What is the intuition behind choosing a variable when applying a change of variables in order...
What is the intuition behind choosing a variable when applying a change of variables in order to solve a PDE? (E.G u=u(x,y))
In other words what are the criteria in choosing our variable?
Homework Answers
As we’ll see it works because it will reduce our partial differential equation down to two ordinary differential equations and provided we can solve those then we’re in business and the method will allow us to get a solution to the partial differential equations.
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What is the intuition behind choosing a variable when applying a change of variables in order...
What is the general intuition behind picking a PARTICULAR solution to a second-order, linear, non-homogenous, ODE...
What is the general intuition behind picking a PARTICULAR solution to a second-order, linear, non-homogenous, ODE y′′+p(t)y′+q(t)y=g(t) instead of following the rules for example when seeing an exponential you know the guess has to include an exponential? P.S I heard the intuition follow somehow checking your guess with the ODE on the left side of the equation and its derivatives before actually applying it, but how?
What is the intuition behind the answer? Imagine that we run the regression y; = Bo+B1xe and recover the OLS estimates...
What is the intuition behind the answer?
Imagine that we run the regression y; = Bo+B1xe and recover the OLS estimates of Bo and B1. If our regressions assumptions hold for the above specification. What is the relationship with the coefficients of the reverse regression x = ao + a1Yi + u;: (a) ao a CORRECT) - (b) @о — — Во = (с) dо — Во &1=-B1 (d) do — Во
Imagine that we run the regression y; =...
Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. p...
Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice for integrating over disks. Once we choose a coordinate system we must figure out the area form (dA) for that system. For example, when switching from rectangular to polar coordinates we must change the form of the area element from drdy to rdrd0. To determine that rdrde is the correct formula how the edges of...
Let the random variable Y represent hourly wages and the random variable X represent education. Suppose we have the...
Let the random variable Y represent hourly wages and the random variable X represent education. Suppose we have the following regression equation in mind to estimate the return to education: (a) Can we say that this regression would capture the causal effect of education on wages? Support your answer with reasoning. (b) Using the sample equivalent of the two equations E(u)-0 and E(uX)-0 derive the regression estimators for A, and β1-Write down each mathe tnatical step, what would be the...
When it comes to applying Newton's method on a single variable function, what are the conditions...
When it comes to applying Newton's method on a single variable function, what are the conditions that must be met in order for the method to work? Do we have to pick a good starting point and interval? How do I choose a good interval and good starting point? What are some type of functions where newton's method doesn't work for one reason or another?
Applying Simple Linear Regression to Your favorite Data. Many dependent variables in business serve as the...
Applying Simple Linear Regression to Your favorite Data. Many dependent variables in business serve as the subjects of regression modeling efforts. We list such variables here: Rate of return of a stock Annual unemployment rate Grade point average of an accounting student Gross domestic product of a country Salary cap space available for your favorite NFL team Choose one of these dependent variables, or choose some other dependent variable, for which you want to construct a prediction model. There may...
Once the dependent variable is determined when building a bivariate or multiple-regression model, what is the...
Once the dependent variable is determined when building a bivariate or multiple-regression model, what is the next step? Multiple Choice Determine what factors contribute to the change in the dependent variable. Define the data series for the model. Specify the correlation between the dependent variables. Identify the other dependent variables.
(1 point) In your answers below, for the variable i type the word lambda, for y...
(1 point) In your answers below, for the variable i type the word lambda, for y type the word gamma; otherwise treat these as you would any other variable. We will solve the heat equation u, = 4uxx: 0<x<2, 120 with boundary/initial conditions: u(0,1) = 0, and u(x,0) = So, 0<x< 1 u(2, 1) = 0, 13, 1<x<2. This models temperature in a thin rod of length L = 2 with thermal diffusivity a = 4 where the temperature at...
I hope you find humor behind my teacher's strange imagination. I understand a and b, but had trou...
I hope you find humor behind my
teacher's strange imagination. I understand a and b, but had
trouble finishing the problem. Any help appreciated, thanks!
7. [27 points A pet store wants to start selling radioactive fish. These come in two typesfour-eyed, and six-eyed, as shown. Let r(t) denote the population of four-eyed fish, and y(t) the population of six-eyed fish. Since the fish will be kept in the same tank, they will fight each other. However, the pet store...
If a function has more than one independent variables, e.g. y = f(x,z), then the change...
If a function has more than one independent variables, e.g. y = f(x,z), then the change in y is generalized to Ay= 4x + Az where the partial derivative oy is the derivative of y with respect tox treating all other independent variables (in this case z) as constant. Example: The area of a rectangle is A = LW. The two independent variables are the length Land width W of a rectangle. Then the average area is Aav = Lay...
What is the intuition behind the answer?
Imagine that we run the regression y; = Bo+B1xe and recover the OLS estimates of Bo and B1. If our regressions assumptions hold for the above specification. What is the relationship with the coefficients of the reverse regression x = ao + a1Yi + u;: (a) ao a CORRECT) - (b) @о — — Во = (с) dо — Во &1=-B1 (d) do — Во
Imagine that we run the regression y; =...
Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice for integrating over disks. Once we choose a coordinate system we must figure out the area form (dA) for that system. For example, when switching from rectangular to polar coordinates we must change the form of the area element from drdy to rdrd0. To determine that rdrde is the correct formula how the edges of...
Let the random variable Y represent hourly wages and the random variable X represent education. Suppose we have the following regression equation in mind to estimate the return to education: (a) Can we say that this regression would capture the causal effect of education on wages? Support your answer with reasoning. (b) Using the sample equivalent of the two equations E(u)-0 and E(uX)-0 derive the regression estimators for A, and β1-Write down each mathe tnatical step, what would be the...
(1 point) In your answers below, for the variable i type the word lambda, for y type the word gamma; otherwise treat these as you would any other variable. We will solve the heat equation u, = 4uxx: 0<x<2, 120 with boundary/initial conditions: u(0,1) = 0, and u(x,0) = So, 0<x< 1 u(2, 1) = 0, 13, 1<x<2. This models temperature in a thin rod of length L = 2 with thermal diffusivity a = 4 where the temperature at...
I hope you find humor behind my
teacher's strange imagination. I understand a and b, but had
trouble finishing the problem. Any help appreciated, thanks!
7. [27 points A pet store wants to start selling radioactive fish. These come in two typesfour-eyed, and six-eyed, as shown. Let r(t) denote the population of four-eyed fish, and y(t) the population of six-eyed fish. Since the fish will be kept in the same tank, they will fight each other. However, the pet store...
If a function has more than one independent variables, e.g. y = f(x,z), then the change in y is generalized to Ay= 4x + Az where the partial derivative oy is the derivative of y with respect tox treating all other independent variables (in this case z) as constant. Example: The area of a rectangle is A = LW. The two independent variables are the length Land width W of a rectangle. Then the average area is Aav = Lay...
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