Work through Chapter 1, pages 17-24, in the lab manual.
This covers the Maple commands dsolve and DEplot
and shows a way to implement Euler's method in Maple.
Since direction field plots are tedious to construct by hand, use Maple to solve problem 1 on page 25 in the lab manual. Also use Maple to assist in solving problems 3, 4, and 5 on pages 22-23, section 1.3 in Nagle & Saff.
Do problems 5 and 8 on page 28, section 1.4 in Nagle & Saff. You may do these problems about Euler's method either by hand or by using Maple, whichever you prefer.
Do problem 12 on page 29, section 1.4 in Nagle & Saff. This is a more theoretical problem, so you should do it by hand.
Do technical writing exercise 2 on page 30, Chapter 1 of Nagle & Saff, which says:
Compare the different types of solutions discussed in this chapter--explicit, implicit, graphical, and numerical. What are the advantages and disadvantages of each?
Your essay should be typed or typeset with a 12-point font, single-spaced, with a margin of 1.5 inches on each side. The length should be not less than one page and not more than two pages.
For many of you, writing an essay for mathematics class will be a new experience. Obviously, there is no "right answer" to this exercise. The main point of this assignment is for you to think about what it really means to "solve" a differential equation and to organize your ideas and to clarify your understanding.
This assignment is more about "Why do we do these computations?" and less about "What steps do we perform to get the right answer?"
A second goal of this assignment is for you to practice your written communication skills. In the real world, being able to solve problems is only the first step: you also have to be able to explain your results to someone else. Therefore, you should pay attention to organizing your essay and to writing clearly.
Be sure to proofread your essay. It is important to use correct spelling, punctuation, and grammar--even in mathematics class.
Read sections 2.1 and 2.2, pages 35-43, in Nagle & Saff. This discusses the explicit solution of one special class of first order differential equations, the so-called separable equations.
Hand in the above homework exercises and the essay at the beginning of class.
Ask questions.
Recapitulate Chapter 1 in Nagle & Saff.
Work on separable first-order equations.
Do as many of exercises 1-26 on page 44, section 2.2 of Nagle & Saff as you feel necessary to be prepared for a quiz next class on separable equations. These problems are not to be handed in.
Do problem 36 (about free fall) and problem 37 (about compound interest) on page 46, section 2.2 of Nagle & Saff, and hand in your solutions at the beginning of class on Thursday, January 29.
Read sections 2.3 and 2.4 (pages 46-52 and 55-63) in Nagle & Saff.
Do problem 7 on page 52, section 2.3 and problem 9 on page 63, section 2.4 in Nagle & Saff. Check your answers in the back of the book. Hand in your solutions at the beginning of class on Thursday, January 29.