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1. Discuss lyapunov function theory and how it can be used to prove global assmptotic stability of solutions.(Give an example form natural and engineering sciences.)
--- Draw level sets of Lyapunov function.
2. Discuss Perron-Frobenius theorem and how it can be used to prove global stability of solutions(Give an example) .
3. Discuss the stability of solutions of non-autonomous system dx/dt=f(x,t).
4. Discuss bifurcation theory, and show how to (theoretically) characterise varies, bifurcation types apriori (saddle node, pitchfork, hopf, transcritical). Show to charactrise super and sub-critical pitchfork and hopf.(Give an example of each)
1) transcritical.
2)pitchfork(super and sub-critical)
3)Hopf(super and sub-critical)
4)saddle-node
Your engineering department estimated the following production function. Q = 15L 2 - 0.5L 3 a. What is the marginal product of labor function, MP L ? b. What is the aver
A pipe has a diameter of 2.5 inches. Insulation which is 0.5 inches thick is placed around the pipe. What is the diameter of the pipe along with the insulation around it? The i
Assumptions The figures known are assumed to be a normal series, that is a series without any violent, unexplained fluctuations in the values. The
Kurtosis - It is a concept, which refers to the degree of peakedness of a described frequency distribution. The degree is generally measured along with reference to general di
Without solving, find out the interval of validity for the subsequent initial value problem. (t 2 - 9) y' + 2y = In |20 - 4t|, y(4) = -3 Solution First, in order to u
A 50-foot pole casts a shadow on the ground. a) Express the angle of elevation θ of the sun as a function of the length s of the shadow. (Hint you may wish to draw this firs
what is the difference between North America''s part of the total population and Africa''s part
how can i build Y=2x
((1/x^1/2-(x-1)^1/2)+(1/(5-3(x-1)^2)^1/2)
how to calculate double summations
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