4 Arc Length [803] 15.5 Velocity and Acceleration [810] 15.6 Curvature [818] 15.7 Chapter Summary [829] Chapter 16 FUNCTIONS OF SEVERAL VARIABLES [831] 16.1 Elementary Examples [831] 16.2 A Brief Catalog of the Quadric Surfaces; Projections [835] 16.3 Graphs; Level Curves and Level Surfaces [844] 16.4 Partial Derivatives [851] 16.5 Open Sets and Closed Sets [860] 16.6 Limits and Continuity; Equality of Mixed Partials [864] 16.7 Chapter Summary [873] Chapter 17 GRADIENTS; EXTREME VALUES; DIFFERENTIALS [875] 17.1 Differentiability and Gradient [875] 17.2 Gradients and Directional Derivatives [882] 17.3 The Mean-Value Theorem; Chain Rules [892] 17.4 The Gradient as a Normal; Tangent Lines and Tangent Planes [904] 17.5 Maximum and Minimum Values [914] 17.6 Second-Partials Test [923] 17.7 Maxima and Minima with Side Conditions [929] 17.8 Differentials [938] 17.9 Reconstructing a Function from Its Gradient [943] 17.10 Chapter Summary [950] Chapter 18 DOUBLE AND TRIPLE INTEGRALS [953] 18.1 Multiple-Sigma Notation [953] 18.2 The Double Integral over a Rectangle [956] 18.3 The Double Integral over More General Regions [965] 18.4 The Evaluation of Double Integrals by Repeated Integrals [968] 18.5 Double Integrals in Polar Coordinates [980] 18.6 Triple Integrals [990] 18.7 Reduction to Repeated Integrals [993] 18.8 Averages and Centroids [1002] 18,9 Integration in Cylindrical Coordinates [1012] 18,10 Integration in Spherical Coordinates [1017] 18,11 Chapter Summary [1023] Chapter 19 LINE INTEGRALS AND SURFACE INTEGRALS [1027] 19,1 Work and Line Integrals [1027] 19.2 The Fundamental Theorem for Line Integrals [1035] 19.3 Green’s Theorem [1041] 19.4 Multiple Riemann Sums; Surface Area [1048] 19,5 The Mass of a Material Surface; Surface Integrals [1057] 19.6 The Divergence Theorem [1064] 19.7 Stokes’s Theorem [1069] 19.8 Chapter Summary [1078] Appendix A SOME ELEMENTARY TOPICS A-1 A.1 Sets A-1 A.2 Radian Measure A-5 A3 Induction A-9 A.4 Complex Numbers A-ll Appendix B SOME ADDITIONAL PROOFS A-17 B. 1 The Intermediate-Value Theorem A-17 B.2 The Maximum-Minimum Theorem A-18 B3 Inverses A-19 B.4 The Integrability of Continuous Functions A-20 B.5 The Integral as the Limit of Riemann Sums A-24 Appendix C TABLES A-25 Table 1 Natural Logs A-25 Table 2 Exponentials (0.01 to 0.99) A-26 Table 3 Exponentials (1.0 to 4.9) A-27 Table 4 Sines, Cosines, Tangents (Radian Measure) A-28 Table 5 Sines, Cosines, Tangents (Degree Measure) A-30 ANSWERS TO ODD-NUMBERED EXERCISES A-33 INDEX I-1 TABLE OF INTEGRALS Inside Covers
Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
---|---|---|---|---|---|---|---|---|
Libros | Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 26 Sa161 (Browse shelf) | Part 2 | Available | A-6387 |
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Contents --
Chapter 12 SEQUENCES; INDETERMINATE FORMS; IMPROPER INTEGRALS [593] --
Sequences of Real Numbers [593] --
The Limit of a Sequence [599] --
Some Important Limits [611] --
Limits as x→±∞ [615] --
The Indeterminate Form (0/0) [619] --
Infinite Limits; The Indeterminate Form (∞/∞) [625] --
Improper Integrals [632] --
12.8 Additional Exercises [638] --
12.9 Chapter Summary Chapter [639] --
13 INFINITE SERIES [643] --
13.1 Sigma Notation [643] --
13.2 Infinite Series [646] --
13.3 The Integral Test; Comparison Theorems [656] --
13.4 The Root Test; The Ratio Test [664] --
13.5 Absolute and Conditional Convergence; Alternating Series [669] --
13.6 Taylor Polynomials in x; Taylor Series in x [675] --
