Vector Calculus 5 Edition
Authors: J. E. Marsden and A. J. Tromba

Index Code :  Science.Mathematics.VectorCalucus

Example Code

Chapters / Sections

Examples
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