代做MATH 2373, SPRING 2024调试数据库编程

REVIEW FOR MT3

MATH 2373, SPRING 2024

Problem 1

Find

in fully simplified form.

Problem 2

For the matrix

find exp(tA) in fully simplified form.

Problem 3

Find the Laplace transform. of

Problem 4

Find using the table of Laplace transforms supplied with this review sheet.

Problem 5

Solve the IVP

using Laplace transforms.

Problem 6

Find the inverse Laplace transforms of

Problem 7

Find the inverse Laplace transform. f(t) of

rewrite f(t) in piecewise form. and sketch its graph.

Problem 8

We consider two brine tanks. Initially:

• Tank A contains 71 gallons of water and 37 pounds of salt.

• Tank B contains 101 gallons of water and 43 pounds of salt.

Starting at time t = 0:

• Brine at a salt concentration of 5 gal/lb is pumped into tank A at rate of 3 min/gal.

• Brine is pumped from tank A to tank B at a rate of 9 min/gal.

• Brine is dumped down the drain from tank A at a rate of 4 min/gal.

• Brine at a salt concentration of 2 gal/lb is pumped into tank B at a rate of 7 min/gal.

• Brine is pumped from tank B to tank A at a rate of 10 min/gal.

• Brine is dumped down the drain from tank B at a rate of 6 min/gal.

Note that the amount of water in each tank remains constant. The brine is kept well-mixed at all times. Let x and y denote the amounts of salt in tanks A and B, respectively. Write down the initial value problem determining x and y for all times t. Justify your answer by drawing a diagram summarizing all the information above. Express your final answer using matrix notation appropriately and correctly.

Problem 9

Solve the following IVP using Laplace transforms:

Problem 10

Solve the initial value problem

using any method taught in class. We give you a diagonalization to use or not, as you please:

Problem 11

Solve yn+2 + 5yn+1 − 24yn = 0, y0 = 22, y1 = 77.