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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
Standard errors of the mean The series of sample means x¯ 1 , x¯ 2 , x¯ 3 ........ is normally distributed or nearly so as according to the central limit theorem. This can be
The set of whole numbers also does not satisfy all our requirements as on observation, we find that it does not include negative numbers like -2, -7 and so on. To
A function is an equation for which any x which can be plugged into the equation will yield accurately one y out of the equation. There it is. i.e. the definition of functions w
Fermat Catalan Conjecture
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what is the unit rate of $112 in 8 hours
If the expression 9y - 5 represents a certain number, which of the following could NOT be the translation? a. five less than nine times y b. five less than the sum of 9 and y c
Here we have focussed on how mathematics learning can be made meaningful for primary school children. We have done this through examples of how children learn and how we can create
In figure, XP and XQ are tangents from X to the circle with centre O. R is a point on the circle. Prove that XA+AR=XB+BR Ans: Since the length of tangents from externa
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