Numerical Methods Texts, mid-level. what are the 3-4 numerical analysis/methods texts, that you value as best? 
I would prefer a mid-level treatment, balanced between theory and applications.
Right now, I'm using the book by Sauer. It is pretty good, but I wish to couple it with a deeper treatment.
Many Thanks.
 A: Here are some recommendations (you can peruse their table-of-contents online):
Theory and applications


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*(1) Numerical Analysis - Burden and Faires

*(2) Numerical Methods - Pal

*(3) Numerical Methods for Engineers, Chapra, Canale


If price is an issue, you might want to look at the following excellent books (note, some of these are more theory than applied, but I included a mix - check out the TOCs online). 
Dover Books 


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*(1) Analysis of Numerical Methods,  Isaacson, Keller 

*(2) Numerical Methods, Dahlquist, Bjorck

*(3) Numerical Methods for Scientists and Engineers, Hamming

*(4) A First Course in Numerical Analysis: Second Edition, Ralston , Rabinowitz

*(5) Introduction to Numerical Analysis: Second Edition, Hildebrand


You might also want to check out your local university library and look into notes/lectures at places like Open Courseware (like MIT and many others).
Lastly, you should certainly have an environment that allows you to explore these methods like a CAS and you can get a commercial one (like Mathematica, Maple, MatLab...) or a free one (like SAGE, Maxima, GP/Pari...).
