Announcements

Announcements

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You are expected to check for new announcements every day.

Dated announcements are periodically moved to the archives

Dec 14 The final is graded. Here is  the solution guide. Letter grades will be determined and handed over to the registrar some time tomorrow. You can pick up your exam in January. And I am happy to recheck anything at that time.

Nov 25 A7 is available.

Nov 19 Typo in A6 handout problem . The function G is

G(z) = (h/2)f(t(k+1),z)  + c

not         G(z) = z + (h/2)f(t(k+1),z)  + c

Nov 19  You do not have to download ode23tx and pchiptx from the NCM website. Just use ode23 and pchip.

Nov 17 In the Lorenz problem, design LorenzZones so that it also returns the t and y values produced by ode45. Thus, if

[tOut,yOut,tE,yE,iE) = ode45(....

then

[Enter1,exit1,Enter2,Exit2,tOut,yOut] = LorenzZones(...

This gives you more to work with in P2.

Nov 14 Assignment 6 is available

Nov 4 Some comments on A5. The ODE in P2 has the property that y(1)+y(2)+y(3) is constant. (Why?) Thus, if sum(y0) = 100 we can interpret these functions as percents, e.g., y1(t) = percent of the original population that is still susceptible. Given that, let's refine what is to be displayed in Figure 3 as follows: Find initial conditions/parameter values so that y1(1) is approximately 1. That is, only 1 percent of the population has yet to be infected.

Regarding the example for Figure 2, find initial conditions/parameter values so that y2(t)) does not increase across [0,1]

In P3, you may assume that 1<=yp<=1.4. And define KeplerCheck by max |Ak - mu|/mu  instead of max | Ak - mu|. (Relative error a little more illuminating than absolute error.)

Oct 31. We will be using the IVP chapter from the online NCM text. Download it!

Oct 24 Midterm Solution. The last date for regrade submissions is Oct 31.

Oct 20 Assignment 4 is graded

Oct 17 Assignment 3 solutions are available. My original grading guide for the TA was a bit harsh so I revisited solutions and made some adjustments. However, in many cases the lack of comments made it impossible to take a charitable, partial credit  point of view.

Oct 16 Comments on Assignment A4. Due date is shifted one day. New due date: Saturday October 18, 6pm.

A test script for P2 is available. Please modify your PeriodicSimpson so that instead of just returning the estimate of the integral, it returns the estimate AND the number of required f-evaluations. Note that CompSimpson(f,a,b,n) requires 2n+1 f-evaluations.You may assume that the lecture code CompSimpson is available. Or you can make it (or a modification) a subfunction

P3 Play with quad, quad1, and quadgk and experimentally determine which is best. Note that  these procedures have "parameters" that can be adjusted, i.e., abstol, reltol, maxIntervalCount. Play around with these. Efficiency is NOT an issue in this problem. And don't go looking for some magic change of variable that makes the whole thing easy! About the only math fact necessary is integral(f,a,b) = integral(f,a,c) + integral(f,c,b).

P4 A test script is provided.

Oct 16  Hints are now available to just about every problem of the day.  Working these problems is one way to prepare for the midterm.

Oct 16. The midterm has been moved from Tuesday Oct 21 to Thursday Oct 23. It is in class and 75 minutes long.

Oct 7 Assignment 4 is available

Sept 26 I have decided NOT to provide test scripts for A3. Instead, here is some advice on how to go about designing your own tests:

P1. You can check the not-a-knot and the complete spline by comparing what you produce with what Matlab's spline function produces. Remember, the spline interpolant is unique once the two end conditions are specified.

P2. Is z is a vector and you want to evaluate B_{k}(z), don't waste time on the z-values that are outside [x(k)-2h,x(k)+2h).

P3. When you take the inner product of two vectors f and g, don't waste time adding those terms  f(i)*g(i) into the running sum if you know (based on the index i) that f(i)*g(i) = 0.

Sept 23 Assignment 3 is available. Some test scripts no later than Monday Sept 29

Sept 10 Assignment 1 is graded. Solutions here.

Sept 8 Assignment 2 is available. Details regarding the 4th and 5th problem will be presented during class. Scripts P4 and P5 in a few days.

Sept 2  Clarification of the CMS-Piazza-Coursewebsite connection. The handout, test scripts, solutions are accessed through th ecourse website. You get a signal that an assignment is "open" or "graded" via CMS. Announcements of the same are also made  on the course website. During an assignment, help is provided via office hours, class time, and piazza. You want to use piazza because it is the easiest way to process typos and other ambiguities.

August 27  The first assignment is available. The test scripts will be available early next week. If you are not in CMS, then send me your net ID and i can set you up.