gibson:teaching:fall-2013:math445:hw5

This homework is meant as review for the second-chance exam to be held Nov 26. It is due Thursday Nov 14th in lecture.

Review topics

**fprintf:**formatted printing function**plotting:**`plot, contour, surf, mesh, meshgrid`

**loops:**`for`

and`while`

**anonymous functions:**defining and using**solving equations:**with`fsolve`

or`newtonsearch`

**monte carlo simulation****log-linear relationships**:`semilogy, semilogx, loglog`

**index operations**

**Problem 1:** Find all real-valued solutions of the equation
by plotting versus , estimating the values of where
, and then solving the equation numerically using those estimates as initial
guesses. Turn in your plot, your matlab code, and the numerical solutions to the equation.

**Problem 2:** Define a `rightshift`

function using Matlab's anonymous function facility
that shifts the elements of a row vector one step to the right, wrapping the last element
around to the first position. For example `rightshift([1 2 3 4])`

should return `[4 1 2 3]`

.

**Problem 3:** Write Matlab code to estimate the probability of drawing four-of-a-kind from
a randomly shuffled 52 card deck. Turn in your code and your estimated probability.

**Problem 4:** Make a 3d plot of versus for the function
for and , on a mesh with . Use Matlab's `meshgrid`

function.

**Problem 5:** Print to five digits accuracy. (Hint: You get in Matlab from `exp(1)`

).

**Problem 6:** Write an `isPrime(n)`

function that returns 1 (true) if `n`

is prime and
0 (false) for a composite. Don't worry about efficiency, just loop over 2 and the odd integers
less than or equal to , and return 0 if any divide `n`

evenly, and 1 if not.
(You might have already done this as an optional problem for exam 1 prep.)

**Problem 7:** Write Matlab code that will compute the first 20 prime numbers, using your
`isPrime`

function from problem 6.

**Problem 8:** Deduce the functional relationship between and for the data shown in this plot

**Bonus:** Write an `primes(N)`

function that returns all primes less than or equal to `N`

using the Sieve of Eratosthenes algorithm.

gibson/teaching/fall-2013/math445/hw5.txt · Last modified: 2013/11/14 12:58 by gibson