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Limits in calculus numerical alegbaical12/16/2023 ![]() (Those who are interested can go off on their own and Julia provides a rich opportunity to do so.) Within this restricted set, are operators that make many of the computations of calculus reduce to a function call of the form action(function, arguments.). This set is sufficient for working many of the problems in calculus, but do not cover thoroughly many aspects of programming. The notes restrict themselves to a reduced set of computational concepts. We feel Julia has a very natural syntax that makes the initial start up not so much more difficult than using a calculator. Our real goal is to get at the concepts using technology as much as possible without getting bogged down in the mechanics of the computer language. Doing the symbolic treatment by hand can be very beneficial while learning, and computer algebra systems make those exercises seem kind of pointless, as the finished product can be produced much easier. Theses notes are a bit different in that Julia is primarily used for the numeric style of computing and the algebraic/symbolic treatment is added on. ![]() ("Siri what is the graph of x squared minus 4?") For learning purposes, computer algebra systems model very well the algebraic/symbolic treatment of the material while providing means to illustrate the numeric aspects. ![]() The popular WolframAlpha website calls the full power of Mathematica while allowing an informal syntax that is flexible enough to be used as a backend for Apple's Siri feature. There are many examples of integrating a computer algebra system (such as Mathematica, Maple, or Sage) into the calculus conversation. These notes use the programming language Julia to illustrate the graphical, numerical, and, at times, the algebraic aspects of calculus. The Harvard style rule of four says that as much as possible the conversation should include a graphical, numerical, algebraic, and verbal component. ![]() Since the mid 90s there has been a push to teach calculus using many different points of view. The package contains some support functions and the files that generate the notes being read now. CalculusWithJulia.jl is a package for a set of notes for learning calculus using the Julia languge. ![]()
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