Math 120B, DUE DATES 2015

Weds, April 8

Ch 5 Churchill has done by in M120A by all but a few students in the class. So unfortunately students who have not seen it will need to put a lot of work in early to become familiar with it. I will hit the high points of Ch 5 in class. Even if you saw it before the topics I emphasize might be new to you and (likely) one will not be in the book. Our TA agreed to give a lecture on the topic (Laurant expansions) in section this weds.

Here is a list of HW exercises,' carefully pruned down to the essentials.
Sec 61   2, 3

Sec 69 (very important)   Let g(z)=(z - 2) (z-3) and let f(z) = p(z)/g(z) where p is a polynomial. What is the radius of convergence of the power series expansion about z_0 = i? (Hint you do not need to compute the expansion)

Sec 65   2
Sec 68   2,3
Sec 72   1

Ch 6
Sec 77   1a, 1b, 2a, 2b, 4b, 6

Weds, April 15

Ch 6
Sec 79   1a, 2a
Sec 81   1, 4, 8
Sec 83   1, 8,10

Weds, April 22

Ch 6
Sec 84 What type of singularity does f(z) = e^{- 1/z^2} have at 0?
What are all solutions to f(z) = e?

Partial Fraction Expansions: What form does the partial fraction expansion have for the functions f_j below.
f_1(z) = z^3/(z-4)(z-2)^2
f_2(z) = z/(z-3)(z-2)
Prove it (as was done in class). You do not need to compute the coefficients precisely.

Chapter 8
Sec 96 p301     2,3,4
Sec 98     2, 3, 12, 13
Sec 100     2,3,6,10
Look at the pictures linked to in Notes Exercises:   LFT Ex 2 and Ex 3.

Weds, April 29

Notes: Sec 1.1.3 Matrices and LFT's: \ Problems 1, 2, 3, 4,5
Sec 102     3, 6
Sec 108     1,2
Connecting systems Sec 2.6 Ex 1, 2
Notes: Sec 1.1.3 Matrices and LFT's: \ Problems 7

Chapter 9   sec 114 Ex 1,2 , 8

DO NOT TURN HW in this week; it will be covered by the quiz.

QUIZ I on Friday May 1
It will cover all HW up to this point; including the list above. Also proofs are fair game if they are both in the book and in the and in the lectures.

Weds, May 6

Notes Ch 3 Ex 4
Do All exercises in the Notes Chapter 4 except for those in sec 4.5.
Do Ex MM2 in sec 4.5
Section 6.6 Ex 1 \

Weds, May 13   Week 7


Section 6.8     Ex 2, 3 \
Section 6.9     All exercises
Section 7.4     EE0, EE1
Section 8.4 All problems
Ch 5     Ex 1, 2, 3, 4, 5

DO NOT TURN HW in this week; it will be covered by the quiz.
Friday May 15 (Quiz II)
The quiz will be cumulative and all material in the course is fair game.
Please bring a blue book.

Weds, May 20     Week 8

Section 9.3 Ex I1

Preliminaries for inverse Laplace Transform
Sec. 85 -86 Improper Integrals   (Read a little)   Sec 86 Ex 2, 4, 9

DO NOT TURN HW in this week; it will be covered by the Midterm.

Midterm on Fri May 22

Weds, May 27   Week 9

Sec 88 Jordan's Thm   Read the theorem ``Jordan's Lemma" in in Sec 88 and think about it.   You do not need to struggle with the proof.
Skip   Indented Paths, Branch Cuts   Skip

Laplace Transform and its Inverse

Laplace Transforms   Notes Sec 10.2.1   Do all exercises.
Sec 95 Churchill Inverse Laplace Transforms     Do Ex 1, 3 with FULL JUSTIFICATION

You might get the app "Wolfram Alpha" for your Tablet ( five bucks).
It is incredibly powerful and easy to use.

Weds, June 3     Week 10

Argument Principle
Notes Ch 13.1   All Exercises.
You must learn to do complex (parametric plots on the computer).

Nyquist Diagrams

Ch 13.2.3   Do Ex 1, 2, ,3, 4, 5

More will be added!

LAST WEEK OF INSTRUCTION--- Do not turn in HW, since it will be covered on the Final.

Final Exam