Math 321: Differential Equations
Fall 2005, 3 Credits, MWF 1:10 pm, MRC 419
Instructor: Dr Michael Wodzak, Associate Professor of Mathematics
Office: MC 530, 796-3659;
Hours: MWF 10--11, R 9—11 and by appointment
Final Exam: THURSDAY DEC 15th 12:50—2:50
Ordinary differential equations; series solutions for linear differential equations; linear operators. Prerequisite: grade of C or higher in 221.
Text: Elementary Differential Equations (8th Edition), Boyce and DiPrima. (Wiley, 2005)
1. Thinking: Students engage in the process of inquiry and problem solving that involves both critical and creative thinking.
- Students will be exposed to the logic of mathematical proof
- Students will develop their problem-solving skills
- Students will use reasoned standards in solving problems and presenting arguments
2. Communication: Students communicate orally and in writing in an appropriate manner both personally and professionally.
- Students will develop their skills of written mathematical communication, specifically learning to properly use the language and notation of the Calculus
- Students will develop their verbal mathematical communication skills, both in small groups and in class discussions
- Students will read with comprehension and the ability to analyse and evaluate.
- Listen with an open mind and respond with respect
- Access information and communicate using current technology
- Students will justify their reasoning and provide precise, rigourous explanations for their work
- Students will model real life problems using differential equations and interpret the solutions of those equations in the appropriate real life setting
- Learn how to solve some theorems
3. Life Values: Students analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems.
- Students will see the importance of integrity regarding their own scholarship
- Listen with an open mind and respond with respect
- Understand the need to do one’s own work, to honestly challenge oneself to master the material
4. Cultural Skills: Students will explore the importance of differential equations in sciences and various applications as well as become familiar with some elements of the historical development of the field
5. Aesthetic Skills: Students will
Develop an appreciation for the austere intellectual beauty of deductive reasoning
Develop an appreciation for mathematical elegance
6. Community Involvement: Students demonstrate skills of interdependent group participation and decision-making.
- Students will work in groups, learning to share their ideas and skills, and respecting the ideas and skills of others
Specific Course Goals:
- Students will explore the problems that lead to differential equations
- Students will learn to solve basic types of first order differential equations that can be done in closed form.
- Students will learn to solve linear differential equations with constant coefficients
- Students will learn to construct and interpret geometrical interpretations of differential equations.
- Become familiar with basic existence and uniqueness theorems
- explore more advanced techniques of solving differential equations
- Investigate systems of differential equations
Semester grades in this course will be awarded according to a standard scale:
675—750pts (90% and above) = A
600—674pts (80%--89%) = B
525—599pts (70%--79%) = C
450—524pts (60%--69%) = D
Less than 450pts (Below 60%) = F
Semester grades are calculated purely on a points basis, that is, the letter grades you earn on individual exams are purely guidelines for you to gauge your progress. For example, if you miss a particular grade on an exam by a certain number of points, it is still possible to make up those points (and get into that grade bracket) in other parts of the course, perhaps on the next exam. On the other hand, just because you got a good grade on one test, you should realize that you can lose enough points to get into a lower grade bracket by doing poorly in another area of the course. Once again: it is points that count.
Homework questions 100 pts.
(Full credit is given for each completed assignment)
Homework will be due one class week after it has been assigned. Any questions regarding how to do particular homework problems will be welcomed in the intervening class meetings or in my office but not in class on the day that the homework is due. Late homework will be penalized by a deduction of 20% of the assigned grade for each schoolday -- including schooldays on which class does not meet – that the work is late, so that, if the work is one week late, it will not receive any points. You may, however, still hand the work in so that you can benefit from corrections and be certain you know how to do a question that could well appear on an exam
Practice Exams 100 pts
There will be four group practice exams worth 25 pts apiece before each in class midterm and before the final exam
Examinations 300 pts
There will be three in class exams worth 100 pts apiece, and lasting 50 minutes each.
Participation 50 pts
Participation points are easy to acquire and you probably already know how to get them; don’t chat to your neighbors when I’m lecturing (asking a neighbor to help if you didn’t understand what I said is, however, always acceptable). General politeness counts. Cheerfulness, engagement, willingness to push buttons on your calculator, asking me to clarify if you are stuck, taking advantage of my office hours, these are all, to quote the Sound of Music, a few of my favorite things.
Cumulative Final Examination 200 pts
Total 750 pts
You can afford to miss no more than the equivalent of one week of class. Any more absences are a dangerous loss of classtime percentage. Once you have had 3 unexcused absences, every unexcused absence from that point onward will incur a penalty of 10 pts from your participation and attendance score.
Make up exams situations will be considered on a case-by-case basis, but invariably they require as much forewarning as possible -- and documentation. You know when the exams are; please do not book flights home, or your wedding, etc, etc on those dates. If your, or your best friend's, or your uncle's hairdresser's poodle's (if you're from the Coast) wedding is already booked for any of those dates, please let me know ASAP. I will not give make up tests without good reason, and if you should miss a test that is not made up, your score for that test will be zero.
