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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
How to conversion into metric
1) Compute the center of mass of the solid of unit density 1 bounded (in spherical coordinates) by p=1 and by φ is greater than or equal 0 and less than or equal pi/4
Explain Congruum?
All the integrals below are understood in the sense of the Lebesgue. (1) Prove the following equality which we used in class without proof. As-sume that f integrable over [3; 3]
The longer base of a trapezoid is 3 times the shorter base. The nonparallel sides are congruent. The nonparallel side is 5 cm more that the shorter base. The perimeter of the trape
find the area of the irregular shape 2cm 4cm 4cm 2cm 5cm 5cm
#questionShow that the system oscillates in simple harmonic motion demonstrated by; , for which the general solution where X = (x – x0)..
The logarithm of the Poisson mixture likelihood (3.10) can be calculated with the following R code: sum(log(outer(x,lambda,dpois) %*% delta)), where delta and lambda are m-ve
Describe Square Roots? When a number is written inside a radical sign (√), the number is called the radicand, and we say that you are "taking the square root of" that number.
a man buy car at rs.50 and sells it at gain of 14% find the sp
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