Work the following problems from Nagle & Saff by hand. Check your answers either in the back of the book or by Maple. Hand in your work at the beginning of class.
Section 2.3, pages 52-54: 9, 14, 18, 21, 28, 32.
Section 2.4, pages 63-64: 12, 15, 21, 25, 32.
Ask questions.
Work on mixing problems and population models.
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. Hand in your solutions at the beginning of class on Thursday, February 5.
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.
Hand in your solutions at the beginning of class on Thursday, February 5.
Read sections 3.3 and 3.4, pages 100-106 and 108-113 in Nagle & Saff.
Groups 3, 10, and 12: complete your projects. Thursday, February 5, you will turn in a report and give a five-minute presentation to the class.