Good book for vector/multivariable calculus

[gangsta316]

What's the best book for multivariable calculus? I'm a second year undergraduate student in Mathematics. Here is the content:

Functions from Rn to Rm: differentiation, contractions, Newton’s method, inverse function
theorem, implicit function theorem, higher derivatives.
Optimisation: extrema, constraints, Lagrange multipliers.
Calculus of variations: Euler-Lagrange, simple applications.
Integrals in Rn: curves, line integrals, Green’s theorem, transformation of integrals.
Vector calculus: vector fields, grad, div, curl, surface integrals, divergence theorem, Stokes’s
theorem, curvilinear coordinates.
Partial differential equations(simple wave, Laplace, heat).
Cartesian tensors: simple properties and notation, invariance.

At the moment I am having some difficulty with the integration (line integrals, surface integrals, divergence theorem, Green's theorem etc.).

Thanks for any help.

 

[mathwonk]

there is no best book. a book is good for you if you can learn from it, so you must participate in deciding which is best for you. I suggest courant, or courant and john, vol. 2, or spivak calculus on manifolds, or apostol vol. 2, or apostol mathematical analysis, or williamson crowell and fox, or fleming, or theodore shifrin's book. there are also many older books that are excellent if more traditional such as by widder, buck, or henry edwards. at a very advanced level there is the book by dieudonne, foundations of modern analysis. oh yes, and some students will benefit from loomis and sternberg, but only those who already know the material well. there are also books by lang, such as analysis I.