Real Functions of Several Variables - Maximum...

A book concerning calculus 2b - Real Functions in Several Variables, Examples of Maximum and Minimum Integration and Vector Analysis

1. Preface

2. The range of a function in several variables
2.1 Maximum and minimum
2.2 Extremum

3. The plane integral
3.1 Rectangular coordinates
3.2 Polar coordinates

4. The space integral
4.1 Rectangular coordinates
4.2 Semi-polar coordinates
4.3 Spherical coordinates

5. The line integral

6. The surface integral

7. Transformation theorems

8. Improper integrals

9. Vector analysis
9.1 Tangential line integral; gradient field
9.2 Flux and divergence of a vector field; Gauss's theorem
9.3 Rotation of a vector field; Stokes's theorem
9.4 Potentials

A. Formulæ
A.1 Squares etc.
A.2 Powers etc.
A.3 Differentiation
A.4 Special derivatives
A.5 Integration
A.6 Special antiderivatives
A.7 Trigonometric formulæ
A.8 Hyperbolic formulæ
A.9 Complex transformation formulæ
A.10 Taylor expansions
A.11 Magnitudes of functions