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### mid2_summary

Course: MATH 134, Fall 2008
School: San Jose State
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134, Math Fall 2005 Summary for Midterm 2 I. Classication of Planar Linear Systems X = AX. 1. The trace-determinant plane. 2. Notion of the ow t (X). 3. Notion of topological conjugacy. 4. Classication of hyperbolic planar linear systems: (X = AX) (X = BX) i A, B have the same number of eigenvalues with negative real part. 5. Examples. II. The exponential of a matrix exp(A). 1. Denition properties and of exp(A)....

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134, Math Fall 2005 Summary for Midterm 2 I. Classication of Planar Linear Systems X = AX. 1. The trace-determinant plane. 2. Notion of the ow t (X). 3. Notion of topological conjugacy. 4. Classication of hyperbolic planar linear systems: (X = AX) (X = BX) i A, B have the same number of eigenvalues with negative real part. 5. Examples. II. The exponential of a matrix exp(A). 1. Denition properties and of exp(A). 2. Computation of the exponential using the canonical form. 3. t (X) = exp(tA)X as the ow of X = AX. III. Non-autonomous linear systems X = A(t)X, X = AX + G(t). 1. X(t) = exp A(s)A(t). t t0 A(s) ds X0...

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San Jose State - MATH - 134
San Jos State University eMath 134, Fall 2005Midterm 1 SolutionsSeptember 28, 2005Name:Granwyth HulatberiScore 1 25 2 25 3 25 4 25 Total 100Explain your work1. (25 points) Consider the dierential equation x = x 2 sin t. (a) Find the ge
San Jose State - MATH - 133
San Jose State UniversityMath 133A, Fall 2005Midterm 2 SolutionsSection 03November 2, 2005Name:Granwyth HulatberiScore 1 25 2 25 3 25 4 25 Total 100Explain your work1. (25 points) Consider the dierential equation dy = y 2 2ty + t2 3
San Jose State - MATH - 133
San Jos State University eMath 133A, Fall 2005Quiz 2 SolutionSuppose we know that the graph below is the graph of a solution to dy/dt = f (y). yy(0) = 3t(a) How much of the slope eld can you sketch from this information? [Hint: Note that t
San Jose State - MATH - 134
THE IMPLICIT FUNCTION THEOREM SLOBODAN N. SIMICThe Implicit Function Theorem (IFT) is one of the most important theorems in mathematics. It is concerned with solvability of equations of the form f (x, y) = 0, where f : X Y Y is some dierentiable
San Jose State - MATH - 133
San Jose State UniversityMath 133A, Fall 2005Solutions to graded Homework 2 problemsEx. 1.3, #14. Denote the values of y for which f (y) = 0 by y0 , y1 , and y2 , where y0 &lt; 0 &lt; y1 &lt; y2 . These are the equilibria of the dierential equation dy/
San Jose State - MATH - 134
MATH 134, FALL 2005 PRACTICE QUESTIONS FOR MIDTERM 2 1. Compute the ow t (X) of the equation X = AX, where A= 0 1 . 4 02. Let1 5 1 1 2 . , B = 12 3 1 1 2 2 Are the ows of X = AX and Y = BY topologically conjugate? A=3. Consider the undamped for
San Jose State - MATH - 133
San Jose State UniversityMath 133A, Fall 2005Solutions to graded Homework 14 problemsEx. 6.2 #5. First use partial fractions to write F (s) = 1 A B = + . (s 1)(s 2) s1 s2Multiplying both sides by (s 1)(s 2), we obtain 1 = A(s 2) + B(s 1
San Jose State - MATH - 133
San Jose State UniversityMath 133A, Fall 2005Sample Final ExamSection 3Name:Score 1 2 3 4 5 6 TotalExplain your work1. Solve the following initial value problem: dy = 2ty 2 + 3t2 y 2 , dt Solution: y(1) = 1.2. Consider the following di
San Jose State - MATH - 133
San Jose State UniversityMath 133A, Fall 2005Solutions to graded Homework 7 problemsEx. 2.3, #5. The function Y (t) = (e2t et , e2t ) is not a solution to the system dx = 2x + y dt dy = y dt because the second component of Y (t), e2t , is not
