User contributions for AlanGetz

15 April 2026

• 04:5504:55, 15 April 2026 diff hist +210 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 12 (c)/Hint 1 Created page with "First, solve for the steady state. Then determine the sign of <math>\frac{dS}{dt}</math> for <math>S</math> on either side of the steady state by considering very small and very large values of <math>S</math>." current
• 04:5304:53, 15 April 2026 diff hist +660 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 12 (c)/Solution 1 Created page with "Let <math>0<R<1</math>. Solving for the steady state <math>0=R-\frac{S}{2+S}</math>, we obtain <math>S = \frac{2R}{1-R}</math>. For <math>S</math> very close to <math>0</math>, we would have <math>R-\frac{S}{2+S}</math> close to <math>R</math>, which is positive, so <math>\frac{dS}{dt}>0</math> for <math>S<\frac{2R}{1-R}</math>. On the other hand, for <math>S</math> very large, we would have <math>\frac{S}{2+S}</math> close to <math>1</math>, so <math>R-\frac{S}{2+S}<..." current
• 04:3804:38, 15 April 2026 diff hist +288 N File:Q12(c) diagram, UBC math 100 December 2024 exam.png Uploaded a work by {{Unknown|author}} from UBC December 2024 math 100 B exam with UploadWizard current Tag: Upload Wizard
• 04:3404:34, 15 April 2026 diff hist +313 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 12 (b)/Solution 1 Created page with "For all <math>S\geq 0</math>, <math>\frac{S}{2+S}<1</math>. Since <math>\frac{3}{2}>1</math>, we have that <math display="block"> \frac{3}{2}-\frac{S}{2+S}> \frac{3}{2} - 1 > 0, </math> so <math>\frac{dS}{dt}>0</math> for all nonnegative <math>S</math>. That is, over time the substrate builds up without bound." current
• 04:0904:09, 15 April 2026 diff hist +82 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 12 (a)/Solution 1 Created page with "The phase diagram is File:Q12(a) diagram, UBC math 100 December 2024 exam.png" current
• 04:0804:08, 15 April 2026 diff hist +288 N File:Q12(a) diagram, UBC math 100 December 2024 exam.png Uploaded a work by {{Unknown|author}} from UBC December 2024 math 100 B exam with UploadWizard current Tag: Upload Wizard
• 04:0604:06, 15 April 2026 diff hist +275 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 12 (a)/Hint 1 Created page with "Set <math>R=0</math> and consider the differential equation <math>\frac{dS}{dt}=-\frac{S}{2+S}</math>. Find the equilibrium points by solving <math>\frac{dS}{dt}=0</math>, then determine the sign of <math>\frac{dS}{dt}</math> for the values of <math>S</math> on either side." current
• 04:0004:00, 15 April 2026 diff hist +564 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 12 (c)/Statement Created page with "Suppose a chemical is being converted to a product in tank. The amount of the chemical is <math>S</math>, which is nonnegative and changes with respect to time. If the chemical is being added to the tank at a constant nonnegative rate <math>R</math>, then the amount of the chemical in the tank satisfies the differential equation <math display="block"> \frac{dS}{dt}=R-\frac{S}{2+S}. </math> Describe in words what happens to the amount of the chemical in the tank over a l..." current
• 03:5903:59, 15 April 2026 diff hist +524 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 12 (b)/Statement Created page with "Suppose a chemical is being converted to a product in tank. The amount of the chemical is <math>S</math>, which is nonnegative and changes with respect to time. If the chemical is being added to the tank at a constant nonnegative rate <math>R</math>, then the amount of the chemical in the tank satisfies the differential equation <math display="block"> \frac{dS}{dt}=R-\frac{S}{2+S}. </math> Describe in words what happens to the amount of the chemical in the tank over a l..." current
• 03:5503:55, 15 April 2026 diff hist +494 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 12 (a)/Statement Created page with "Suppose a chemical is being converted to a product in tank. The amount of the chemical is <math>S</math>, which is nonnegative and changes with respect to time. If the chemical is being added to the tank at a constant nonnegative rate <math>R</math>, then the amount of the chemical in the tank satisfies the differential equation <math display="block"> \frac{dS}{dt}=R-\frac{S}{2+S}. </math> Draw a phase diagram for the differential equation, for <math>S\geq 0</math>, whe..." current
• 03:5203:52, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 14 No edit summary current
• 03:5203:52, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 13 No edit summary current
• 03:5103:51, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 12 (c) No edit summary current
• 03:5103:51, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 12 (b) No edit summary current
• 03:5103:51, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 12 (a) No edit summary current
• 03:5003:50, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (d) No edit summary current
• 03:5003:50, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (c) No edit summary current
• 03:5003:50, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (b) No edit summary current
• 03:4903:49, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (a) No edit summary current
• 03:4903:49, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 10 No edit summary current
• 03:4803:48, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 09 (b) No edit summary current