The sad fact is that it is a rare semester when some student doesn't have to rush home to tend a family crisis, or bury a loved one. Often this interferes with exams. Should such sadness happen to you, I will need to ask you for some sort of verification (obituary, hospital record, etc) and then we will try to get your semester moving again.
Homework: Let me urge you to make it a regular part of your day to try working the homework problems. There will never be enough time for us to go through every listed problem in class, and it is probably unrealistic to think that you will be able to find the time to work through every listed problem, but you should at least spend some time thinking about virtually every problem, and working the more interesting or challenging to completion. The daily homework assignments will not generally be collected or graded. They are intended to structure your learning so that you regularly challenge yourself to see that you understand the material we are looking at. The important thing is that you at least look at all the assigned problems. You should also feel free to work other problems if you deem it necessary for your comprehension of the content.
You should view homework assignments as a test to see how well you understand the material and you should bring to the next class any questions you might have.
However, from time to time, certain homework problems will be assigned and collected as mentioned above. I will award semester points for homework by calculating the percentage you got on all assigned homework and awarding this as a score out of 100pts
Americans with Disability Act:
If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me or Wayne Wojciechowski in MC 320 (796-3085) within 10 days to discuss your accommodation needs.
Schedule, Fall Semester 2005
29 Aug [1.1],[1.2] Introduction p7 #1-25 odd
31 Aug [1.3],[2.1] Classification and Integrating Factors p39 #1-19 odd
2 Sep [2.1] Continued
(n.b. This is the last day to add or change sections of a class)
5 Sep Labor Day Break ;-)
7 Sep [2.2] Separable Equations p 47 #1-27 odd
9 Sep [2.3] Modeling p 59 #1,7,12,1314,17,20,23
12 Sep [2.5] Autonomous Equations p88 #1-5 odd, 9-11 odd, 23
(13 Sep: Last day to take a course Credit/No Credit)
14 Sep [2.6] Exact Equations p99 # 2-31 odd
16 Sep [3.1] Homogeneous Equations p142 #1-27 odd
19 Sep [3.2] Linear Homogeneous Equations p 152#1-27odd
21 Sep [3.3] Linear Independence p 158 #1-23 odd
23 Sep Review
26 Sep EXAM #1 (100 Points)
28 Sep [3.4] Complex Roots p 164 #1-29 odd
30 Sep [3.5] Repeated Roots p 172 #1-29 odd, 38, 39
3 Oct [3.6] Nonhomogeneous Equations p 184 #1-25 odd 31,32
5 Oct [3.7] Variation of Parameters p 190 #1-19 odd, 21-27 all
7 Oct [4.1],[4.2] nth order Homogeneous Equations p222 #1-17 every other odd,
p230 #1-33 every other odd.
10 Oct [4.3] [4.4] Higher Order Analogues of 2nd Order Methods p235 #1-17 every other odd
P240 #1-17 every other odd
12 Oct Review
14 Oct EXAM #2 (100 points)
17 Oct [5.1] Power Series p 249 #1-27 odd
(n.b.This is the last day for submitting D/F slips)
19 Oct [5.2] Series Solutions Near Ordinary Points I p 259 #1-27 odd
(20 Oct:The last day to drop a full semester course and have it removed from the record)
21 Oct Mid-Semester Break ;-)
24 Oct [5.3] Series Solutions Near Ordinary Pts II p 265 #1-21 odd
26 Oct [5.4] Regular Singular Points p 271 # 1-27 odd
28 Oct [5.5] Euler Equations p 278 # 1-31 odd
31 Oct [5.6] Series Solutions Near RSPts I p 284 # 1-15 odd
2 Nov [5.7] Series Solutions Near RSPts II p 292 #1-21 odd
4 Nov Catch Up
7 Nov Review
(n.b.This is the last day to drop a full semester course with a grade of “W”)
9 Nov EXAM #3 (100 points)
11 Nov [7.1] Systems of First Order ODEs p 360 # 1-23 odd
14 Nov [7.2] Matrices p 372 # 1-25 odd
16 Nov [7.3] Linear Algebra p 383 # 1-23 odd
18 Nov [7.4] Basic Theory p 389 # 1-9 all
21 Nov [7.5] Homogeneous Systems p 398 # 1-27 odd
23 Nov Thanksgiving Break ;-)
24 Nov Thanksgiving Day ;0)
25 Nov Thanksgiving Break ;-)
28 Nov [7.6] Complex Eigenvalues p 410 # 1-23 odd
30 Nov [7.7] Fundamental Matrices p 420 # 1-17 odd
2 Dec [7.8] Repeated Eigenvalues p 426 # 1-21 odd
5 Dec [7.9] Nonhomogeneous Systems p 439 # 1-17 odd
7 Dec Catch Up
(8 Dec: The last day to request a grade of Incomplete)
9 Dec Review
Final Exam (200 Pts): THURSDAY DEC 15th 12:50—2:50