San Jose State - MATH - 134
San Jose State UniversityMath 134, Fall 2005Sample Final ExamName:Score 1 2 3 4 5 6 TotalExplain your work1. Consider the following differential equation on the real line: x = x3 - 2x2 - 3x. (a) Find the equilibria and identify their type
San Jose State - MATH - 133
San Jose State UniversityMath 133A, Fall 2005Solutions to graded Homework 3 problemsEx. 1.5, #8. Let f (y) = (y 2)(y 3)y. Then our ODE is dy/dt = f (y). The equilibria are 0, 2, and 3, since f equals zero there. Does the (unique) solution y(
San Jose State - CHEMISTRY - 265
Combination Differences Consider the following partial energy level diagram:It is clear that since the R(J) and P(J) transitions share a common lower rotational level (FJ), the energy difference between the R(J) and P(J) transitions gives the energ
San Jose State - CHEMISTRY - 261
Maxwell RelationsThe beauty of thermodynamics is in the relationships between the variables U, H, A and G. One of the clearest examples of these relationships is to be found in the Maxwell Relations. Euler Reciprocity Relation The Euler Reciprocity
San Jose State - CHEMISTRY - 261
Chem 261 Exam II October 20, 2004 (Happy National Chemistry Week!)Name _Instructions: Write your solutions to the problems in the blue book provided. Begin each problem on a new page. Clearly indicate each problem number and section letter. 1. Fo
San Jose State - CHEMISTRY - 178
First, here are the parameters as given in the problem. R 8.314 J mol . K M 16.043 kg 1000 mol T ( 37 273.15 ) KAnd here are the uncertainties. R 0.001 J mol . K M 0.001 kg 1000 mol T 1KNow, let's evaluate the RMS velocity: 3 .R . T Mc( R , T ,
San Jose State - CHEMISTRY - 178
Gauss-Jordan EliminationDefine Parameters: number of eqs. = n Dim X(n,n) Dim y(n)StartProcess Complete k=0 yes k = k+1 kswap = knok=nX(k,k) = 0A For i = 1 to n If i &lt;&gt; k then xfactor = X(i,k) For j = 1 to n X(i,j) = X(i,j) - X(k,j) * xfa
San Jose State - CHEMISTRY - 178
Chemistry 178 Chemistry and the Computer Spring 2006Instructor:Code: 28971 Cr. Hrs: 3 San Jose State UniversityPatrick E. Fleming Lecture Hours: 10:30-11:20 MW, 10:00-11:50 R Duncan Science Hall 5A Location: DH 503 Phone: 924-5449 email: pflemin
San Jose State - CHEMISTRY - 178
Chem 178 Exercise 1Simultaneous Determination of Two Species in SolutionTheory: A Beer's Law approach can be used to determine the concentrations of two absorbing species in solution so long as the species have different extinction coefficients at
San Jose State - CHEMISTRY - 178
Chem 178 Assignment #9 Due: Thursday, April 17, 2008Least Squares Fitting: fitting to a polynomialWrite a FreeBASIC program, using the sub programs we have developed in class in the form of a library, to perform a least-squares fit to a polynomial
San Jose State - CHEMISTRY - 178
Chem 178 Assignment #4 Due: Thursday, February 21, 2008 In this assignment, we will examine various methods of data smoothing aimed at increasing signal to noise ratio in experimental data. The methods we will use include 1. Co-adding of data scans 2
San Jose State - CHEMISTRY - 178
Chem 178 Assignment #8 Due: Thursday, April 4, 2008Gauss-Jordan Elimination: Solving Simultaneous Linear EquationsWe have developed a program to solve a set of simultaneous linear equations using Gauss-Jordon Elimination. Now lets use it to find u
San Jose State - CHEMISTRY - 178
Assignment #3 Due: Thursday, February 14, 2008 Write a MathCad worksheet that will 1. read a set of x,y data pairs from a disk file 2. construct the matrices and vectors needed to do a least squares fit to a polynomial of order m from the data in the
San Jose State - CHEMISTRY - 178
