Problem Set 1.

This set of questions is not graded for correctness only for participation. Please answer the multiple choice questions, if you think you know the correct answer mark it, otherwise don’t guess but mark “don’t know.” Do not spend more than 30 seconds, on a question, if you don’t know the answer right away don’t try to look for it, this is trying to probe your current state of knowledge and help in aiming the course at the right level.

Basic Math

1. The absolute value of the complex number z = 1 + i is

a) 2 b) Ö2 c) 1 d) don’t know

2. The exponential function over the real numbers is

a. monotonic

b. periodic

c. symmetric

d. don’t know

3. e^ix = A cos x + B sin x, if

a. A = 1 and B = i

b. A = 1 and B = -I

c. Don’t know

4. If z is a complex number equal to its conjugate, then

a. z is purely imaginary

b. z is real

c. such z does not exist

d. Don’t know

5. At a minimum of a function

a. The first derivative is zero and the second derivative is nonnegative

b. The second derivative is zero and the first derivative is nonnegative

c. Don’t know

6. The indefinite integral is the inverse of the

a. Derivative

b. The absolute value

c. The definite integral

d. Don’t know

7. If f(x) is a function and f’(x) its derivative, name the function for which f(x) = f’(x)

a. exp(x)

b. sin(x)

c. cos(x)

d. log(x)

e. don't know

8. The first two terms in the expansion of sin x are

Sinx ~ x – x³/6 + O(x⁵)

A taylor expansion

The integral of a function is graphically represented by the

Length of the curve of the graph of the function

The area between the x-axis and the graph of the function

The area between the y-axis and the graph of the function

If f(x) is a function and g(x) is a function than the derivative of f(g(x)) = f’(x) + g’(x)

F’(g(x)) + f(g’(x)), f’(g(x))g’(x)