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Numerical Analysis

Quantitative Methods : Actual, Absolute and Maximum Relative Errors in Data

A touring company has the following box office takings for the recent month. Venue Clarion West Riding West End Burlington Huntingdon Erie Adelphia Wilson Reading How do I estimate the abosolute and relative maximum and average errors in the total of the above rounded data? How do I determine the actual error i

Mixture Problem as a Differential Equation.

Please solve using separation of variables method. A certain chemical is converted into another chemical by a chemical reaction. The rate at which the first chemical is converted is proportional to the amount of this chemical present at any instant. Ten percent of the original amount of the first chemical has been convert

Breking an Eigenvalue Equation into Domains and using Traces and Nodes

Examine the eigenvalue equation below and then break the domain into four different regions (like a>0) and b=0 is one such domain. Describe the behavior of the equation in each domain.... Please see the attached file for the fully formatted problems. keywords: differential equations, trace, node

Adam collects stamps.

Adam collects stamps. He has 18 bird stamps,9 flower stamps and 12 butterfly stamps. For a school project, he will display an equal number of each kind of stamp on a small poster boards. What is the greatest number of poster boards Adam can make if he uses all of the stamps?

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. ---

Solving 2 ODE's with One Unknown

Given that: dMN/dt = P¬oert - pMN + m(MS - MN) dMS/dt = m(MN - MS) - pMS¬ MN¬ (0) = MS (0) = 0 And using: M¬N + MS = [Po/(r + p)](ert - e-pt) Show that MS(t) = And show that R = MN(t) / MS(t) = Please see the attached file for the fully formatted problems.

PDE : Riemann's Method for Solving Cauchy Problem

Hello. Thanks for help! I will use * to indicate a partial derivative. For example, u*x denotes the partial derivative of u with respect to x. This is the probelm: Use Riemann's method to solve the Cauchy problem: u*xx + 4u*xy +3u*yy = 1, u=1 and u*n = square root of 5 times x, on the intial curve y=2x. If this

Initial Value Problem

I am looking for the solution of this problem. It involves a little bit of theory in the second part. In the solution give a detailed solution showing all assumptions and theorems.

Numerical Methods - Spline

Consider the natural cubic spline function s(x) interpolation the following data... Please see attached for full question.

Heat Equation, Boundary & Steady State Conditions, Initial Value

Please help with the following problems involving numerical analysis. (a) Find all the separated solutions of the attached heat equation (satisfying the attached boundary condition) (b) Use these separated solutions to write a series solution for the initial value problem posed by the attached pde and the attached boundar

Using malthus method

Suppose that a culture of bacteria has initial population of n=100. If the population doubles every three days, determine the number of bacteria present after 30 days. How much time is required for the population to reach 4250 in number

Dipoles, Quadrupoles and Laplacian : Limiting Potential

Consider a dipole of strength D, oriented along the x-axis and located at the point x =E/2 , y = 0, z = 0, and a dipole of strength -D, oriented along the x-axis at the point x = - , y = 0, z = 0. Write the expression for the potential for these two dipoles. Take the limit as , and show that the limiting potential is given

Rectangular Drum Problem #9

Just #9, please. Solve the rectangular drum problem u_xx + u_yy = (c^-2)u_tt 0 < x < a 0 < y < b t > 0 u(x,y,t) = 0, u(a,y,t) = 0 0 < y < b t > 0 u(x,0,t) = 0, u(x,b,t) = 0 0 < x < a t> 0 u(x,y,0) = xy and (u_t)(x,y,0) = 0. Find the solution explicitly in the case

Initial Value Problem (IVP); Euler's Method; Step Sizes

4. Consider the initial value problem (IVP): y'(t) = 3+t+y y(0)=1 a) Approximate y(1) using Euler's method and step sizes of 0.2. Perform these calculations by hand. What is the exact value of y(1)? b) Use the computer (e.g. ODE Architect, ODE Toolkit, or your own program) to approximate y(1) using step sizes of 0.1, 0.05,

Solve: A Second Order ODE

Please solve for the following: Find a particular solution to y'' + 5y' +4y = -13te^(3t) Show all work.

Important information about mixture

A tank contains 1320L of pure water.A solution that contains .o1kg of sugar per liter enters a tank at the rate 3L/min The solution is mixed and drains from the tank at the same rate. Solve for function of t So far I have the equation:

Bisection and newton's method

Q Using the bisection method, find the positive root of 2x(1 + x^2)^-1 = arctan x. Using this root as x0; apply Newton's method to the function f(x) = arctan x: Interpret the results you obtain.

Minimal Surface Equation

Please see the attached file for the fully formatted problems. Show that Z(x, y) = ln(sin y/sin x) is a solution to the minimal surface equation. (1 + Z)Z1 + 2ZXZZX + (1 + Z)Z = 0, in the region 0 < x < ir, 0 < y < pi. What happens on the boundary of this region? Suppose we consider a constant multiple of Z(x, y) ? is i


PDE- SEND ANSWER AS ATTACHMENT What happens on the boundary of the region? Suppose we consider a constant multiple of Z(x, y). Is it still a solution of the PDE? See attachment for question and details

Laplace and polar coordinates

(lap) means the Laplacian Vrr means the second derivative of V with respect to r V(theta theta) means the second derivative of V with respect to theta Solve: (lap)V(r,theta)= Vrr+(1/r)Vr+(1/r^2)V(theta theta)=0 0 < r < 1, -(pi) < theta < pi V(1,theta) = {1, -(pi/2) < theta < (pi/2) {0, elsewhere Ple

Solve an IVP ODE using the method of variation of parameters

Please see the attached file for the fully formatted problems. Solve an IVP ODE using the method of variation of parameters Find the solution of the system X' using the method of variation of parameters 2 0 0 cos(t) X' = -1 0 -1 X + sin(t) 1 1 2 e^-t that satisfies the int