Download link to the powerpoint file which contained the jeopardy

Jeopardy!
April 2008
Office hours
Friday 12-2 in Everett 5525
Monday 2-4 in Everett 5525
Or Email for appointment
Final is Tuesday 12:30 here!!!
Rules
 Pick a group of two to six members
 When ready to answer, make a noise + raise your hand
 When it is unclear which group was ready first, the group
who has answered a question least recently gets
precedence (if none of the groups has answered a
question, its instructor’s choice)
 Your answer must be in the form of a question
 The person from your group answering the question will
be chosen at random
 If you answer correctly, you get the points
 If you answer incorrectly, you do not lose points. Other
groups can answer, but your group cannot answer that
question again
 The group which answers the question correctly chooses
the next category
 If we have time for a final question, you will bet on your
ability to answer the question
final
Existence
Uniqueness
Solution
Methods
100
Linear
Algebra
Laplace
Transform
100
100
100
200
200
200
200
300
300
300
300
400
400
400
400
500
500
500
500
return
Existence/Uniqueness
Conditions necessary near x=a
for the existence of a unique solution for
y ' '4 y '5 y  sin( x)
return
Existence/Uniqueness
Conditions necessary
near x=a
for the existence of a unique solution for
y
(n)
 pn 1 ( x) y
( n 1)
   p0 ( x) y  f ( x)
return
Existence/Uniqueness
Conditions necessary
near t=a
for the existence of a unique solution for
x1 '  p11 (t ) x1  p12 (t ) x2    p1n (t ) xn  f1 (t )
x2 '  p21 (t ) x1  p22 (t ) x2    p2 n (t ) xn  f 2 (t )

xn '  pn1 (t ) x1  pn 2 (t ) x2    pnn (t ) xn  f n (t )
return
Existence/Uniqueness
Conditions necessary near x=a
for the existence of a unique solution for
y ' P( x) y  Q( x)
return
Existence/Uniqueness
Conditions necessary near x=a
for the existence of a unique solution for
y '  f ( x, y )
return
Solution Methods
A method you would use to solve
y ' ' y  0
Chose your solution from the methods we have discussed:
Integrate both sides using calculus II techniques
Separation of Variable
Integrating Factor
Characteristic equation
Characteristic equation/Method of Undetermined Coefficients
Characteristic equation/Variation of Parameters
Transform into a system of linear equations/matrix methods
Laplace Transform
Power Series Methods
return
Solution Methods
A method you would use to solve y ' '3 y '2 y  tan( x)
Chose your solution from the methods we have discussed:
Integrate both sides using calculus II techniques
Separation of Variable
Integrating Factor
Characteristic equation
Characteristic equation/Method of Undetermined Coefficients
Characteristic equation/Variation of Parameters
Transform into a system of linear equations/matrix methods
Laplace Transform
Power Series Methods
return
Solution Methods
A method you would use to solve x' '  5 x  y  cos(t )
y ' '  3 x  2 y  sin( t )
Chose your solution from the methods we have discussed:
Integrate both sides using calculus II techniques
Separation of Variable
Integrating Factor
Characteristic equation
Characteristic equation/Method of Undetermined Coefficients
Characteristic equation/Variation of Parameters
Transform into a system of linear equations/matrix methods
Laplace Transform
Power Series Methods
return
Solution Methods
A method you would use to solve
y
( 3)
 t y'3ty  t
2
Chose your solution from the methods we have discussed:
Integrate both sides using calculus II techniques
Separation of Variable
Integrating Factor
Characteristic equation
Characteristic equation/Method of Undetermined Coefficients
Characteristic equation/Variation of Parameters
Transform into a system of linear equations/matrix methods
Laplace Transform
Power Series Methods
return
Solution Methods
A method you would use to solve
( x  1) y'3xy  6 x
2
Chose your solution from the methods we have discussed:
Integrate both sides using calculus II techniques
Separation of Variable
Integrating Factor
Characteristic equation
Characteristic equation/Method of Undetermined Coefficients
Characteristic equation/Variation of Parameters
Transform into a system of linear equations/matrix methods
Laplace Transform
Power Series Methods
return
Linear Algebra
The inverse of
5  6
3  4


return
Linear Algebra
The eigenvalues and eigenvectors of
5  6
3  4


return
Linear Algebra
The number of solutions to all equations below
x  3y  2z  5
x  y  3z  3
3 x  y  8 z  10
return
Linear Algebra
The solution(s) to both equations below
x  3y  9
2x  y  8
return
Linear Algebra
A basis for the solution space of both equations below
3x  7 y  z  0
5x  2 y  8z  0
return
Laplace Transform
The Laplace Transform of
t  2e
3t
return
Laplace Transform
The Inverse Laplace Transform of
1
s( s  3)
return
Laplace Transform
The Inverse Laplace Transform of
2s  1
2
s( s  9)
return
Laplace Transform
Laplace transform of x if x solves
x' '6 x'25 x  0
x(0)  2
x' (0)  3
return
Laplace Transform
Inverse Laplace transform of
3s  5
2
s  6s  25
Final Question
The Laplace transform of
0 t  5
f (t )  
1 t  5