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skysaw
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13 Jan 2009, 10:05 am

Hello WP'ers. I was a math(s) student many years ago, a very lazy one who has now forgotten almost everything he learnt.
I am interested to see if there are any math(s) books or online lecture notes you guys can recommend.
I'm particularly looking for books that cover basic first year undergrad stuff like Taylor expansions, Euler's Formula ( e^ix = cos(x) +i*sin(x) ), hyperbolic trig functions, ODEs, l'hopital's rule, sequences and series etc.
A single book that covered all this stuff would be cool.
I've got books on set theory and discrete maths already, and a book on laplace transforms and fourier analysis.

Also, are there any books covering stuff like continued fractions, Egyptian fractions etc, i.e., the sort of stuff that is sort of inbetween high school and first year undergrad level and that often ends up not getting taught at all?



twoshots
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13 Jan 2009, 11:47 am

Can't recommend anything right now but to point you in the right direction:

Quote:
Taylor expansions...hyperbolic trig functions...l'hopital's rule, sequences and series etc.

These should be covered in any calculus text, although if you're looking for more in depth and you're otherwise comfortable with the calculus you might want to look into an analysis or advanced calc text.
Quote:
Euler's Formula ( e^ix = cos(x) +i*sin(x) )

Will be covered in any complex variables text.
Quote:
ODEs

Basic (seperable) ODEs will be covered in a calc book, but you'll probably need a book devoted to the subject.


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Kangoogle
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13 Jan 2009, 1:08 pm

Look at the Schaum's outlines series. If you are after online lecture notes (and videos) Google Open Courseware.



Wurzel
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13 Jan 2009, 11:24 pm

Spivak's Calculus is the best. For a book on ODEs try Carrier and Pearson.



Kangoogle
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13 Jan 2009, 11:31 pm

Wurzel wrote:
Spivak's Calculus is the best. For a book on ODEs try Carrier and Pearson.

Spivak is supposed to a bit advanced for 1st year Calculus, asides Salas Hille and Etgen is just as good really. But Schaums have the advantage of being as cheap as chips - plus they are so concise that they save an awful lot of time in doing my degree.



mixtapebooty
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14 Jan 2009, 3:09 am

Wurzel wrote:
Spivak's Calculus is the best. For a book on ODEs try Carrier and Pearson.


I've heard the same thing about Spivak's Calculus from a Particle Physics post graduate. I guess if someone has already taken Calc I & II a while back, that it could work for them. Consider your investment wisely.