I expect you mean "evaluate" transcendental functions, not "solve". I suggest you google "Taylor Series".
I need to know what math literature would be the most appropriate for a beginner like me when trying to solve transcendental funtions. While it is nice to have a calculator to find PI, e, non-perfect roots, etc... for example, I instead, would like to find all of them myself using sheer brain power with paper and pencil. So if any of you know of what books from Amazon.com could help me get started please list them.
I want some math text that covers these topics. Perhaps a math text covering number theory would give me insight into evaluating transcendental functions (I did not originally post here by-the-way, it was moved)? I hope Google or hiring an instructor is not my only resources. It appears a very large majority of math experts are unable to help me which is kind of strange because I tried almost every where. I really hope the calculator or computer did not destroy the old ways of solving these functions.
ProveIt's reply is quite to the point: the most efficient method for calculating transcendental functions such as sin(x), cos(x) and e^x is by using Taylor approximating polynomials (finite sums of an infinite Taylor series). Such a topic can be found on several calculus websites, and/or textbooks. Until well into the 20th century, these WERE the methods people used to calculate long-hand.
here is one such web-site: Pauls Online Notes : Calculus II - Taylor Series
(if this is not self-explanatory to you, you can navigate to where you can pick up his notes. it's a reasonably accessible site containing notes for several math courses).
here is a freely-available pdf calculus textbook from a professor at MIT: http://ocw.mit.edu/ans7870/resources...s/Calculus.pdf
the mathematics behind Taylor series is too involved to explain in the space allotted for forum posting.