Math 340 Spring 99

Homework Assignments

Homework 01:   due Tuesday, Jan. 19     
    Section 1.1: 1.1.3-1, 1.1.3-2, 1.2.3-3, Section 1.2: 1.2.2-2

Homework 02:   due Tuesday, Jan. 25     
    Section 1.2: 1.2.2-1, 1.2.2-3, Section 1.3: 1.3.3-1, 1.3.3-5

Homework 03:   due Tuesday, Feb. 2      
    Section 2.1: 2.1.5-2 
    Section 2.3: (1) Exercise, (2) Find two equations of your own and
apply Newton's iteration program to solve them, after using their graph
to get initial guess.
    Read Section 2.2

Homework 04:   due Tuesday, Feb. 9      
    2.1.4-1, 2.1.4-4, Section 2.4 Exercise
    3.1.7-1, 3.1.7-2

Homework 06: due Tuesday, Feb. 23
   (1) your unfinished quiz for partial credit
   (2) 4.2.7-2, 4.2.7-3
   (2) extra 5 points: Josephus problem (3.3.4-2)

Homework 07: due Tuesday, Feb. 25
   (1) 4.2.7-4,  4.3.5-1
   (2) In an issue of Parade, a question was debated in the column Ask Marilyn: If a family has exactly two kids and at least one of them is a boy, what is the probability that both kids are boys. Marilyn vos Savant, the columnist, gave the answer 1/3 but many readers didn't agree. One of the readers thought the answer should have been 1/2 and challenged Marilyn with a $1000 bet. Write a program to simulate the experiment and settle the bet.

    The simulation part should consists of the following components
     (1) generate two kids (in an array, with entries either `boy` or `girl`), each one has a 50/50 chance of being a boy or girl.
     (2) repeat the last step until at least one of the two kids is a boy (so you'll need a "while...do" loop and a "flag")

   To assign the gender to each kid, you can generate a random integer from 1 to 2 and designate them as boy/girl.

Homework 08: due Tuesday, March 30
   4.4.3: Monty Hall dilema

Homework 09: due Tuesday, March 30
   5.1.4-1, 5.1.4-2, 5.2.3-1
  Extra 5 points:  5.1.4-3

Homework 10: due Tuesday, April 6
   least squares problems (http://www.neiu.edu/~zzeng/340/leastsqr.mws)
   6.1.5-1

 Homework 11: due Tuesday, April 13
   Problem 1: #6.2.3
   Problem 2: #6.3.4-1
   Problem 3: Redo problem 1 using Runge-Kutta program RKmxm
   Extra credit problem: (pencil work) Set up the IVP of a 3x3 system of ODE for 6.2.5-1 and explain your modeling in detail. You can use the program RKmxm to solve the problem.
 

 Homework 12: due Tuesday, April 20
   Problem 1:   #6.4.2.2-2
   Problem 2:   Section 6.3.5 Project: Three-leaved rose
   Problem 3:   Section 6.3.5 Project: Folium of Descarts
   Problem 4:   6.4.3-1 (Correction: Use your program to solve 6.4.2.2-1, not "problem (2) in project 2")

Homework 13: due Tuesday, April 27
   Problem 1:  Earth is moving on a trajectory nearly a circle. Let's assume that the location of earth is
                           (5 cos (t/20),  5 sin (t/20) )
at time t. A spaceship is initially at (6,0) and moving at velocity (0,1). Ths spaceship is subject to the gravity force from the earth. Find the trajectory of the spaceship. For simplicity, let M be the mass of the earth and G the gravity constant, in such a way that G*M = 1 unit.
   Problem 2:   An airplane (target) can fly at 0.5 km/second. A missile can fly at 1 km/second. The missile is chasing the airplane, that is, the velocity of the missile is along the direction from the missile to the plane. The plane is trying to escape the missile by flying along the direction perpendicular to the missile direction. Namely, if the missile is flying along the direction of (alpha,beta), then the plane is flying along the direction of (-beta,alpha) Let the location of the missile be (x(t),y(t)) and the location of the plane be (u(t),v(t)) at time t. Construct an initial value problem of ODE system for x(t), y(t), u(t), v(t) and solve the problem with R-K_mxm program. Plot the trajectories of both airplane and the missile.  (Notice that the time interval [a,b] is such that a=0, with b to be determined. b is the moment before the missile hitting the target. If b is bigger than that, R-Kmxm may get a division by zero. Use trial and error to get a value for b).