<p>Taylor series are much more interesting in complex analysis, where they are the central concept on which most of the theory is built.</p>
<p>Yeah, the tail wags the dog in calc II as my prof would say. : )</p>
<p>Taylor series only look hard now... they are not so bad and they are fairly important so get them down now. Taylor series should not be optional, you will see them again.</p>
<p>I found Calc II to be easier than Calc I and really enjoyed it (had a great professor though.)
DiffEq was easy but you don't appreciate DiffEq if you take it before you really know what diffeqs are used for, otherwise it just seems like a mess of equations.
LinAlg was fairly easy but there was a lot of material, fascinating topic though.</p>
<p>we use stewart as well and i like it, but maybe that's because it's the only one i've ever used. what would you guys change about it?</p>
<p>Stewart isn't that bad.</p>
<p>Another thing that my math prof likes to say -- "Math books are written by mathematicians for mathematicians."</p>
<p>They are inherently difficult to understand without a supplementary lecture.</p>
<p>Tom apostle wrote the book on calculus and thats why top schools use it, my school uses stewart I couldent learn from it, so I asked my professor he he had a copy of apostle for me to learn from surly he had everything the man had ever written, so then i used that and became great in calc, if the book has a great looking cover and nice pictures it usually sucks,</p>
<p>Calc 3 - went to class, up to 2 hrs per week outside of class. I got through this because of what I did for physics in high school.
Linear Algebra - About 5 hrs/ week total including class / hw. (found it really boring so I did not go)
Diff q - went to class and about 4-5 hrs outside of class a week. Useful for other classes I took, just wish it went more into analysis.</p>
<p>Hey, can somebody tell me why exactly taylor series are so important in engineering? I'm just curious to their application haha.</p>
<p>Taylor series are the one concept I struggled with in BC calc, and although I am pretty sure I am going to test out of calc I and II, if Taylor series are that important I may retake calc II in college.</p>
<p>Taylor series allow you to approximate a function very closely. If the function is a pain to integrate, the Taylor series is easier to integrate 9 times out of 10. Really a nice thing to be able to integrate a polynomial instead of something that is a god awful mess.</p>
<p>What should I especially be paying attention to for my physics degree? Obviously, I try to do the best I can and learn everything. I did get an A in Cal I. I'm thinking about taking a 5-week Cal II class over the summer, but I really don't want to do so.</p>
<p>And even if you don't have a closed-form function to work with, but just data. Taylor series proves invaluable in those situations as well.</p>
<p>There are a couple of uses of taylor series I can think of...approximation is one. </p>
<p>For example, in physics one of the first derivations we did is multipole expansions, which can be extremely complicated to solve in closed form, but fairly simple to find the large-distance approximation using the taylor series - you can determine a dipole field falls off as 1/r^3, for example, since all you care about is finding the first nonzero coefficient in the taylor series.</p>
<p>Another is to simplify calculations(more approximation), for example, the calculations to find the beta(amplification gain) in a bipolar transistor has a whole lot of hyperbolic functions in it, which are wholly unnecessary since the values you are taking, say, the sech of, are very close to 1, so you can replace with a few terms of taylor series and make expressions simpler without losing too much accuracy.</p>
<p>Third use is entirely unrelated - you can solve differential equations by the power series method. This can involve more approximation or can be solved precisely.</p>
<p>You shouldn't be too worried, though, if any of that seems overwhelming. Really all you need to know at minimum is what a taylor series/power series is, that it converges to that function for values within some radius of convergence, and know how to read the summation notation (i.e. the big E thing)...you're not going to be hit up on a test and asked what's the taylor series expansion of tan(x) is :)</p>