371 Presentation Problem List

1. 6, 11, 14 (I will divide this in class into four problems, so 1-4 can be done by four different people), 23, 31

(problems to not write up:  17-20, 24, 34, 36)

2.1 (I will accept presentations of any two of the eight parts of this, from two people.  The remaining six parts may be written up for the Chapter 2 problem set), 9, 13 (9 and 13 will happen on the same day), 35, 40, 54

(problems to not write up: 11, 15-29)

Two new problems for chapter 2:

10.5  Check the four solutions discovered on p. 28 for Proposition 2.1.  Demonstrate why two work and two don't, depending on the sign of b. 

10.6  When we completed Proposition 2.1 in class using different algebra, we found a different solution for x, something like x=b/±√(something) instead of x = ±√(something).  Demonstrate that these two answers are the same.  Please ask me if you do not understand this question (it's not easy to typeset here). 

Chapter 3

1, 20, 27, 31

Additional problems: 
3.4.5.  Your favourite hyperbola is likely y=1/x.  Write an equation for it in the form of (7).  Your favourite parabola is likely y=x^2.  Write an equation for it in the form of (9).  I'm guessing you don't have a favourite ellipse (perhaps aside from the earth's orbit).  Show all algebraic work necessary to demonstrate that the complex equations are equivalent to the forms that you are more familiar with. 

3.18.5.  Consider the zero-set Phi(z)=0.  If A ≠ 0, which circle does it prescribe?  If A = 0, which line does it prescribe? 

(omit 5-17 from writeups)

Chapter 4

2.16, 2.22, 2.26, 2.29, 4.3, 4.15

Chapter 5

4, 8, 15, 20 (omit 35-43 from writeups)

Chapter 6

anytime 5.29

XM2Rejects second #1 - about parametrisations, 3,

What is the integral of z/(1-z^2) counterclockwise around the circle of radius 1/2 centred at the origin?  and what is it counterclockwise around the circle of radius 2 around the origin? 

11

Chapter 7

Relating to the question from 6.4 above, what are the residues of z/(1-z^2) at 1 and -1?  7 pick any one you like.  We'll let the others be individual assignment problems.  (omit 8-15 from writeups)