In his first lesson (transcripted in "Tips on Physics"), Feynman talks about math for physicists in a very cool and practical way. And at the end of the section he talks something like "so the first thing to do is to learn to learn derivative, integral and algebra" (I don't know how much precise I'm being because I've read it in Portuguese). I would to know if there is some book that deals with math as Feynman did it in this lesson (respecting formalities, but teaching how to use the practical rules)? Also, someone have any recommendations for algebra book (college level)?
Higher maths for beginners is ana amzing little book on all the subjects you mentioned, written by one of the fathers of Soviet nuclear bomb, and theoretical phsyicists.
On math physics, the best introductory test is Elements of applied math physics, it has dufferential equations and complex analysis and other cool topics. Unfortunately, it may not have English version.
The comprehensive analysis text is Fundamentals Mathematical Analysis. It's a Russian textbook, but it's old school, i.e. very readable.
Another must have book is Differential Equations and Calculus Variations.
The best reference on PDEs is PDE by Bitsadze, I consult it all the time, it's very thin, and chapters are mostly self-contained.
All these books were used by Physics students, I can guarantee that.
Tthis is again probably a duplicate. See here for a full list of links to book questions.
By 'alrebra book (college level)' what do you mean exactly?
Algebra in maths is a HUGE area.
If you mean Linear Algebra, then maybe I.M. Gelfand is a great book, but probably not the best for a first read.
Anton & Roerrs would be better for a first book, especially if you're not a pure mathematician, it has lots and lots of nice examples of applications of linear algebra.
If you mean Modern (Abstract) Algebra, which includes group theory and many other things used in physics, then I would recommend J.R. Durbin as a great first (maths) book on abstract algebra.
I have little doubt in your ability to search for these online and you will find lists of contents.
For linear algebra regarding matrices (gaussian elimination, eigenvectors, laplace transforms etc.) try the MIT opencourseware playlist on youtube.
In case of link rot in the future :
Course Title : MIT 18.06 Linear Algebra, Spring 2005
Instructor: Prof. Gilbert Strang
Abstract : This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. *Please note that lecture 4 is unavailable in a higher quality format. Find more lecture notes, study materials, and more courses at http://ocw.mit.edu.