Question: A function f (x, z, y, t) of four variables, x, z, y, t, that satisfy the following PDE is called the heat equation: ft

A function f (x, z, y, t) of four variables, x, z, y, t, that satisfy the following PDE is called the heat equation:
ft = a2 (fxx + fyy + fzz)
where a is a constant. According to the heat equation, first partial with respect to t is proportional to the sum of second partials with respect to the variables in the function. Do the following functions satisfy the heat equation?
(a) f (x, y, z) = e[29a2π2t+π(3x+2y+4z)]
(b) f (x, z, y) = 3x2 + 3y2 − 6z2 + x + y − 9z −3

Step by Step Solution

★★★★★

3.48 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

We are given the form of the heat equation f t a 2 f xx f yy f zz 351 a fx y z ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

912-B-F-F-M (5076).docx

120 KBs Word File

Students Have Also Explored These Related Finance Questions!

Starting with the finished version of Example 9.3, change the fixed marketing cost to $4000 (really $4 million) in cell B5, and change the decision criterion to maximize expected utility, using an...

You are given a function f(x, z, y) of three variables, x, z, y. The following PDE is called Laplaces equation: According to this, in Laplaces equation, the sum of second partials with respect to the...

A function f(x, z, y, t) of four variables, x, z, y, t, that satisfy the following PDE is called the heat equation: Where a is a constant. According to the heat equation, firs partial with respect to...

Consider the function Y = X Z, X, Z 0. a. Graph the Y = 4 contour line for this function. How does this line compare to the Y = 2 contour line in Figure 1A.5? Explain the reasons for any...

Help in solving this problem.k 6. (10) Consider the discrete time monetary-search model we saw in class. As in the baseline model, in the day time trade takes place in a decentralized market...

10 Green's functions for PDEs In this final chapter we will apply the idea of Green's functions to PDEs, enabling us to solve the wave equation, diffusion equation and Laplace equation in unbounded...

CHAPTER 15 DIFFERENTIATION IN SEVERAL VARIABLES 10. Determine whether the partial derivatives af /ax and af/dy are posi- tive or negative at the point P on the graph in Figure 6. 29 . W = erts 30. Q...

Republic of Iraq Ministry of Higher Education and Scientific Research University of Technology Chemical Engineering Department MODELING AND SIMULATION OF FCC RISERS A RESEARCH SUBMITTED TO THE...

Partial Differential Equations The Black-Scholes-Merton (BSM or just BS) PDE for the value Ct, S) of a derivative security as a function of time t and underlying asset price level S(t) = S takes the...

D F G K L Hturn Z X C V B N M ) - x In(y?). 1xx(2.3) north. The angle D between magnetic north and true north is called the magnetic declination. Use Figure 10 to determine which of the following...

Math 1152 Project #4 Solving Initial Value Problems using Power Series and the Laplace Transform Due: Tuesday, April 11 Name(s): - - - - - - - - - - - - - - - - - - - - Description - - - - - - - - -...

Vancouver bank agrees to lend $ 180,000 to surrey corporation. on November 1, 2020 and the company signs a six-month,6% note maturing on may 1,2021. Surrey corp. follows IFRS and has a December 31,...

Jean Walker is making plans for spring break at the beaches in Florida. In applying techniques she learned in her quantitative methods class, she has identified the activities that are necessary to...

Let f ( t ) = { ( 0 if t 3 ) , ( 4 ( t - 3 ) if 3 = t 6 ) , ( 1 2 if t > 6 ) : } Find the Laplace transform, F ( s ) of f ( t ) F ( s ) = \ sigma ^ ( 4 ) ( e ^ ( - 3 s ) ) / ( s ^ ( 2 ) ) - 4 ( e ^ (...

At December 31, 2014, Finzelberg Company had a credit balance of $15,000 in Allowance for Doubtful Accounts. During 2015, Finzelberg wrote off accounts totaling $11,000. One of those accounts...

Repeat (a) and (b) of Problem 11.16, assuming that only 50 decision makers involved in Big Data purchases for each company size were surveyed. Discuss the implications of sample size on the x2 test...

Gepetto Shoe Store uses the retail inventory method for its two departments, Womens Shoes and Mens Shoes. The following information for each department is obtained. Instructions Compute the estimated...

Use the following contingency table: a. Compute the expected frequencies for each cell. b. Compute x2STAT. Is it significant at = 0.05? c. If appropriate, use the Marascuilo procedure and = 0.05 to...

Use the following contingency table: a. Compute the expected frequencies for each cell. b. Compute x2STAT. Is it significant at = 0.05? Total 10 90 40 45 50 135 225 30 50 Total 50 75 100

5. Determine the revised X and S-control limits for the data in Example 13.3.a.

1. Given a fair, six-sided die, what is the probability of rolling the die twice and getting a 1 each time? 2. What is the probability of getting a 1 on the second roll when you get a 1 on the first...

Use the data in the table to answer Questions 9 through 11. 1. Determine SS xx , SS xy , and SS yy . 2. Find the equation of the regression line. What is the predicted value when 3. Is the...

A group of students from three universities were asked to pick their favorite college sport to attend of their choice: The results, in number of students, are listed as follows: Supposed a student is...

A firm is considering two mutually exclusive projects, X and Y, with the following cash flows: 0 1 2 Project X -$1,000 $100 $300 5430 $750 Project Y $1,000 $1,100 $100 545 $45 The projects are...

A stock that is currently selling for $47 has the following six-month options outstanding: Strike Price Market Price Call Option $45 $4 Call Option $50 $1 a. Which option(s) is (are) in the money? b....

Consider the following multifactor (APT) model of security returns for a particular stock. Factor Factor Beta Factor Risk Premium Inflation 1.0 9 % Industrial production 0.5 10 Oil prices 0.2 8 a. If...