This homework is meant as review for the second-chance exam to be held Nov 26. It is due Thursday Nov 14th in lecture.
plot, contour, surf, mesh, meshgrid
semilogy, semilogx, loglog
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
Problem 5: Print to five digits accuracy. (Hint: You get in Matlab from
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
using the Sieve of Eratosthenes algorithm.