Give a counterexample:
a) Xn + Yn converges if and only if both Xn and Yn converge.
b) Xn Yn converges if and only if both Xn and Yn converge.
In: Advanced Math
1)Find the power series solution for the equation y'' − y = x
2)Find the power series solution for the equation y'' + (sinx)y = x; y(0) = 0; y'(0) = 1
Provide the recurrence relation for the coefficients and derive at least 3 non-zero terms of the solution.
In: Advanced Math
Find a particular solution to the following non homogenous equations
1) y''' + y = t^3 + sin (t) + 11e^t
2) y'' + y = 2tsin(t)
3) y''''' - 4 y''' = e^2t + t^2 +5t + 4
In: Advanced Math
Solve the initial value problem
11. xdx−y2dy=0, y(0)=1
12. dydx=yx, y(1)=−2
16. dydx=sinxy, y(0)=2
17. xy′=√1−y2, y(1)=0
23. Mr. Ratchett, an elderly American, was found murdered in his train compartment on the Orient Express at 7 AM. When his body was discovered, the famous detective Hercule Poirot noted that Ratchett had a body temperature of 28 degrees. The body had cooled to a temperature of 27 degrees one hour later. If the normal temperature of a human being is 37 degrees and the air temperature in the train is 22 degrees, estimate the time of Ratchett's death using Newton's Law of Cooling.
In: Advanced Math
(abstract algebra)
(a) Find d = (26460, 12600) and find integers m and n so that d is expressed in the form m26460 + n12600.
(b) Find d = (12091, 8439) and find integers m and n so that d is expressed in the form m12091 + n8439.
In: Advanced Math
Explain the outcome of 3^4^5. In particular, what is the order of execution of the two exponentiation operations?
Write (5^4^3)−1 as a product of prime numbers.
The greatest common divisor of two integers a and b can be written as a linear combination (with integer coefficients k and ℓ) of a and b: gcd(a,b)=ka+ℓb.
In Sage this is achieved with the command xgcd. Look in the help page of this command to write the greatest common divisor of 12214 and 2012 as an integer linear combination of these two numbers.
Use Sage to verify your result.
What is the difference in Sage between 1/3+1/3+1/31/3+1/3+1/3 and 1.0/3+1.0/3+1.0/31.0/3+1.0/3+1.0/3? Explain.
In: Advanced Math
In: Advanced Math
"We want to verify that IP(·) and IP^-1(·) are truely inverse operations. We consider a vector x = (x1, x2, . . . ,x64) of 64 bit. Show that IPfive bits of x, i.e. for xi, i = 1,2,3,4,5.
In: Advanced Math
Sketch the region of continuity for f (x; y) on a set of axes and sketch the region of
continuity for df/dy (x. y) on a separate set of axes. Apply Picard’s Theorem to determine whether the
solution exists and whether it is unique.
a) y' = 2x2y + 3xy2 ; y(1) = 2
b) y' = sqrt(2x - 3y) ; y(3) = 2
In: Advanced Math
Let S be a subset of a vector space V . Show that span(S) = span(span(S)). Show that span(S) is the unique smallest linear subspace of V containing S as a subset, and that it is the intersection of all subspaces of V that contain S as a subset.
In: Advanced Math
1.let {v=(1,2,3,5,9),v2=(3,1,2,8,9),v3=(2,-5,5,9,4)} and {u1=(0,1,1,1,2),u2=(0,2,-2,-2,0)} be basis of subspaces V and U of R5 respectively.find a basis and the dimension of V+U and V intersection U.
2.does a matrix have a right inverse ?if so find one A=[2,-3,-7,11;3,-1,-7,13;1,2,0,2]
3.find the interpolating polynomial that passes through the point (1,2),)(-1,-8) and (2,1)
In: Advanced Math
Consider the equation uux + uy = 0 with the initial condition
u(x, 0) = h(x) = ⇢ 0 for x > 0
uo for x < 0, with uo< 0.
Show that there is a second weak solution with a shock along the line x = uo y / 2
The solution in both mathematical and graphical presentation before and after the shock.
In: Advanced Math
Find the adjoint of matrix A, the determinant of matrix A, and the determinant of the adjoint A.
A= 1 1 0 2
2 1 1 0
0 2 1 1
1 0 2 1
In: Advanced Math
A SEIRS model with stochastic transmission :project proposal
In: Advanced Math
National governments issue debt securities known as sovereign bonds, which can be denominated in either local currency or global reserve currencies, like the U.S. dollar or euro. First define what these bonds are. Why are these issued? Then discuss the issues that can arise when investors invest in these types of bonds. What are the advantages and disadvantages of these bonds? Are there unique issues that can arise only with this type of bond? Would you invest in sovereign bonds?
In: Advanced Math