Vector calculus / Jerrold E. Marsden, Anthony J. Tromba.
Editor: New York : W. H. Freeman, c1988Edición: 3rd edDescripción: xiv, 655 p. : il. ; 25 cmISBN: 0716718561Tema(s): Calculus | Vector analysisOtra clasificación: 26-01 (26B12 26B20)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]
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 M364v (Browse shelf) | Available | A-6643 |
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] --
MR, REVIEW #
There are no comments on this title.