Sometimes a complicated differential equation can be made simpler by a special change of variables. Look up the appropriate tricks in section 2.6 of Nagle & Saff and use them to solve the following problems on page 76: 9, 17, 21, 29.
Do problems 1, 3, and 9 in section 3.2, pages 98-99 of Nagle & Saff by hand. Since these are word problems, your solutions should also contain words! In particular, identify all variables that you introduce, and state how you got the differential equation that models the situation described in the problem.
Also do problem 13 on page 99 of Nagle & Saff, which is a follow-up to problem 9 but with a different model of population growth. If you look at the complicated formulas given in the book, you will see that this problem could be tedious to work out by hand. Instead use Maple to solve the problem. You can use dsolve to get the general solution of the logistic equation and then pass the given data to the solve command in order to determine the parameters in the logistic model.
Read sections 3.3 and 3.4, pages 100-106 and 108-113 in Nagle & Saff.
Groups 3, 10, and 12: complete your projects.
Ask questions about the homework. A solution using Maple of the problem on population growth with a logistic model is available as a Maple worksheet, as a text file, and in Acrobat .pdf format.
Learn from the presentations of group projects.
Group 3: comparison of Euler's method and the Taylor series method for finding numerical approximations to an initial value problem for a first-order differential equation. You can also read brief biographies of Euler and of Taylor.
Group 10: discussion of Picard's method of successive approximations for solving an initial value problem (recast as an integral equation). You can also read a brief biography of Picard.
Group 12: examination of magnetic field lines and equipotential lines as examples of orthogonal trajectories.
The homework was not collected today, as the questions about the assignment were extensive. Revise and correct this homework, and turn it in at the beginning of class on Tuesday, February 10.