Am I ready for Chem 539?

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 compare your results with the answers provided.

Differentiation:

1. (2x³ + sin(2x) - log(x²) + x⁵/(x² +1))' = ?
2. y(x) = 3x² - 1; f(y,x) = xy + x; df/dx = ?
3. (x³/(e^5x - 1))' = ?

Integration:

Complex numbers:

1. i^1/2 = ?
2. (cos(x) + i sin(x)) (cos(x) - i sin(x)) = ?
3. iⁱ = ?

Solving equations:

1.

Matrices:

If the two matrices are:

Calculate:
1. A + B
2. A x B
3. B x A
4. A / B

Quantum Mechanics:

1. Out of the three potentials, parabolic, rectangular with infinite walls, and coulombic, which one has equaly spaced energy levels, levels with decreasing gaps from the bottom to the top, and the levels with increasing gaps?

2. How many electrons can be placed onto the shell with n = 9 in a hydrogen like atom?
3. Show that the function y = x²e^-ax is an eigen function of the operator A:

A = d²/dx² - 2/x² + 4a/x

What is the eigen value?

Last updated on 11/20/09