Math 5378

Problem Set 1

Due Wednesday, January 30, 2002

The problem set is due at the beginning of the class on Wednesday.

Section 1.1:    Exercises 1.2, 1.4, 1.5, 1.6, 1.8, 1.10, 1.11, 1.12, 1.13

Section 1.2:    2.1

Hint to Exercise 1.1.4: Although, I usually prefer if you graph curves analytically, it is impossible to do it in this particular case. Graph this curve, say, for lambda=2, either by plotting a few points between t=0.1 to 1.1 or using a graphic calculator, if you have one. To find the angle, solve the equation x=2*lambda for t (the resulting 4th degree polynomial equation will have a simple linear factor) and work with the velocity vector at this point. The answer in the text is given only for a negative lambda for some reason: it should be 45 degrees for a positive lambda.