Polynomial Equations : Complex Solutions, Conjugates and Shift Operator

Prove that if p is a polynomial with real coefficients, and if is a (complex) solution of P(E)z = 0, then the conjugate of z, the real part of z, and the imaginary part of z are also solutions. Note: This is from a numerical analysis course, and here P(E) refers to a polynomial in E, the "shift operator" for a sequence.

Solutions of Recurrence Relations

Consider the recurrence relation . Show that the general solution is . Show that the solution with starting values and corresponds to and . Please see the attached file for the fully formatted problems.

A thin glass pipe with the internal diameter of 3 mm was probed into a heart tissue (membrane) and air pressure was plied through the pipe to expand the membrane. Assuming its thickness to be negligible, the circular arc of the bulged membrane was to be 3.6mm (see picture below). Find the volume of the excessive space between the end of the glass pipe and piece of membrane. Need a solution in matlab.

A thin glass pipe with the internal diameter of 3 mm was probed into a heart tissue (membrane) and air pressure was plied through the pipe to expand the membrane. Assuming its thickness to be negligible, the circular arc of the bulged membrane was to be 3.6mm (see picture below). Find the volume of the excessive space between th ...continues

Closed Locker Problem

School is about to begin. The janitor has all the lockers closed. All 1000 of them. Student #1 comes along and opens ALL of the lockers. Student #2 comes along and closes doors 2, 4, 6, 8, 10, etc.... Student #3 comes along and changes the state of every 3rd locker ( 3, 6, 9, 12, 15). Student #4 comes along and c ...continues

Convergence to a Fixed Point of a Function and Matlab Program for the Newton-Raphson Method.

1. Let g: R→R+ be such a function that g∈ C^1(R) and for all x ∈ R, -1 ...continues

Numerical Stability

(See attached file for full problem description with equations) --- There is a function f of the form for which and . Determine and , and assess the sensitivity of these parameters to slight changes in the values of f at the two indicated points. ---

Solve Finite Difference Equation

See attached file for full problem description with equation. --- Find analytically the solution of this difference equation with the given initial values: Without computing the solution recursively, predict whether such a computation would be stable. (Note: A numerical process is unstable if small errors made at one ...continues

Analysis of Bisection Method applied to a Continuous Function

Let and . Here , with , denotes the successive intervals that arise in the bisection method when it is applied to a continuous function f. a. Show that . b. Show that . c. Is it true that Explain. d. Show that . e. Show that for all n and m, . Please see the attached file for the fully formatte ...continues

Financial Decision-Making : Borrowing Decisions Simulation and Simulation Based Cash-Budgeting

Help me understand questions that reflect the borrowing decisions simulation.

Newton's Method Two- Part Question

(See attached file for full problem description with proper symbols) --- A) Let Newton's method be used on where q > 0. Show that if has k correct digits after the decimal place, then will have at least correct digits after the decimal place, provided that and . B) Suppose that r is a double zero of the func ...continues