Differential Equations, Mathematics 315, Spring 2011
Final Test: will be in Fulmer 226 and in Fulmer 201, 8:00 - 10:00 am, Friday May 6
Textbook: Differential Equations 2nd Edition by Polking, Boggess, and Arnold
Classroom: Fulmer Hall 201
Problem Sessions: MTuTh 5-6pm, Wed 5:30 - 6:30, Location: usually in Fulmer 201, except(!) on Feb 10, Mar 10 and April 14 when it will be in Todd 130
Meeting Times: MWF 10:10am - 11:00am
Teaching Assistant: TBA
My Contact Info: <vixie@speakeasy.net>
Tests: I will give eight quizzes based on homework -- do the homework and you will do very well on the quizzes. Instead of grading the homework, there will be 4, 1 hour problem sessions a week in which you can go and ask questions about the homework and the reading. I will drop the first test if that improves your final grade. There will be a comprehensive final, again taken directly from the homework. There will be extra credit problems and projects for the more ambitious. The quizzes will count for 80% of your grade and the final, 20%. A = (100 - 90), B = (89 - 80), C = (79 - 65), D = (65 - 50), F = (50 - 0). There will be no makeup quizzes, but I will take improvement into account in assigning the final grade.
Reading: I expect everyone to read the text before class. I know that this is not the habit of many students, but you will do much better and you will be much better equipped to take advantage of the lectures if you do. The lectures will not be just an audible version of the text!
What We Will Cover: Most of chapters 1-5 and 9-10 of Polking, Boggess, and Arnold. I will also cover a bit of Chapter 11. This means about 10 pages of reading/study for each class day. I will (typically) assign 5-10 problems per class day, but will occasionally assign as many as 15-20 in one day.
Academic Integrity: Those who are caught cheating on tests will be given F's. I had hoped that would not be an issue in this class, given that it is an upper division mathematics course. To be excessively clear about it, using anything other than your pen or pencil and the test paper will now (as of March 28, 2011) be considered cheating. Those who are interested in anything close to the cutting edge in their career either don't need me to say this, or will, from this point forward take a much more serious approach to learning. I am of course grateful to the significant number of you for which this message is unnecessary.
Grades: Final Grades
Notes and Links:
- April 20, quiz 8
- April 22, discussion of quiz 8
m-file used to generate the period doubling route to chaos figure, April 27, 2011
The Final Test:
What it will cover: (a) Chapter 4 from textbook and (b) notes and the problems they contain, from April 11 - April 27
Structure: There will be 8 problems, 5 from chapter 4 (drawn from homework as usual) and 3 from the notes. The problems on the final covering the material in the notes will be very similar to problems in the notes, but not necessarily identical. Then there will be one problem that is a challenge problem that is for the bored and underchallenged student. You should most definitely NOT attempt this problem unless the previous 8 are done well -- it will not be a way to make up points for sloppy or careless work elsewhere.
References: Books and papers for further study
Robert L. Devaney's Chaotic Dynamical Systems. See the long first chapter which is devoted to one dimensional dynamical systems (iterated functions). It is the place you should go to see much more of what you saw on Wednesday, April 27 2011.
Steven Strogatz' Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering. Superbly written text on dynamical systems. Mark Schumaker teaches 415 from this book and if you have any interest in learning more in differential equations you should take that course.
Dominic Jordan and Peter Smith's Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers. I like this book quite a bit. It has an Applied/engineering perspective that neither Strogatz nor Devaney really has and is worth having and studying. The first chapter has (much!) more of the kinds of things we did on April 18, 2011.
Here is the link to the Mandelbrot set applet I used in class on April 27, 2011. http://math.bu.edu/DYSYS/applets/Quadr.html There are more things to explore on the homepage from which that applet came: http://math.bu.edu/DYSYS/.
Homework and Reading Assignments: The reading should be done before you come to class, homework should be completed before the next class.
