Quiz 9 w/ Solutions
Math 322. Fall, 2009.
October, 30 2009. Instructor: Bole Yang, Erica McEvoy NAME:
Please show ALL of your work.
Given the following Sturm-Liouville problem y + y = 0 y (0) = 0 y ( ) = 0
1. Prove that there are no eigenfunctions for < 0
Complex Numbers Complex
Section 13.1 &13.2 Concept tests
Setting up your cards
Press the GO button Press 2 then 7 (that is, you chose the channel 27 for the frequency); after you pressed 7, you should get a green light
(Hint. Use both hands to press the
Linear Algebra Linear
Clicker questions
& 1 2# &1 2 3 10# Let A = $ ! and C = $1 6 ' 8 0 ! . Is the product CA %3 4 " % "
defined?
1. Yes 2. No
0 of 5
10
Let
& 1 2# &1 2 3 10# . What is the product A=$ ! and C = $1 6 ' 8 0 ! of %3 4 " % "
A with the third
Math 322, Section 4. Fall 2009.
September, 18 2008. Instructor: Bole Yang NAME:
Quiz 4
Please show ALL of your work.
Find the rank and basis for the row space of the matrix 2 3 1 8 9 5 233 Hint: Notice 2 3 3 = 2 8 9 5 7 2 3 1 So, the rank is 2 and the bas
Quiz 2 Solutions
Math 322 Fall, 2009.
September, 4 2009. Instructor: Bole Yang, Erica McEvoy NAME:
Please show ALL of your work.
1. Consider the function f (z ) = z 2 + 5. Use the Cauchy-Riemann equations to check if f (z ) is an analytic function. For z
Quiz 3 Solutions
Math 322, Fall 2009
September, 11 2009. Instructor: Bole Yang, Erica McEvoy NAME:
Please show ALL of your work.
1. Find the principal value of Ln(z ) when z = 2i.
Rewrite z into polar form, so that z = 2ei( 2 +2n) . Then Ln(z ) = ln(r) +
Quiz 8 Math 322 Spring 2010 Name: Signature: This Quiz will count both as a quiz 8 and as the homework for the March 27 week.
Question 1. Solve the initial value problem y 3y + 2y = ex y (0) = 1, y (0) = 0
2
Question 2. (a) Write down the second order die
Math 322, Sample Exam # 2
Partial credit is possible, but you must show all work.
Name: I hereby testify that this is individual work. Signed: 1 2 3 2
1. (a) Find the eigenvalues and eigenvectors of the matrix A =
(b) By starting with the denition A = ,
Math 322 (SPRING 2010)
Math Analysis for Engineers
Course: TR 1100AM1215 PM; ILC 150 All course materials will be available through D2L; http:/d2l.arizona.edu Instructor: Dr. Lotfi Hermi Contact information: Office: Math 710, Tel: 621-4838 Email: [email protected]
Math 322, Section 4. Fall 2009.
Oct, 2 2009. Instructor: Bole Yang NAME:
Quiz 6
Please show ALL of your work.
Find the eigenvalues and the corresponding eigenvectors of the following matrix 1 2 1 0 1 1 0 0 3 Hint: 1 = 1 with 1 0 . 0 1 1 . 0 3 1 . 4
2 = 1
Denitions and examples The wave equation The heat equation
Denitions and examples The wave equation The heat equation
Denitions Examples
1. Partial dierential equations
A partial dierential equation (PDE) is an equation giving a relation between a functio
Ordinary dierential equations Linear dierential equations and systems Nonhomogeneous linear equations and systems
Ordinary dierential equations Linear dierential equations and systems Nonhomogeneous linear equations and systems
Denitions Existence and uni
Math 322. Spring 2008 Review Problems For The Final Exam Additional Problems Problem A.1: Solve the the following initial value problem with Laplace transform. d2 y y = (t 3) dt2 y (0) = 0 y (0) = 0 Problem A.2: Solve the following wave equation. utt a2 u
Topic 3: Null Space. Q6: A=
10 0
12 16
we want Ax = 0, x = (x1 , x2 , x3 )T , which is just x1 10 1 2 x2 = 0 016 x3 Thus, we have 10x1 + x2 + 2x3 = 0, (1) x2 + 6x3 = 0, (2)
Look at the second equation, we get x2 = 6x3 Plug it into the rst equation, we get
Math 322. Spring 2008 Review Problems For The Final Exam Topics for midterm I & II
Topic 1: Complex Numbers Specic topics: Polar form of complex number; Operations of complex numbers; Roots of complex number; Continuity, Differentiability and analyticity