• First day handout, PDF file first day handout .
• A zeroth Maple sheet Algebra and Calculus stunts with Maple
• A first Maple sheet Euler's method and slope fields.
• Homework p 23: 4, 8, and 9; p 29: 11, 12, 16. Due Wed Jan 23.
• Another Maple sheet, with answers to the first quiz, and a discussion of Taylor's series. Taylor's series mod to Euler's method, and quiz 1.
• Yet another Maple sheet, somewhat related to the first homework assignment. hints on homework 1 .
• More homework, this due Wed. Jan 30. p 46 # 7, 16, 19, 27 parts b and d. For d, as a check and for comparison, use Maple's evalf and Int to get a second estimate. The idea is that Maple will numerically evaluate a definite integral without even necessarily trying to do the integral in the abstract. Example: theintegral:=Int(exp(-sin(x^4)),x=0..1); thenumber:=evalf(theintegral); should give you a numerical value for the integral of e to the power negative sin(x to the fourth), for x from 0 to 1. Also, on p 55, # 1 through 6 (note, you don't work any of these. You just classify them into one of four cases: neither separable nor first order linear, separable but not first order linear, etc. ), and (now you do work them) p 55 # 8, 13, and 25. But in part 25b, instead of using Simpson's method to get a numerical value, you can just use evalf(integral) Maple commands.
• Here's a Maple worksheet that does for second order linear differential equations what an earlier sheet did for first order. a wave that changes shape, and why .
• That Maple sheet about undetermined coefficients, that didn't get attached in email.
• The Maple worksheet we used in class Friday Feb 8 to illustrate nonconstant "p(x)" behavior . I threw in an example of how to get Maple to run the numbers and give the solution when the differential equation has a canned solution. One uses the command "dsolve".
• Another discussion of methods for solving second order nonhomogeneous differential equations. With both these methods, it is assumed you already have at hand two solutions, y_1 and y_2, say, to the corresponding homogeneous equation. Maple worksheet link. As usual, save to file, then open with Maple. A Maple worksheet is, from the strictly geek viewpoint, an ASCII text string. Even the graphs are just strings of letters and numbers specifying which pixels to color what color. Naturally, when read without Maple interface, it's largely gibberish.
• Solutions to Exam 1 . (Link updated to correct typos and layout.) There were two versions, slightly different. The last problem, a bonus problem in either case, was different, and there were minor differences in some of the earlier problems. Both direction fields have the same general layout; the isoclines are straight lines and there is a single straight line solution: y=x. The difference is that this solution attracts all the others in one case as x increases, and repels them as x decreases. In the other version, it's the other way around.
• A Maple sheet about the daily ups and downs of temperature inside an unheated building.
• A Mathematica notebook about Euler's method for systems of differential equations two water tanks.
• Homework for April 9: p 548 # 2,8,9,19,20, p 559 # 2, 3, 9,10,12,17,35, and p 567 # 2,3,5,13.