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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
a recipe good for 4 servings require 1/8 tsp. black pepper and 1/2 tsp. of salt. how much black pepper and how much salt needed for 2 servings?
what is the domain of the function f(x)= 2x^2/x^2-9
Root Test- Sequences and Series This is the final test for series convergence that we're going to be searching for at. Like with the Ratio Test this test will as well tell wh
i need help in math
Given f (x) =10x^3 - x^5 , find all intervals(in Interval Notation) of Concavity and the x-values of all Inflection Points.
Common Graphs : In this section we introduce common graph of many of the basic functions. They all are given below as a form of example Example Graph y = - 2/5 x + 3 .
x ?8x ?16x ? 0, x?0? ? 0, x?0? ? 2
Last year Jonathan was 603/4 inches tall. This year he is 651/4 inches tall. How many inches did he grow? Subtract to find outthe difference in heights. You will need to borro
Ahmad borrowed $450000.00 at 3% compounded semi-annually for ten years to buy an apartment. Equal payments are made at the end of every six months. a) Determine the size of the se
It may seem like an odd question to ask and until now the answer is not all the time yes. Just as we identify that a solution to a differential equations exists does not implies th
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