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Multivariable Calculus/Calculus & Geometry textbook suggestions 
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#1
May1711, 10:20 PM

P: 71

Hello all,
I am currently in University and I am retaking a course that I dropped last year due to the fact that there was no textbook and the time I spent in the course was a frantic scramble for reliable information and attempting to understand what the professor was teaching. I have looked before and the only textbook that I found that was remotely close to the material that is covered in the course is Multivariable Calculus by Edwards and Penney. I am asking the community for any suggestions for textbooks that cover most, if not all of the topics listed below:  Differentiation in Several Variables Partial derivatives, directional derivatives, del operator, Meanvalue theorem for a function of several variables, differentiation through an integral, Leibniz's Rule 2nd order derivatives and Clairaut's theorem, Hessian Matrix. Functions from several variables to several variables, Jacobian Matrix  Inverse  and Implicit functions in several variables Inverse function theorem Implicit function theorem  Quadratic forms Matrix Representation Change of variable & diagonalization by congruence Positive & Negative definiteness, Semidefinieness, determinantal criteria Sylvester's Theorem  Extrema Local extremacritical points, local max, local min, saddle points, determinantal tests on the Hessian Matrix Global extremaexistence for continuous functwions on closed, bounded sets, finiding constrained extrema by the method of Lagrange multipliers  Curves and Surfaces Space curves defined parametricallytangent, normal, binormal, arc length, curvature, torsion Surfacesimplicit and parametric definitionstangent plane, normal line Space curves defined as intersecting surgaces, related quadratic & cubic forms  Integration in several Variables Multiple and iterated integrals Change of order of variables Change of variable formula in general Polar, cylindrical & spherical coordinates Line integrals, consecutive and nonconsecutive vector fields, curl operator Surface integrals, projection onto a plane, parametric surgace integrals Stokes' theorem, boundary curve, orientation Gauss' theorem, boundary surgace, div operator Any suggestions will be greatly appreciated and sorry for the long list, I didn't want to leave anything out. 


#2
May1711, 10:48 PM

Sci Advisor
HW Helper
PF Gold
P: 3,162

Either of these should do the trick:
Courant,Introduction to Calculus and Analysis, Vol. II Apostol, Calculus, Vol. 2 


#3
May1811, 02:08 AM

P: 210

I fully second Apostol and Courant.



#4
May1811, 07:10 AM

P: 792

Multivariable Calculus/Calculus & Geometry textbook suggestions
Apostol and Courant are excellent but they are mathematically rigorous and I don't know if that is what you want. If not, then there is the book by Schey Div, Grad, Curl and All That for intuition; Marsden and Tromba Vector Calculus is an intermediate sort of book; and the old favourite is Stewart Multivariable Calculus or the relevant chapters in his Calculus. Stewart gives the simplest presentation of calculus.
I suggest going to the library and looking through all these books and deciding for yourself which one best suites your needs. 


#5
May1811, 10:29 AM

P: 141

any multivariable calculus text will fit your description..



#6
Jun2812, 09:07 PM

P: 4

I agree that Courant and Apostol are NOT light reads. Stewart has an excellent MV book that is good for all audiences. A lesser known book is Howard Anton's Calculus, A new horizon, which has a lot of good applications of calc added in. Of course the Khan Academy has very easytounderstand lectures, but not in all of the above mentioned topics.



#7
Jul112, 01:38 PM

P: 18

There's a good free book available here:
http://quod.lib.umich.edu/cgi/t/text...97602.0001.001 It covers all those topics, has solutions to exercises, and doesn't really toy around like some Calc texts do. 


#8
Jul112, 05:16 PM

HW Helper
P: 1,347




#9
Jul212, 12:30 AM

P: 18

Sorry, that was the link to volume I. Here's the link to volume II which includes multivariable calc, linear algebra, and geometry:
http://quod.lib.umich.edu/cgi/t/text...97602.0002.001 


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