Vector Calculus 5 Edition |
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Authors: J. E. Marsden and A. J. Tromba | |||||||||||||||||
Index Code : Science.Mathematics.VectorCalucus |
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Example Code |
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Chapters / Sections |
Examples |
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1. The Geometry of Euclidean Space | |||||||||||||||||
1.1 Vectors in Two- and Three-Dimensional Space | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
1.2 The Inner Product, Length, and Distance | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |||||
1.3 Matrices, Determinants and the Cross Product | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |||||
1.4 Cylindrical and Spherical Coordinates | 1 | 2 | 3 | ||||||||||||||
1.5 n-Dimensional Euclidean Space | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |||||
2. Differentiation | |||||||||||||||||
2.1 The Geometry of Real-Valued Function | 1 | 2 | 3 | 4 | 5 | 6 | |||||||||||
2.2 Limits and Continuity | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | ||
2.3 Differentiation | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |||||||
2.4 Introduction to Paths and Curves | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ||||||||
2.5 Properties of the Derivative | 1 | 2 | 3 | 4 | 5 | 6 | |||||||||||
2.6 Gradients and Directional Derivatives | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||||||||
3. Higher-Order Derivatives; Maxima and Minima | |||||||||||||||||
3.1 Iterated Partial Derivative | 1 | 2 | 3 | 4 | 5 | 6 | |||||||||||
3.2 Taylor's Theorem | 1 | 2 | 3 | 4 | |||||||||||||
3.3 Extrema of Real-Valued Functions | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |||||||
3.4 Constrained Extrema and Langrange Multipliers | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |||||
3.5 The Implicit Function Theorem | 1 | 2 | 3 | 4 | |||||||||||||
4. Vector-Valued Functions | |||||||||||||||||
4.1 Acceleration and Newton's Second Law | 1 | 2 | 3 | 4 | |||||||||||||
4.2 Arc Length | 1 | 2 | 3 | 4 | 5 | 6 | |||||||||||
4.3 Vector Fields | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||||||||
4.4 Divergence and Curl | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
5. Double and Triple Integrals | |||||||||||||||||
5.1 Introduction | 1 | 2 | 3 | 4 | |||||||||||||
5.2 The Double Integral Over a Rectangle | 1 | 2 | 3 | ||||||||||||||
5.3 The Double Integral Over More General Regions | 1 | 2 | 3 | ||||||||||||||
5.4 Changing the Order of Integration | 1 | 2 | 3 | ||||||||||||||
5.5 The Triple Integral | 1 | 2 | 3 | 4 | 5 | 6 | |||||||||||
6. The Change of Variables Formula and Applications ... | |||||||||||||||||
6.1 The Geometry of Maps From R2 to R2 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||||||||||
6.2 The Change of Variables Theorem | 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||||||||||
6.3 Applications | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||||||||
6.4 Improper Integrals | 1 | 2 | 3 | 4 | |||||||||||||
7. Integrals Over Paths and Surfaces | |||||||||||||||||
7.1 The Path Integral | 1 | 2 | |||||||||||||||
7.2 Line Integrals | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |||||
7.3 Parameterized Surfaces | 1 | 2 | 3 | 4 | 5 | ||||||||||||
7.4 Area of a Surface | 1 | 2 | |||||||||||||||
7.5 Integrals of Scalar Functions Over Surfaces | 1 | 2 | 3 | 4 | 5 | ||||||||||||
7.6 Surface Integrals of Vector Fields | 1 | 2 | 3 | 4 | 5 | 6 | |||||||||||
7.7 Applications to Differential Geometry, Physics, ... | 1 | 2 | |||||||||||||||
8. The Integral Theorems of Vector Analysis | |||||||||||||||||
8.1 Green's Theorem | 1 | 2 | 3 | 4 | |||||||||||||
8.2 Stokes' Theorem | 1 | 2 | 3 | 4 | 5 | ||||||||||||
8.3 Conservative Fields | 1 | 2 | 3 | 4 | |||||||||||||
8.4 Gauss' Theorem | 1 | 2 | 3 | 4 | 5 | 6 | |||||||||||
8.5 Some Differential Equations of Mechanics and ... | |||||||||||||||||
8.6 Differential Forms | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |