## Quiz #0. Am I ready for Chem 537?

There are a few mathematical skills that you need to have in order to succeed in this class. Among others, they include: differentiation, integration, solving equations and manipulation with complex numbers and matrices. Try these problems below and submit your answers. This quiz will not be graded. I only need to see to what extent these topics have to reviewed. It is OK if you can't solve all of them. It is also OK if you use some mathematical software such as Mathematica, Mathcad, etc.(if necessary) as long as you know what it does.

1) Differentiation:

(2x3 + sin(2x) - log(x2) + x5/(x2 +1))' =
y(x) = 3x2 - 1; f(y,x) = xy + x; df/dx =
(x3/(e5x - 1))' =

2) Integration:

3) Complex numbers:

(-4)1/2 =
i1/2 =
(cos(x) + i sin(x)) (cos(x) - i sin(x)) =
ii =
eip = .

4) Matrices. If the two matrices are:

 A = ( 1 3 -5 )           and B = ( 3 2 1 ) 3 2 4 1 4 2 3 3 2 0 -1 1

Calculate (use comas to separate numbers in a row):

A + B =       A x B =
B x A =      A x B-1 =
A-1 =

5. Solving differential equations:

y' = sinx;             y =
y' = - 3x5y3;        y =