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Calculus of Several Variables: Lecture Notes

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Author(s): Prof. James McKernan
Publisher: Massachusetts Institute of Technology (MIT)
Year: 2010

Language: English
City: Cambridge, MA
Tags: 18.022; calc; calculus; mathematics; maths; math; single variable; limits; differentiation; differential; integration; integral; continuity; differentiability; analysis; real; complex; multiple variables; multivariable; multivariate; several variables

1. Vectors in R2 and R3
2. Dot product
3. Cross product
4. Planes and distances
5. n-dimensional space
6. Cylindrical and spherical coordinates
7. Functions
8. Limits
9. The derivative
10. More about derivatives
11. Higher derivatives
12. Chain rule
13. Implicit functions
14. Parametrised Curves
15. Arclength
16. Moving frames
17. Vector fields
18. Div grad curl and all that
19. Taylor Polynomials
20. Maxima and minima: I
21. Maxima and minima: II
22. Maxima and minima: II
23. Inclusion-Exclusion
24. Triple integrals
25. Change of coordinates: I
26. Change of coordinates: II
27. Line integrals
28. Manifolds with boundary
29. Conservative vector fields revisited
30. Surface integrals
31. Flux
32. Stokes Theorem
33. Gauss Theorem
34. Forms on Rn