Question: we look at a model for how heat is exchanged between two rooms, with the variables y1 and y2 like the two temperatures. we set

we look at a model for how heat is exchanged between two rooms, with the variables y1 and y2 like the two temperatures. we set this up as a system of two differential equations. first, we define it the mathematical model at

y1'= F (y1, y2) = 1/2(y2-y1),

y2'=G (y1, y2) = y1-y2

(a) interpret the differential equations. what does it mean we have y1-y2 in the one equation and in the y1-y2 second? what is the significance of coefficient 1/2?

(b) assume that the temperature in the two rooms is repeatedly 22 and 19 degrees at 10. solve the equation numerically using Euler's 50 step method to find the temperature at 7pm on the same day. plot the solution and describe it. what happens to the temperature in the two rooms.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

I was given the following file "ScriptFigs.m": % % Script for generating figures and testing stuff. % n = 10; x = 1:n; y = randn(n,1); pp = spline (x, y); %% Plot the results delta = 0.05; x2 =...

Algorithms in Artificial Intelligence (or, the old name: Introduction to Algorithmic Decision Making) Part 1 Based on slides by David Sarne and Lirong Xia Course Tentative Schedule Introduction...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

Q9some type is wrong, can refer to the attach file. In a study of the relationship between an explanatory variable Z and a response variable Y , n independent observations are taken in the form of...

ML in a nutshell Optimization, and machine learning, are intimately connected. At a very coarse level, ML works as follows. First, you come up somehow with a very complicated model y = M(x, 0), which...

tudy of an innovative method based on complementarity between ARIZ, lean management and discrete event simulation for solving warehousing problems Fatima Zahra Ben Moussa a, , Roland De Guiob ,...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

Suppose that R(A, B, C) is a relational schema with functional dependencies F = {A, B C, C B}. (i) Is this schema in 3NF? Explain. [2 marks] (ii) Is this schema in BCNF? Explain. [2 marks] (b)...

How we achieve our personal vision without developing self-motivation skills? Write a short, to-the-point answer. Word Limit: 50 words.

Write a C Program for extracting only operators from a large string. n.b: solve the question properly. run it from codeblocks & show the output.

What amount are permitted for inclusion in the capitalized cost of PP&E ?

On 1 March 2007 DB Limited issued R560 000 15% debentures at R98. The debentures were to be redeemed at par in four equal annual payments starting 28 February 2010. Required: Journalise the above...