HOW TO MAKE A PHASE PORTRAIT [if A has real, distinct eigenvalues]: If we are given a matrix
equation x0 = Ax and we nd that A has distinct, real eigenvalues, then we can create a phase diagram by
following the steps below:
(i) For each eigenvector, draw
C4 - cos(t)
> dsolve('Dy=sin(t)', 'y(0)=3')
4 - cos(t)
Warning: Explicit solution could not be found; implicit solution
> In dsolve (line 208)
Denition ofa derivative: _
. f'(x) = limw or f'(x) = 1mm ,provided the limit exists.
h z-x Z . x
1. Derivative of a Constant Functio :
2. Constant Multiple Rule: %(cf(x) = CE = cf '(x).
. . d d d
3. Sum Rule for Der
1. What is the date of your MATLAB quiz? What day of the week is that?
Answer: Tuesday, March 14, 2017
2. What time is your MATLAB quiz?
Answer: It is 1:00 pm- 1:50 pm, the same time of day as my regular discussion
3. Where is your M
Capacitance: 1.088e-3 0.01 F
Resistance: 101.3e3 0.1
Diameter inner: 1.9 0.1 cm
Diameter outer: 3.8 0.1 cm
Average radius: 2.85 0.05 cm
Table of voltage measurementsInterator
Circuit Peak Voltage Mearusment
With 10 resistor
Rtot= 10.7+163 = 173.7 0.2
With 100 resistor
Rtot= 1007+163 = 263.7 0.2
V=V0et/ => Mathematical function I chose to fit is y=Ae x/B + C
Fit for circuit with 100 resistor
Parameter 1: p(1) = 3.549402e-01 +/- 2.123457e-04
b) We want to plot the direction field to we how the solution y(x) of dy
will behave as x
Yes, it is
The solution would go to either - or as x go to if the initial value were
not exactly (1, 1)
Print Name: _
Sign Name: _
Exercise 1.1 (Matlab Quiz)
a. Date: Dec 1, Thursday
b. Time: 11-11:50am
c. Location: APM B432
d. Registration for alternate quiz time ends: Friday of second-to-last week of the quarter.
Practice Midterm Exam 2
February 23, 2014
1. Write your Name, PID, and Section (for example A02).
2. You have fifty minutes to complete this exam.
3. You are not allowed to use any calculators, books, notes, or electronic
> f=@(x,y) (exp(-x)-y)*(exp(-x)+2+y)
> xmin=-10; xmax=10
slopefield(f, [xmin, xmax], [-10, 10], 20)
drawode(f, [xmin, xmax], 2, 3)
drawode(f, [xmin, xmax], 0, 1)
Output: f= @(x,y)(exp(-x)-y)*(exp(-x)+2+y)
Determine whether each of the equations in problems 2.6.1 thru 2.6.10 is exact. If it is
exact, nd the solution.
Problem 2.6.1. (2x + 3) + (2y
2)y 0 = 0
Proof. Notation as in Theorem 2.6.1 from the book. Then M (x, y) = 2x + 3 and N (x, y) =
Undefined function or variable 'arcsin'.
Did you mean:
> help sin
sin Sine of argument in radians.
sin(X) is the sine of the elements of X.
See also asin, sind.
Reference page for sin
function s = mysum (r, n)
> mysum (3, 12)
> f = @(x) (sin(x)/x)
function_handle with value:
> fplot(f, [-10, 10])
Warning: Function fails on array inputs. Use eleme
Introduction to MATLAB
a. The MATLAB quiz is in December first, its on Thursday.
b. It will be started at 9 p.m.
c. The location is in APM B432.
d. Its on second-to -last weeks Friday. Rescheduling will not be available after the
close on Fri
A represents the temperature of the environment.
1) dy/dx = 0.4*(41-y), y (0) = -6
2) In order to stimulate the conditions in the fridge, parameter A should be 41 F.
3) dy/dx= 0.4* (A-Y), Y(t)=39
It takes about 8 hours to defrost the chicken.
drawode(f, [xmin, xmax], 0, -1/3)
drawode(f, [xmin, xmax], 1, -1/4)
drawode(f, [xmin, xmax], -1, -1/4)
Output: f= @(x,y)(x+2*y)
It would greatly afect the solution of the diferential equation if the initial value
werent exactly (0, -1/4)