Brushing up on calc to prepare for QM

[robertjford80]

I make way too many mistakes in calc so I'm going to go back and brush up so as to prepare for the exciting moment when I finally start studying QM. I'm using the Thomas text on calc, it's contents are listed below. What sections do you think I should really master. Plus David Griffiths' book uses Legendre, Hermite and Laguerre polynomials, spherical harmonics, Bessel, Neumann and Hankel functions, Airy functions and even the Riemann zeta function, plus Fourier transforms, Hilbert spaces, hermitian operators, Clebsch-Gordan coefficients and Lagrange multipliers, so you don't need to recommend studying those.

 

[Mattowander]

I just finished my first quantum mechanics course and really you should be comfortable with all of these topics. More than anything we used math from linear algebra and PDE's so calculus is just one area of math that you should study to prepare for quantum mechanics.

 

[genericusrnme]

Uuuugh, stay away from Griffiths buddy, for your own good

Pick yourself up a copy of M Boas' Mathematical Methods in the Physical Sciences and read up on whatever you need to know when you encounter it.

I'd also recommend the first third of Landau and Lifgarbagez book on non relitivistic QM as an intro to QM over Griffiths' book.

 

[dextercioby]

[...]

Pick yourself up a copy of M Boas' Mathematical Methods in the Physical Sciences and read up on whatever you need to know when you encounter it.
[...]

To me Arfken and Weber's book is a valid alternative, too.

 

[robertjford80]

as for Griffith's book, yea, I looked at it and it looked extremely poor on explanations which is what I hate more than anything. I'm just going to use that book in case I can't find a problem explained elsewhere, or maybe that will be the last book I read before I move on to QFT. As for Arken, that book gets really bad reviews on Amazon.com. I think the solution manual has no answers. I hate books without answers. There's no point in doing exercise if you can't find out if you've done it right.

 

[clope023]

as for Griffith's book, yea, I looked at it and it looked extremely poor on explanations which is what I hate more than anything. I'm just going to use that book in case I can't find a problem explained elsewhere, or maybe that will be the last book I read before I move on to QFT. As for Arken, that book gets really bad reviews on Amazon.com. I think the solution manual has no answers. I hate books without answers. There's no point in doing exercise if you can't find out if you've done it right.

You could try Schaum's Outline of Advanced Mathematics for Engineers and Scientists by Spiegel or Advanced Engineering Mathematics by Kreizig; both have the same maths as Boas but they are both far more organized and less wordy so they get straight to the point. The schaum's is chock full of fully solved problems and examples; Kreizig is too and I believe it has a separate solution manual.

 

[Jorriss]

If your goal is calculus for physics then make sure you have developed your geometric/physical intuition for calculus. What does the derivative mean physically (usually)? The integral? What's the logic behind the derivative tests?

Otherwise - outside of knowing how to take derivatives and integrals - specifically review integration by parts, polar and spherical coordinates, and complex numbers.

 

[robertjford80]

If your goal is calculus for physics then make sure you have developed your geometric/physical intuition for calculus. What does the derivative mean physically (usually)? The integral? What's the logic behind the derivative tests?

That's the hardest part, but I'm working on that.