Chemistry 178 Assignment 5 Due: Thursday, February 28, 2008 In this problem, we will examine the calculation of pH for a mixture including a strong base and a weak acid. It might be useful to review your notes from Chem. 1B or Chem 55 or the handout
San Jose State - CHEMISTRY - 178
Chem 178 Assignment #4 Due: Thursday, February 21, 2008 In this assignment, we will examine various methods of data smoothing aimed at increasing signal to noise ratio in experimental data. The methods we will use include 1. Co-adding of data scans 2
San Jose State - CHEMISTRY - 178
Chem 178 Assignment #10 Due: April 24, 2008Acid-Base TitrationWrite a BASIC program to calculate the pH for each mL of 0.100 M NaOH solution (from 0.00 mL to 50.00 mL) added to 25.00 mL of 0.100 M acetic acid solution (pKa = 4.76.) Use the SelectC
San Jose State - CHEMISTRY - 178
Chem 178 Assignment #9 Due: Thursday, April 17, 2008Least Squares Fitting: fitting to a polynomialWrite a FreeBASIC program, using the sub programs we have developed in class in the form of a library, to perform a least-squares fit to a polynomial
San Jose State - AU - 2001
Chem 161A Fall, 2001 Exam I 1.Name_Consider two hypothetical gasses A and B. The molecular weight of A is twice that of B and the radius of A molecules is twice that of B molecules (under the assumption that both molecules behave as hard spheres.
San Jose State - PS - 08
Chemistry 161a Problem set #8 Due: Monday, December 9, 2002 1. Atkins, Exercise 25.5a and 25.5b 2. Atkins, Exercise 25.7a and 25.7b 3. Atkins, Exercise 25.9a and 25.9b 4. Atkins, Exercise 25.11a 5. Atkins, Exercise 25.16a and 25.16b 6. Atkins, Proble
San Jose State - PS - 03
Chemistry 161a Homework #3 Due: Wednesday, February 27, 2002 Use Cv = 3/2 R and Cp = 5/2 R for these problems unless otherwise specified. 1. Consider the adiabatic, reversible expansion of 1.00 mole of an ideal gas from 26.4 L and 1.00 atm to 38.2 L.
San Jose State - CHEMISTRY - 262
Chemistry 262 Chemical Kinetics Spring, 2003Instructor:Code: 21346 Cr. Hrs: 3Patrick E. Fleming Lecture Hours: 5:30-6:45 MW Duncan Science Hall 5A Location: DH 415 Phone: 924-5449 email: pfleming@sjsu.edu Office Hours: M 2:00, MTWR 3:00 and by a
San Jose State - CHEMISTRY - 265
Notes on the Quantum Mechanical H-AtomRecall the Spherical Harmonics: 2l + 1 l ml ! ml im Yl ( , ) = Pl (cos( ) )e l 4 l + ml ! 2 1mlThese functions have the properties that: h2 HYl ml ( , ) = l (l + 1) Yl ml ( , ) 2I 2 ml L Yl (
San Jose State - B - 260
Chapter 6It is a truth very certain that when it is not in our power to determine what is true we ought to follow what is probable. Descartes1Decision Making and Risk: Certainty Equivalents and UtilityThe certainty equivalent (CE) is the payof
San Jose State - BUS - 10
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San Jose State - B - 231
Technical reportHow to Get More Value from Your Survey DataDiscover four advanced analysis techniques that make survey research more effectiveTable of contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
San Jose State - BUS - 290
The story about the tiny frogs.(ARevision and Reminder )There once was a bunch of tiny frogs,. who arranged a running competition. The goal was to reach the top of a very high tower.A big crowd had gathered around the tower to see the race
San Jose State - BUS - 290
Michael Porter's Five Forces Model Homework Please type the answers out and submit a word-processed document. No handwritten homework will be accepted. Total length: 2 pages, not including the questions. Please do the following: 1. Selecting a famili
San Jose State - BUS - 290
COPY EXACTLY STRATEGIESGLOBAL BUSINESS STRATEGY 2001THE LEARNING/KNOWLEDGE PARADOX LEARNING IS ALWAYS SITUATED BUT KNOWLEDGE IS NOT THE PARADOX: LEARNING IS LOCAL KNOWLEDGE IS WIDELY SHAREDLEARNING IS SITUATED LEARNING IS CONTEXT DEPENDENT