Math 308-510 Syllabus
Catalog Description. Credit 3. Linear ordinary differential equations, solutions in series, solutions using Laplace transforms, systems of differential equations.Prerequisite: Math 251 (third semester of calculus).
Textbooks. Fundamentals of Differential Equationsand Boundary Value Problems by Nagle and Saff, and Solving Differential Equations with Maple V Release 4 .
Content.Differential equations is a stool with 3 legs. The first leg is plain old calculation. Back-of-the-envelope stuff, as the engineers say. The techniques are stated in the text, they'll be explained in lecture, and there is homework so you can practice them.
These techniques are also basic to an understanding of the more conceptual aspects of differential equations. Calculations of this sort can often be done by Maple if parsed into standard form, but the emphasis here will be on facility without Maple prosthetics.
The second leg is modeling, plotting, and estimation. Story problems come into this category, as will the course project you will be doing. For this project, and only for the project, group work is permitted. Groups should be limited to four members and each member should contribute in a major way. Graphical insight into the solutions of differential equations requires a look at the graphs, and for this one needs Maple. The tests will include Maple tasks along these lines.
The third leg is direct numerical solution. Here, Maple is far from the most powerful package, but its generality and (we hope) familiarity make it a good choice for instructional purposes. We shall not dwell on the details of the various numerical methods in this course, but one needs to have a sense for the limitations and strengths of the methods. This leg is not disposable; write a differential equation at random and most likely it will not be possible to solve it with formal methods. (The same holds for integrals, for that matter.)
There are some parts of the course where we shall have to blend numerical, symbolic, and graphical approaches. Systems of linear differential equations can in principle be solved by pencil-and-paper methods, but unfortunately the typical case requires hideous amounts of arithmetic. In practice, we shall need Maple to cut through the arithmetic and algebra, and (again) to give us some pictures to go with the analytical solutions.
The final exam will be held at the regular University-scheduled time and will be comprehensive but with an emphasis on the more recent material. All exams will include a hand-calculation component where computers are not available, and a smaller but significant component where it is intended that Maple be used. Grades will be based on short regular Thursday quizzes (15%), hour exams (15% each for 45% in aggregate), a course project (15%), and a final (25%). Grading scale is 85, 75, 60, 50.
In Faculty Senate-approved wording the first day handout, "As commonly defined, plagiarism consists of passing off as one's own the ideas, words, writings, etc., which belong to another. In accordance with this definition, you are committing plagiarism if you copy the work of another person and turn it in as your own, even if you should have the permission of that person. Plagiarism is one of the worst academic sins, for the plagiarist destroys the trust among colleagues without which research cannot be safely communicated."
More legalese: "The handouts used in this course are copyrighted. By "handouts," I mean all materials generated for this class, which include but are not limited to syllabi, quizzes, exams, lab problems, in-class materials, review sheets, and additional problem sets. Because these materials are copyrighted you do not have the right to copy the handouts, unless I expressly grant permission." Permission IS granted to students currently enrolled in this section (308-506) to copy these materials for individual use...you may download these files to your home computer or calclab account, you may print them out for your own use, and so on. Any further transmission or copying of these materials must include acknowledgment of the source, and must include this (this here) paragraph in its entirety.
Week 1: Jan 20-22 Maple orientation, Nagle and Saff chapter 1, SDEMV chapters 0 and 1.
Hwk p. 14 # 1, 2, 6, 8, 12, 15 (use Maple?), 18, 23, 30. p 23 # 2, 3, 6, 9, 10
Hwk p. 28 # 8, 14, 16.
Week 2 Jan 27-29 Sections 2.1-2.3.
Week 3 Feb 3-5 Sections 2.4, 2.5, Exam 1 (Thurs)
Week 4 Feb 10-12 Sections 3.1-3.4, SDEMV chapter 2.
Week 5 Feb 17-19 Chapter 4 sections 1 thru 4, SDEMV chapter 3.......
Week 6 Feb 24-26 Chapter 4 sections 5 thru 8, SDEMV chapter 3 continued.
Week 7 Mar 3-5 Chapter 5 sections 1 thru 3, SDEMV chapter 4.
Week 8 Mar 10-12 Exam 2 (Tues), 4.10, 5.4
Week 9 Mar 24-26 5.7, 6.1, SDEMV chapter 6.
Week 10 Mar 31-Apr 2 6.2, 6.3, SDEMV chapter 6 continued.
Week 11 Apr 7-9 7.1, 7.2, SDEMV chapter 5.
Week 12 Apr 14-16 7.3-7.5, SDEMV chapter 5 continued.
Week 13 Apr 21-23 Exam 3 (Tues), 7.6 (Wed.)
Week 14 Apr 28-30 8.1-8.3