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Consider the Van der Pol oscillator
x′′- µ(1 - x2)x′ + x = 0
(a) Write this equation as a system of first order equations
(b) Taking µ = 2, use MatLab's routine ode45 to compute the solution for the initial value problem x(0) = 0 and x′ (0) = 5 from t = 0 to t = 40. Plot x as a function of t and also plot x vs x′ in phase-space.
(c) Repeat for the initial conditions x(0) = 0 and x′ (0) = 0.01.
(d) What is the ?xed point of the system? Use your numerical results to argue what the long time behavior of the system is.
Devise data that link a certain relationship OF YOUR CHOOSING between two variables. Write a rationale stating why you chose this particular data and what you are planning to STAT
Is the group of order 10 simple?
a bathroom measure 250 cm by 175 cm calculate the side of the largest square tile that can tile the floor
tens digit of a 2-digit number is twice its unit digit. If the sum of the digit is 12, find the number.
Trig function
Q. Determine Z-scores and Percentiles? Ans. Z-scores help measure how far a piece of data is from the mean. More specifically, Z-scores tell how far a piece of data is fr
Proof of the Derivative of a Constant : d(c)/dx = 0 It is very easy to prove by using the definition of the derivative therefore define, f(x) = c and the utilize the definiti
1
Linear Approximations In this section we will look at an application not of derivatives but of the tangent line to a function. Certainly, to get the tangent line we do have to
Partitioning - an action of taking away or removing some objects, and finding out how many remain. (e.g., there were 15 toffees in this container, and 10 have been eaten. How many
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