Calculus 2a - Real Functions in Several Variables

A book concerning Calculus 2a - Real Functions in Several Variables.

Preface

1. Integration of trigonometric polynomials

2. Complex decomposition of a fraction between two polynomials

3. Integration of a fraction between two polynomials

4. The domain of a fraction

5. The chain rule

6. Calculation of the directional derivative

7. Approximating polynomials

8. Gradient fields; antiderivatives

9. An overview of integration in the plane and in the space

10. Reduction of a plane integral; rectangular version

11. Reduction of a plane integral; polar version

12. Reduction of a space integral; rectangular version

13. Reduction of a space integral; semi-polar version

14. Reduction of a space integral; spherical version

15. Line integrals

16. Surface integrals

17. Transformation theorems

18. Improper integrals; bounded domain

19. Improper integrals; unbounded domain

20. The setting up of a line, a plane, a surface or a space integral

21. Tangential line integrals; gradient field

22. Flux and divergence of a vector field; GauB's theorem

23. Rotation of a vector field; GauB's theorem

24. Green's theorems in the plane

25. Nabla calculus

26. Partial integration in higher dimension

27. Vector potential

28. Global maximum and minimum

29. Extrema; local investigation

A. Formulæ
A.1 Sguares 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