This is the course website for Dr. Peterson's sections of MA153, Fall 2008. Be sure to bookmark this page!
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Instructor NotesImportant announcements and notes will be posted here. See the archive with all posts or subscribe to receive updates. Good luck on the TEE posted on 1229361035|%e %b %Y, %H:%M (%O ago) Study hard, and have a Merry Christmas/Happy Holidays!  TEE Information & Review Sheets posted on 1229084012|%e %b %Y, %H:%M (%O ago) The TEE is scheduled for Tuesday, 16-Dec from 0735-1105 in the following locations:
You are authorized 5 handwritten note sheets for the exam (front/back). Calculators are not permitted. A review session will be held on Saturday, 13-Dec from 0830-1100 in Thayer Hall 342. Here are the checklists from the first for blocks: WPR Drop posted on 1228357469|%e %b %Y, %H:%M (%O ago) The lowest WPR score has been dropped in AMS. Some of you should see your grades go up quite a bit! Remember that there are still roughly 1/3 of the course points to be assigned, between the Project and the TEE! Optional Lecture posted on 1227186139|%e %b %Y, %H:%M (%O ago) When/where: I'll be speaking on November 20, in Thayer Hall 344 from 1355-1450. See abstract below. Dynamic Mathematics and Pursuit/Evasion Games Abstract: Pursuit/Evasion Games are simple games in which the primary objective is either to chase down the opposing team, or to avoid capture by the opposing team. These games are played out all around us. Think of football, ultimate frisbee, and capture-the-flag… and what would Hollywood do without car chases? Exact solutions can be found for simple versions of these games using differential equations. However, this talk focuses on visualizations of these games when there are two or more teams and lots of players involved. Several scenarios will be illustrated using a Java platform that automatically updates solutions whenever parameters are changed. This visual approach is one example showing how making mathematics "dynamic" can lead to additional insights into the underlying situation. Guest Lecture 4 posted on 1227185897|%e %b %Y, %H:%M (%O ago) When/where: This Friday we will have a guest lecture in Thayer Hall 144 during Dean's Hour. See abstract below. Mathematics and the "Age of Biology" Abstract: I will address what I feel will become the most significant new technical challenges that lie ahead of us - specifically the manner in which humans will join with the information network - thereby highlighting both the promise and the peril of human enhancement. I will attempt to show why computer science, engineering, physics and mathematics are the basic disciplines that will lead the way in forcing new biological understandings of what it means to be human. I will mention a new effort that has just begun at NSA to understand the place of neuroscience in computation and communication, then conclude with a look at some of the new things that you can get this Christmas which will allow you, yourself to become an actual "player" in the Age of Biology that is dawning. |
Recent posts on the AI page below (subscribe) 16.5.13 on Finding the potential function for a vector field1226577508|%e %b %Y, %H:%M %Z|agohover Given , the problem is to find a scalar function f such that . We can solve this problem by recognizing that we are given three partial derivatives for f, so all of the following have to be true for f: (1) Solve these by integrating with respect to the appropriate variable, while keeping the others fixed. For example, , where is any function of y and z. This is necessary since if it depends on just y and z. Continuing in this manner for the other two equations, we have: (2) Now
Why don't constants show up for double integrals?1224268773|%e %b %Y, %H:%M %Z|agohover Received via email: "Sir, I have a general question I’ve been wondering. In integration, you normally add a constant to the end of the function, why is this not done for double and triple integrals? Where does the constant cancel out?" My response: Great question. The reason is just like the difference between a definite integral and an indefinite integral. When you have limits of integration, the constants “cancel”: (1) For double (& triple) integrals, our definition as
Solution to Problem #17 on page 877 (section 14.2)1223304052|%e %b %Y, %H:%M %Z|agohover In B/H hour today, we went over the problem of computing the limit (1) One approach is to remove the radical from the denominator: (2) Alternately, use the trick I mentioned in class: for small values of , Thus, we can write (3)
Question on CalcLabs p. 98 #10ab1223048643|%e %b %Y, %H:%M %Z|agohover I had the following question via email: In the first calclab question, it asks to show how specific values of u corresponds to either the positive or negative gradient of f. what does this ask for? The question is worded wrong here. It should state: "For those values of , verify that corresponds to either ." When you calculate the directional derivative at a point with , you obtain a single-variable function with input “” (the angle) and output the slope. So the question is�
Calclabs "grad" function & Lagrange optmization1223041349|%e %b %Y, %H:%M %Z|agohover I had a question about using grad for CalcLabs. If you do use grad, make sure to first define it in mathematica using the code on page 96. When solving a Lagrange multipliers question, the command given has Thread and Flatten and is all together quite ugly. I recommend using a different approach that eliminates this excess stuff. Here's how I'd do Example 4.5.7 on page 109: f[x_,y_,z_]:=x y z g[x_,y_,z_]:=x y+2x z+2y z fx:=D[f[x,y,z],x];fy:=D[f[x,y,z],y];fz:=D[f[x,y,z],z]; gx:=D[
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