Analysis
workAplus
3 years ago
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files (1)msu23finalpractice.zip
msu23finalpractice.zip
attachment_2 (3).pdf
NAME: EID: Exam 4 Question 2 427J
2. (12 points) Consider the system
d
dt ~x = A~x where A =
[ 1 4 −1 −3
] (a) Compute the general solution to the system.
(b) Compute the matrix exponential eA t.
(c) Give the name of the type of phase portrait and graph the phase portrait.
attachment_1 (9).pdf
NAME: EID: Exam 4 Question 1 427J
1. (12 points) Consider the system
d
dt ~x = A~x where A =
[ 4 13 −2 −6
] (a) Compute the general solution to the system.
(b) Compute the matrix exponential eA t.
(c) Give the name of the type of phase portrait and graph the phase portrait.
attachment_3 (1).pdf
NAME: EID: Exam 4 Question 3 427J
3. (13 points) Consider the Heat Equation
ut = α2uxx
u(x, 0) =
{ x, 0 < x ≤ 1 0, 1 < x < 2
u(0, t) = u(2, t) = 0, t ≥ 0
(a) Give the Sine Series for u(x, 0). Include the first four nonzero terms. Each coefficient should be a single reduced fraction. (b) Give the solution to the Heat Equation, u(x, t). Include the first four nonzero terms. Each coefficient should be a single reduced fraction.
attachment_4.pdf
NAME: EID: Exam 4 Question 4 427J
4. (13 points) Consider the Heat Equation
ut = α2uxx
u(x, 0) =
{ −1, 0 < x ≤ π 1, π < x < 2π
u(0, t) = u(2π, t) = 0, t ≥ 0
(a) Give the Sine Series for u(x, 0). Include the first four nonzero terms. Each coefficient should be a single reduced fraction. (b) Give the solution to the Heat Equation, u(x, t). Include the first four nonzero terms. Each coefficient should be a single reduced fraction.