• 03:4803:48, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 09 (a) No edit summary current
• 03:4703:47, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 08 No edit summary current
• 03:4703:47, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 07 No edit summary current
• 03:4703:47, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 06 No edit summary current
• 03:4603:46, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 05 No edit summary current
• 03:4603:46, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 04 (c) No edit summary current
• 03:4603:46, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 04 (b) No edit summary current
• 03:4503:45, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 04 (a) No edit summary current
• 03:4503:45, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 03 (b) No edit summary current
• 03:4503:45, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 03 (a) No edit summary current
• 03:4403:44, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 02 (c) No edit summary current
• 03:4403:44, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 02 (b) No edit summary current
• 03:4303:43, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 02 (a) No edit summary current
• 03:4303:43, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 01 (c) No edit summary current
• 03:4203:42, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 01 (b) No edit summary current
• 03:4203:42, 15 April 2026 diff hist +3 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 01 (a) No edit summary current
• 03:4003:40, 15 April 2026 diff hist +406 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (d)/Solution 1 Created page with "From the sketch, we see <math>y(x)</math> is concave down. That means its tangent lines lie above the curve, so linear approximations produce over approximations. Hence, the first step of Euler's method produces an over approximation. Additionally, <math>y(x)</math> is increasing, so an initial over approximation plus a linear approximation will produce an over approximation in the second step as well." current
• 03:3603:36, 15 April 2026 diff hist +188 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (d)/Hint 1 Created page with "From your sketch in part (a), does the curve look concave up or concave down? What does this imply about whether Euler's method will yield an over approximation or an under approximation?" current
• 03:3103:31, 15 April 2026 diff hist +307 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (d)/Statement Created page with "In this question, we’ll investigate solutions to the differential equation <math display="block"> \frac{dy}{dt}= (y-1)(3-y). </math> Is your numerical approximation from (c) using Euler’s method larger or smaller than <math>y(1)</math>? You may use your previous work, but you must explain your answer." current
• 03:2903:29, 15 April 2026 diff hist +1 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (c)/Solution 1 No edit summary current
• 03:2803:28, 15 April 2026 diff hist +355 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (c)/Solution 1 Created page with "Let us denote <math>f(y) = (y-1)(3-y)</math>. At <math>t=0</math>, we have <math>y_0=y(0)=2</math> and <math>f(y_0)=f(2)=(2-1)(3-2)=1</math>. Hence, at our next time step, we have <math>y_1=1+(1/2)=5/2</math> and <math>f(y_1)f(5/2)=(3/2)(1/2)=3/4</math>. At our final time step, we have <math>y_2=5/2+(1/2)(3/4)=23/8</math>, which is our approximation."
• 03:1703:17, 15 April 2026 diff hist +170 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (c)/Hint 1 Created page with "Since we are using Euler's method with two steps, beginning at <math>t=0</math> and ending at <math>t=1</math>, our time step will need to be <math>\Delta t = 1/2</math>." current
• 03:1403:14, 15 April 2026 diff hist +191 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (c)/Statement Created page with "In this question, we’ll investigate solutions to the differential equation <math display="block"> \frac{dy}{dt}= (y-1)(3-y). </math> Use Euler’s method with two steps to approximate y(1)." current
• 03:1203:12, 15 April 2026 diff hist 0 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (b)/Hint 1 No edit summary current
• 03:1103:11, 15 April 2026 diff hist +101 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (b)/Hint 1 Created page with "Where does it look like the curve sketched out in part (a) intersects with the line <math>x=1</math>."
• 03:0503:05, 15 April 2026 diff hist +156 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (b)/Solution 1 Created page with "Based on the sketch in part (a), <math>y(1)</math> is approximately <math>2.75</math>, though any answer in the interval <math>(2.5,3)</math> is acceptable." current
• 03:0103:01, 15 April 2026 diff hist +211 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (b)/Statement Created page with "In this question, we’ll investigate solutions to the differential equation <math display="block"> \frac{dy}{dt}= (y-1)(3-y). </math> Using your sketch from (a), give an approximate value for <math>y(1)</math>." current
• 03:0003:00, 15 April 2026 diff hist +1 Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (a)/Statement No edit summary current
• 02:5802:58, 15 April 2026 diff hist +86 N Science:Math Exam Resources/Courses/MATH100 B/December 2024/Question 11 (a)/Solution 1 Created page with "The solution is given by File:Q11(a) diagram, UBC math 100 December 2024 exam.png" current