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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
Factor Expressions Involving Large Powers, Radicals, and Trig Functions You can use substitution to factor expressions involving large powers, radicals, and trig functions
Q. Find a common factor of the numerator and denominator? Ans. There's only one key step to simplifying (or reducing) fractions: find a common factor of the numerator and
Calculus with Vector Functions In this part we need to talk concisely on derivatives, limits and integrals of vector functions. Like you will see, these behave in a quite pred
1. Simon's monthly take home pay (after taxes) is $2200, if he pays 19% of his gross pay(before taxex) in tax, what is his gross pay? 2 . Convert the following quantities to th
Standard Basis Vectors The vector that is, i = (1, 0,0) is called a standard basis vector. In three dimensional (3D) space there are three standard basis vectors, i → = (1
A rectangular field is to be fenced in completely. The width is given as 22 yd and the total area is 990 yd 2 . Determine the length of the field? a. 31 yd b. 45 yd c. 968
The math equation is written exactly this way: 0+50x1-60-60x0+10=??? The answer I get is 10 and others say 0 0+50=50 50x1=50 50-60=-10 -10-60=-70 -70x0=0 0+10=10
three complain forces of magnitudes 20N 30N and 45N
Can you explain that it is true that a line that slopes downward from left to right has a positive slope?
In Daniel's fifth grade class, 37.5% of the 24 students walk to school. One third of the walkers got a ride to school presently from their parents. How many walkers got a ride to s
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