Vector calculus / Jerrold E. Marsden, Anthony J. Tromba.

Por: Marsden, Jerrold EColaborador(es): Tromba, AnthonyEditor: New York : W. H. Freeman, c1988Edición: 3rd edDescripción: xiv, 655 p. : il. ; 25 cmISBN: 0716718561Tema(s): Calculus | Vector analysisOtra clasificación: 26-01 (26B12 26B20)
Contenidos:
1 THE GEOMETRY OF EUCLIDEAN SPACE [1]
1.1 Vectors in three-dimensional space [1]
1.2 The inner product [21]
1.3 The cross product [30]
1.4 Cylindrical and spherical coordinates [47]
1.5 n-dimensional Euclidean space [57]
Review exercises for Chapter 1 [68]
2 DIFFERENTIATION [75]
2.1 The geometry of real-valued functions [76]
2.2 Limits and continuity [95]
2.3 Differentiation [118]
2.4 Properties of the derivative [131]
2.5 Gradients and directional derivatives [145]
2.6 Iterated partial derivatives [157]
*2.7 Some technical differentiation theorems [168]
Review exercises for Chapter 2 [180]
3 VECTOR-VALUED FUNCTIONS [189]
3.1 Paths and velocity [189]
3.2 Arc length [201]
3.3 Vector fields [211]
3.4 Divergence and curl of a vector field [220]
3.5 Vector differential calculus [231]
Review exercises for Chapter 3 [238]
4 HIGHER-ORDER DERIVATIVES; MAXIMA AND MINIMA [241]
4.1 Taylor’s theorem [242]
4.2 Extrema of real-valued functions [248]
4.3 Constrained extrema and Lagrange multipliers [265]
*4.4 The implicit function theorem [280]
4.5 Some applications [291]
Review exercises for Chapter 4 [298]
5 DOUBLE INTEGRALS [303]
5.1 Introduction [303]
5.2 The double integral over a rectangle [314]
5.3 The double integral over more general regions [329]
5.4 Changing the order of Integration [336]
*5.5 Some technical Integration theorems [342]
Review exercises for Chapter 5 [352]
6 THE TRIPLE INTEGRAL, THE CHANGE OF VARIABLES FORMULA, AND APPLICATIONS [355]
6.1 The triple integral [355]
6.2 The geometry of maps from R2 to R2 [364]
6.3 The change of variables theorem [371]
6.4 Applications of double and triple integrals 389 *6.5 Improper Integrals [401]
Review exercises for Chapter 6 [408]
7 INTEGRALS OVER PATHS AND SURFACES [413]
7.1 The path integral [413]
7.2 Line Integrals [419]
7.3 Parametrized surfaces [440]
7.4 Area of a surface [449]
7.5 Integrals of scalar functions over surfaces [463]
7.6 Surface integrals of vector functions [472]
Review exercises for Chapter 7 [486]
8 THE INTEGRAL THEOREMS OF VECTOR ANALYSIS [490]
8.1 Green’s theorem [490]
8.2 Stokes’ theorem [504]
8.3 Conservative fields [517]
8.4 Gauss’ theorem [528]
*8.5 Applications to physics and differential equations [544]
*8.6 Differential forms [566]
Review exercises for Chapter 8 [582]
ANSWERS TO ODD-NUMBERED EXERCISES [585]
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Libros Libros Instituto de Matemática, CONICET-UNS
Libros ordenados por tema 26 M364v (Browse shelf) Available A-6643

ANÁLISIS MATEMÁTICO II A

CÁLCULO DIFERENCIAL E INTEGRAL II

CÁLCULO II


1 THE GEOMETRY OF EUCLIDEAN SPACE [1] --
1.1 Vectors in three-dimensional space [1] --
1.2 The inner product [21] --
1.3 The cross product [30] --
1.4 Cylindrical and spherical coordinates [47] --
1.5 n-dimensional Euclidean space [57] --
Review exercises for Chapter 1 [68] --
2 DIFFERENTIATION [75] --
2.1 The geometry of real-valued functions [76] --
2.2 Limits and continuity [95] --
2.3 Differentiation [118] --
2.4 Properties of the derivative [131] --
2.5 Gradients and directional derivatives [145] --
2.6 Iterated partial derivatives [157] --
*2.7 Some technical differentiation theorems [168] --
Review exercises for Chapter 2 [180] --
3 VECTOR-VALUED FUNCTIONS [189] --
3.1 Paths and velocity [189] --
3.2 Arc length [201] --
3.3 Vector fields [211] --
3.4 Divergence and curl of a vector field [220] --
3.5 Vector differential calculus [231] --
Review exercises for Chapter 3 [238] --
4 HIGHER-ORDER DERIVATIVES; MAXIMA AND MINIMA [241] --
4.1 Taylor’s theorem [242] --
4.2 Extrema of real-valued functions [248] --
4.3 Constrained extrema and Lagrange multipliers [265] --
*4.4 The implicit function theorem [280] --
4.5 Some applications [291] --
Review exercises for Chapter 4 [298] --
5 DOUBLE INTEGRALS [303] --
5.1 Introduction [303] --
5.2 The double integral over a rectangle [314] --
5.3 The double integral over more general regions [329] --
5.4 Changing the order of Integration [336] --
*5.5 Some technical Integration theorems [342] --
Review exercises for Chapter 5 [352] --
6 THE TRIPLE INTEGRAL, THE CHANGE OF VARIABLES FORMULA, AND APPLICATIONS [355] --
6.1 The triple integral [355] --
6.2 The geometry of maps from R2 to R2 [364] --
6.3 The change of variables theorem [371] --
6.4 Applications of double and triple integrals 389 *6.5 Improper Integrals [401] --
Review exercises for Chapter 6 [408] --
7 INTEGRALS OVER PATHS AND SURFACES [413] --
7.1 The path integral [413] --
7.2 Line Integrals [419] --
7.3 Parametrized surfaces [440] --
7.4 Area of a surface [449] --
7.5 Integrals of scalar functions over surfaces [463] --
7.6 Surface integrals of vector functions [472] --
Review exercises for Chapter 7 [486] --
8 THE INTEGRAL THEOREMS OF VECTOR ANALYSIS [490] --
8.1 Green’s theorem [490] --
8.2 Stokes’ theorem [504] --
8.3 Conservative fields [517] --
8.4 Gauss’ theorem [528] --
*8.5 Applications to physics and differential equations [544] --
*8.6 Differential forms [566] --
Review exercises for Chapter 8 [582] --
ANSWERS TO ODD-NUMBERED EXERCISES [585] --

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