HW Wed
Exam 1 March 6 (Ch 1, 2, 3.1)
Lab 1 Assignment on Homepage (Due March 8)
can have 2 solutions following same path different because displaced in time
eg If phase plane has
One solution curve is actually picture of more solutions displaced in time
Daily for Fri; 2.1 #15
Weekly for Wed;
1.9 #5, 7
2.1 #1, 2, 17, 19, 21
2.2 #11
Tentative Exam I date : March 6th (will cover chapter 1 & 2)
1. In physics Force = mass x accel
accel is a second derivative
deal with equation in viewing
2. Much better models
Weekly Wed
1.6: #15, 17, 19, 20, 29, 31, 33, 40
1.7: #11
1.8: #1, 2, 4, 19, 23, 25, 27, 29
Daily Fri
1.8: #3
Last time: Linearity Principle
If y (t), y (t) are solutions of
= a(t)y
then k y (t) + k y (t) is also a solution (where k , k are any constants)
Exam returned in discussion (and go over),
If I were to give a letter grade, only based on this exam,
85~ some sort of A
70~85 some sort of B
60~70 C, C+
But it also depends on HW!
For Wed 27th
3.2: 1-13 odds, 21, 23
3.3: 1, 3, 5, 13, 15, 21
3.4: 3-15 od
Wed
2.6 #3, 4, 5
3.1 #1, 2, 17, 18
Exam 1 - March 6th
Lab 1 - March 8th
SIR
Lab will be a good preparation for the exam
So far.
So when we can nd formulas for general solution, very valuable.
Lot of time solving linearly, autonomous, constant coefcient,
Next Weds
4.1 #1-12 odds, 25, 27, 29, 36
4.2 #1-14 odds, 17, 20
4.3 #3-13 odds, 21
Question, For xed k, m
What choice of b gives typical solution
underdamped solution
like
over-damped typical solution
like
(and staying near zero) quickest?
Complex #'s
Add a row #. i =
(or j if you are E.E.)
So need bi for b real #
So need a + bi for a real #
Complex #'s = = cfw_a+ib: a, b
= real #'s
Algebra for
usual rules apply
(a+ib) + (x+iy) = (a+x) + i(b+y)
(a+ib) (x+iy) = ax - by + i(ay+bx)
] = szral - 53w) - a'm
Laelace Hons-Form
Impulse Forcing
Living in +he s-domoin
Impulse {zoning is Sh0r+ duro+ion -Forces How shor+ is i+?
t
Like model +0 have 0 duro+ion +ime
50 Salt) = [m if 15:0 Del+a Function
0 C t:=° Dirac. dam Jéunc+ion
2$o(l:) =
After break ,
7-8 lectures on Ch 3
4-5 lectures on Ch 4
Then Ch 6 and 5.1,2
Tues-Weds-12th + 13th Look west at dusk
Today, review/preview/story
model
displacement = y
restoring force = -ky
damping = -b(dy/dt)
Question-
How could we experimentally determ
Exam 1 Weds
HW wed
Lab 1 due Fri
(Lectures as usual story of Hancock tower)
First sentence,
We study an epidemic that is assumed to be accurately modeled by the SIR
model.
Discussion
Extra OH
Tues 2:30 - 5
Wed 9 - 9:45
weekly due on Wed
Turns out method of undetermined coefcients only works when a(t) = constant!
Luckily happens a lot (eg. RC circuits)
(constants coefcient linear equations)
When we guess y (t) forced response, share characteristics with forcing.
eg if b
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