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    Calculus and Analysis

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    Laplace Equation in a Unit Disk

    Find the solution of the Laplace equation: (See attachment) in the unit disk given by Fourier method (separation of variables). Then compare your answer with the one given by the Poisson Integral Formula to compute the definite integral. (see attachment)

    Solving Non-Homogeneous Differential Equations

    1. For nonhomogeneous differential equation: y′′+ 3y′+ 2y = 4e^x - Find two linearly independent solutions for the homogeneous portion of DE. - Find a particular solution of the given differential equation using the method of variation. - Find the general solution of non-homogeneous differential equation.

    Calculus Questions - Automotive Examples

    See the attached file for full description. 40) The value of a certain automobile purchased in 1997 can be approximated by the function v(t)=25(0.85)^t , where t is the time in years, from the date of purchase, and v is the value, in thousands of dollars. (a) Evaluate and interpret v(4). (b) Find an expression for v1(t) inclu

    New stock price after the increase of beta.

    A stock currently trades with a beta of 1. Company management is considering a bold new venture that will greatly increase the stock's perceived risk. If beta increases to 2, would you expect the stock price to be cut in half, if other variables are held constant?

    Partial Differential Equations : Heat Equations

    1) Let A(x,y) be the area of a rectangle not degenerated of dimensions x and y, in a way that the rectangle is inside a circle of a radius of 10. Determine the domain and the range of this function. 2) The wave equation (c^2 ∂^2 u / ∂ x^2 = ∂^2 u / ∂ t^2) and the heat equation (c ∂^2 u / ∂

    Solving Differential Equations and Modeling

    (a) Find the solution of the initial-value problem? dy/dx = cos(4x) / 3 − sin(4x), y = 6 when x = 0. (b) (i) Find, in implicit form, the general solution of the differential equation dy/dx = −e^x + e^−x / y(e^x − e^−x + 1)^3 (y > 0). (ii) Find the corresponding explicit form of this general solution.

    Total Differentials

    I have 2 functions I would like to take the total differential of: I= I (R-PI) and C=C(Y-T, R-PI)) Where PI is Pi. If you can walk me through the process, that will help me better understand it and be able to work on other problems

    Ordinary Differential Equations Fourth Order Runge Kutta Method

    Question Use Runge-Kutta method of order four to approximate the solution to the given initial value problem and compare the results to the actual values. y'=e^(t-y) , 0 <=t <=1 , y(0)=1 with h = 0.5(Interval) Actual solution is y(t)= In((e^t+e-1). For full description of the problem, please see the attached question

    Geometry Questions

    1. Consider the graph of y = tan x. (a) How does it show that the tangent of 90 degrees is undefined? (b) What are other undefined x values? (c) What is the value of the tangent of angles that are close to 90 degrees (say 89.9 degrees and 90.01 degrees)? (d) How does the graph show this? 2. A nautical mile depends on

    Differential Equations : Phase Lines

    Suppose you wish to model a population with a differential equation of the form dP/dt = f(p), where P(t) is the population at time t. Experiments have been performed on the population that give the following information: ? The population P = 0 remains constant. ? A population close to 0 will decrease. ? A population of P =

    Four problems are solved in this posting. One is involved Taylor Series expantion about x - 0, the second is involved finding Partial Derivatives, the third is involved Double Integral and the fourth is involved finding Divergence and Curl of a given vector field. For complete description of the questions, please see the posted questions.

    Question (1) Write the Taylor series with center zero for the function f(x) = In(1 + x^2 ) Question (2) Compute the first-order partial derivatives of f(x, y) = 2x/(x-y) Question (3) Evaluate the double integral (1 to 3)(0 to 1) of (2x-3y)dx dy Question (4) Calculate the divergence and curl of the vector field F(x,

    How Old is the Fossilized Piece of Bone

    If only 15% of the carbon-14 remains in a fossilized piece of bone, how old is the bone? A(t)= Aoekt I am trying to solve this decay problem the o is a subscript and the k and t are superscripts in the equation. The problem is: if only 15% of the carbon-14 remains in a fossilized piece of bone, how old is the bone? (use 57

    Solving Inseparable Differential Equations

    Consider the following very simple model of blood cholesterol levels based on the fact that cholesterol is manufactured by the body for use in the construction of cell walls and is absorbed from foods containing cholesterol: Let C(t) be the amount (in milligrams per deciliter) of cholesterol in the blood of a particular person a