Jan 10 (reading = chapter 1); (problems on 14-15: 3,4,5,6,9,10,15,16,19,20,25,26) Jan 12 (reading = sections 2.1 & 2.2); (problems on 35-37: 3,4,9,10,24,30,34,40,42,44) Jan 14 (reading = section 2.3); (problems on 44-46: 1,2,3,4,14,16,18) Jan 17 HOLIDAY Jan 19 (reading = section 2.4); (problems on 55-56: 3,4,16,17,21,22,34,35,42,43) Quiz 1 Jan 21 (reading = section 2.5); (problems on 61-62: 1,2,7,8,9) Jan 24 (reading = section 2.6); (problems on 75-76: 3,4,11,12,41,42 ) Jan 26 (reading = section 2.7); (problems on 86-87: 1-6,13,14,18,19,24) Jan 28 (reading = section 2.8); (understand examples 8.1 and 8.6: (parts of them might be on the quiz)) Jan 31 (reading = section 2.9); (problems on 100-102: 7,8,9,10,15,17,19,21,29) Quiz 2 Feb 2 (reading = section 4.1); (problems on 145: 13,15,17,19,21,23,25 ) Feb 4 (reading = section 4.2); (no problems assigned) Feb 7 (reading = section 4.3); (problems on 156: odd problems) Feb 9 (reading = section 4.4); (problems on 163-164: 1,5,7,9,11,12,15,16,20,21) Feb 11 (reading = section 4.5); (problems on 172-173: 3,8,9,11,12,19,20,24,25,31,32,,37,38) Quiz 3 Feb 14 (reading = section 4.6); (problems on 177: all odd problems) Feb 16 (reading = section 4.7); (problems on 185-187: all odd up to problem 21) Feb 18 (reading = reread section 4.7); (problems on pages 185-187: all odd from 23 to 45) Feb 21 HOLIDAY Feb 23 (reading = section 5.1); (prblms on 196-197: odd problems from 1-29, extra credit 30,31,32) Feb 25 (reading = section 5.2); (prblms on 201-202: 3,5 9,11,13,21,25,32,33,35,37,39, extra credit 42,43,44) Quiz 4 Feb 28 (reading = section 5.3); (prblms on 208-209: odd problems 1-17, 19,25,29,33) Mar 2 (reading = section 5.4); (prblms on 214-215: 3,7,9,11,15,17,21,25,27,29,32,35, extra credit 37-41 ) Mar 4 (reading = section 5.5); (prblms on 225-227: 1,3,5,7,9,11,15,17,21,25,26-29, extra credit 33-35) Mar 7 (reading = section 5.6); (all odd prblms on 232-233) Mar 9 (reading = section 5.7); (all odd prblms on 241) Quiz 5 Mar 11 (reading = section 5.8 (review)); (no homework) Mar 14 SPRING BREAK Mar 16 SPRING BREAK Mar 18 SPRING BREAK Mar 21 (Guest Lecturer Rick Cangelosi) (reading = Chapter 7); (homework assigned in class) Mar 23 (Guest Lecturer Rick Cangelosi) (reading = Chapter 7); (homework assigned in class) Mar 25 (Guest Lecturer Rick Cangelosi) (reading = Chapter 7); (homework assigned in class) Mar 28 (reading = 9.1 ); (prblms on 376-378: all problems numbered 1+4n, n = 0,1,2,3, ... 13 ) Quiz 6 Mar 30 (reading = 9.2 ); (prblms on 389-392: all problems numbered 1+4n, n = 0,1,2,3, ... 15 ) Mandatory Quiz !! Apr 1 (reading = 9.3 ); (prblms on 401-402: all odd problems) Apr 4 (reading = 9.4 ); (prblms on 406-407: all odd problems) Apr 6 (reading = 9.5 ); (prblms on 414-416: all problems numbered 1+4n, n = 0,1,2,3, ... 13) Apr 8 (reading = 9.6 ); (prblms on 426-428: all problems numbered 1+4n, n = 0,1,2,3, ... 11) Quiz 7 Apr 11 (reading = 9.6 ); (prblms on 426-428: all problems numbered 1+4n, n = 0,1,2,3, ... 11) Apr 13 (reading = 9.9 ); (prblms on 452-454: all problems numbered 1+4n, n = 0,1,2,3, ... 9) Apr 15 (I will lecture from notes); (prblms assigned in class) Apr 18 (I will lecture from notes); (prblms assigned in class) Apr 20 (I will lecture from notes); (prblms assigned in class) Quiz 8 Apr 22 (I will lecture from notes); (prblms assigned in class) Apr 25 (I will lecture from notes); (prblms assigned in class) Apr 27 (I will lecture from notes); (prblms assigned in class) Apr 29 (I will lecture from notes); (prblms assigned in class)