Differential Equations/linear Algebra, A good Review

Hello All,

I am going back to graduate school but I need to take a Differential Equations/Linear Algebra course as part of a prerequisite. Being and organic chemist I really haven't used my calculus in a while. I am reviewing my integrals at the moment but I thought I should ask the PhysOrg community at large for some advice on what to focus on nailing down since many of you do this stuff for a living. So I am looking for maybe a short list of Integration/Differentiation techniques to really nail down so I can do well. Any other advice is as always very welcome.

Regards,
Caleb

For differentiaition, the chain rule and the product rule. Then the quotient rule (I always just use the product rule and invert one function!)

For integration, once you've got the basics you'll need to be comfortable with integration by parts, then you'll start integration by inspection which is less of a rule and more of a skill...

Good luck!

For Differential Equations, I would make sure that you're comfortable with Leibniz notation in calculus, differentials, that you know your trig identities and trig derivatives/integrations, and that you're able to do partial fractions.

http://www4.ncsu.edu/unity/lockers/users/f...rs/partial.html



When I took Intro ordinary differential equations, partial fractions was probably the hardest thing (Sadly. It has nothing to do with calculus, per se, yet it killed me...) Also, integration by parts is crucial, as has been mentioned.

Oh, one more thing that was useful for me: Be comfortable with adding/subtracting exponents. You'll see a lot of e^-1, e^-x and so forth.

This post has been edited by Grasshopper on Aug 14 2008, 06:14 PM

Thank you all for your suggestions. So many memories coming back I also want to apologize for the double post...not really sure what happened there.

Regards,
Caleb

Also be sure to learn all the "prerequisite" functions by heart, they come up a LOT and it makes things a lot easier if you know them off the top of your head.

Things like the integrals/derivatives of e^x, cos(x), sin(x), etc.

This post has been edited by excaza on Aug 14 2008, 07:00 PM

As a chemist, you certainly have access to a "Handbook of Chemistry and Physics".

In the appendix for maths, you have extensive lists of differentials and integrals. Too extensive to learn - and they give also small variations and combinations, which is nice to use when you've forgotten your calculus - but picking some at the beginning of the list would cover all the functions you need to know.

Then, you have also to learn the techniques to combine all these functions.

Interestingly I was looking through this exact section and is why I inquired here as I had an information over load

Regards,
Caleb