13.7 Taylor Polynomials in x - a\ Taylor Series in x — a [687] --
13.8 Power Series [691] --
13.9 Differentiation and Integration of Power Series [697] --
13.10 The Binomial Series [709] --
13.11 Series Solutions of Differential Equations [711] --
13.12 Additional Exercises [715] --
13.13 Chapter Summary [718] --
Chapter .14 VECTORS [721] --
14.1 Cartesian Space Coordinates [721] --
14.2 Displacements and Forces [725] --
14.3 Vectors [729] --
14.4 The Dot Product [738] --
14.5 Lines [748] --
14.6 Planes [758] --
14.7 The Cross Product [766] --
14.8 Some Geometry by Vector Methods [774] --
14.9 Additional Exercises [776] --
14.10 Chapter Summary [779] --
Chapter 15 VECTOR CALCULUS [781] --
15.1 Vector Functions [781] --
15.2 Differentiation Formulas [789] --
15.3 Curves [793] --
15.4 Arc Length [803] --
15.5 Velocity and Acceleration [810] --
15.6 Curvature [818] --
15.7 Chapter Summary [829] --
Chapter 16 FUNCTIONS OF SEVERAL VARIABLES [831] --
16.1 Elementary Examples [831] --
16.2 A Brief Catalog of the Quadric Surfaces; Projections [835] --
16.3 Graphs; Level Curves and Level Surfaces [844] --
16.4 Partial Derivatives [851] --
16.5 Open Sets and Closed Sets [860] --
16.6 Limits and Continuity; Equality of Mixed Partials [864] --
16.7 Chapter Summary [873] --
Chapter 17 GRADIENTS; EXTREME VALUES; DIFFERENTIALS [875] --
17.1 Differentiability and Gradient [875] --
17.2 Gradients and Directional Derivatives [882] --
17.3 The Mean-Value Theorem; Chain Rules [892] --
17.4 The Gradient as a Normal; Tangent Lines and Tangent Planes [904] --
17.5 Maximum and Minimum Values [914] --
17.6 Second-Partials Test [923] --
17.7 Maxima and Minima with Side Conditions [929] --
17.8 Differentials [938] --
17.9 Reconstructing a Function from Its Gradient [943] --
17.10 Chapter Summary [950] --
Chapter 18 DOUBLE AND TRIPLE INTEGRALS [953] --
18.1 Multiple-Sigma Notation [953] --
18.2 The Double Integral over a Rectangle [956] --
18.3 The Double Integral over More General Regions [965] --
18.4 The Evaluation of Double Integrals by Repeated Integrals [968] --
18.5 Double Integrals in Polar Coordinates [980] --
18.6 Triple Integrals [990] --
18.7 Reduction to Repeated Integrals [993] --
18.8 Averages and Centroids [1002] --
18,9 Integration in Cylindrical Coordinates [1012] --
18,10 Integration in Spherical Coordinates [1017] --
18,11 Chapter Summary [1023] --
Chapter 19 LINE INTEGRALS AND SURFACE INTEGRALS [1027] --
19,1 Work and Line Integrals [1027] --
19.2 The Fundamental Theorem for Line Integrals [1035] --
19.3 Green’s Theorem [1041] --
19.4 Multiple Riemann Sums; Surface Area [1048] --
19,5 The Mass of a Material Surface; Surface Integrals [1057] --
19.6 The Divergence Theorem [1064] --
19.7 Stokes’s Theorem [1069] --
19.8 Chapter Summary [1078] --
Appendix A SOME ELEMENTARY TOPICS A-1 --
A.1 Sets A-1 --
A.2 Radian Measure A-5 --
A3 Induction A-9 --
A.4 Complex Numbers A-ll --
Appendix B SOME ADDITIONAL PROOFS A-17 --
B. 1 The Intermediate-Value Theorem A-17 --
B.2 The Maximum-Minimum Theorem A-18 --
B3 Inverses A-19 --
B.4 The Integrability of Continuous Functions A-20 --
B.5 The Integral as the Limit of Riemann Sums A-24 --
Appendix C TABLES A-25 --
Table 1 Natural Logs A-25 --
Table 2 Exponentials (0.01 to 0.99) A-26 --
Table 3 Exponentials (1.0 to 4.9) A-27 --
Table 4 Sines, Cosines, Tangents (Radian Measure) A-28 --
Table 5 Sines, Cosines, Tangents (Degree Measure) A-30 --
ANSWERS TO ODD-NUMBERED EXERCISES A-33 --
INDEX I-1 --
TABLE OF INTEGRALS Inside Covers --
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