Bill Goodwine's Courses

Reading: Chapter 2 through section 2.4 (you might as well read the whole chapter, section 2.5 is the last section).

Exercises: I'm working on a better way to do it, but for this week you have to click again here.

For numbers 3 and 4 on the reason why are we supposed to give a conceptual answer or a mathematical proof?

jmcgill1 wrote:For numbers 3 and 4 on the reason why are we supposed to give a conceptual answer or a mathematical proof?

I'm not sure I see the distinction in the present case. Just explain or point out the step where the process broke down or became invalid. If that doesn't answer your question, please ask again, but maybe with a different wording, like what you see as the distinction between a conceptual answer and a proof.

For the first part Problem 7, I am having trouble solving the differential equation because I get that dV/dt = kA which cannot be solved because kA has units of r not t. Can you point me in the right direction/give me any advice on how to set up the differential equation that only has 2 variables?

kpulliam wrote:For the first part Problem 7, I am having trouble solving the differential equation because I get that dV/dt = kA which cannot be solved because kA has units of r not t. Can you point me in the right direction/give me any advice on how to set up the differential equation that only has 2 variables?

the LHS has units of volume/time. A has units of area, so k will have units of length/time. So the problem isn't the units (although it was very good to think about them).

You need to express both V and A as a function of r and you will have an equation in only one variable.

For Problem 1, is there a specific range you would like us to graph x(t) over?

matthewpolicelli wrote:For Problem 1, is there a specific range you would like us to graph x(t) over?

In all such cases the answer is to plot the solution for the amount of time it takes to clearly display the nature of the solution. If it continues to change in new ways, then you must plot it for longer. If it reaches a steady-state or starts repeating, then enough time to show all of that is enough. The point is communication: your plot should communicate the nature of the solutions and the differences and similarities among them.

goodwine wrote:

matthewpolicelli wrote:For Problem 1, is there a specific range you would like us to graph x(t) over?

In all such cases the answer is to plot the solution for the amount of time it takes to clearly display the nature of the solution. If it continues to change in new ways, then you must plot it for longer. If it reaches a steady-state or starts repeating, then enough time to show all of that is enough. The point is communication: your plot should communicate the nature of the solutions and the differences and similarities among them.

Thank you!

For Problem #1, are we allowed to draw the plots by hand or should they be plotted in MatLab? Thank you.

cmjarocki wrote:For Problem #1, are we allowed to draw the plots by hand or should they be plotted in MatLab? Thank you.

Either way is fine.

The statement for 5.1 reads: "Show that if x(t) represents the number of grams of chemical in the solution at time t..." and gives an equation. Would you like us to show the derivation for that equation, or prove that it works by solving the rest of the problem? Thanks!

khayes2 wrote:The statement for 5.1 reads: "Show that if x(t) represents the number of grams of chemical in the solution at time t..." and gives an equation. Would you like us to show the derivation for that equation, or prove that it works by solving the rest of the problem? Thanks!

Derivation.

For that problem I put a number problem first, and then a more general one with symbols. If you think you can do the symbol one easily, then do that one first and just plug in the numbers to do the first part.

goodwine wrote:

khayes2 wrote:The statement for 5.1 reads: "Show that if x(t) represents the number of grams of chemical in the solution at time t..." and gives an equation. Would you like us to show the derivation for that equation, or prove that it works by solving the rest of the problem? Thanks!

Derivation.

For that problem I put a number problem first, and then a more general one with symbols. If you think you can do the symbol one easily, then do that one first and just plug in the numbers to do the first part.

Okay, thank you very much.