Mathematics 267: Elementary Differential Equations with Laplace Transforms. Section D
Fall 2012, 4 credits
Professor Stephen J. Willson
office: Carver 411
Professor Andy Ylvisaker
office: Carver 456.
Professor Willson's office hours:
MTWThF 1:10 - 2:00 in Carver 411.
Please also feel free to make an appointment if the office hours are inconvenient for you.
Professor Ylvisaker's office hours:
MF 2:10 - 3:00, TTh 12:10-1:00, W 1:10 - 2:00 in Carver 456.
Class meetings: MTThF 11:00-11:50 am in Pearson 1115.
The first class is Monday, August 20, and the last class is Friday, December 7. The final exam will be sometime during the week of December 10-14. There are no classes on Labor Day (September 3) and Thanksgiving Break (the week of November 19 - 23). The last day to drop the course is Friday, October 26.
The final exam will take place Wednesday, December 12, 4:30-6:30 pm in Coover 2245.
Current course grades
Current course grades and all recorded scores are available on Blackboard by clicking
If a score has been
incorrectly recorded, you should contact the instructor.
Most homework assigned will be ungraded. Ungraded problems on the homework will usually be the basis for the beginning of the next class period. These assignments may also be found by clicking
Prerequisites: Grade C- or better in Math 166 (Calculus II).
Catalog description: Solution methods for ordinary differential equations. First order equations, linear equations, constant coefficient equations. Laplace transforms and series solutions to ordinary differential equations. Eigenvalue methods for systems of first order linear equations. Introduction to stability and phase plane analysis.
Fundamentals of Differential Equations with Boundary Value Problems, sixth edition, by R. Kent Nagle, Edward Saff, and Arthur Snider.
Likely order of topics:
Not all sections in the chapters will be covered.
- Chapter 1. (Introduction) (1.1-1.4)
- Chapter 2. (First-Order Differential Equations) (2.2-2.4, 2.6)
- Chapter 3. (Mathematical Models) (3.2-3.3)
- Chapter 4. (Linear Second-Order Equations) (4.2-4.6, 4.9)
- Chapter 7. (Laplace Transforms) (7.1-7.8)
- Chapter 8. (Series Solutions) (8.1-8.3)
- Chapter 5. (Introduction to Systems) (5.1, 5.4)
- Chapter 9. (Matrix Methods for Linear Systems) (9.1-9.8)
Comparison with Math 266.
Mathematics 267 (4 credits) includes all
the material from Math 266 and in addition includes the topics of Laplace transforms (chapter 7) and an introduction to
series solutions (chapter 8), of special interest to electrical engineers. If you take Math 266 (3 credits)
and then need Math 267, you may instead take Math 268 (1 credit) to get only the extra
material in Math 267 but not in Math 266.
Grading: Grades will be based on points accumulated. All graded work will be announced ahead of time. Points will be awarded for four hour exams, four in-class quizzes, and a final exam. Possibly there will be some graded homework in addition. Each quiz counts 25 points and takes approximately half a period; each hour exam counts 50 points and takes an entire period. The final exam is based on all material in the course and counts 100 points. Thus there will be a total of about 400 points possible in the course. All exams and quizzes are written by the instructor; there are no uniform exams. While calculators may be useful, one must show all work on quizzes and exams in order to receive credit. There is no extra credit. Grades may include a plus or a minus. Grade cutoffs will be announced for each exam and quiz. The cutoff for a given level (for example A-) in the course will be the sum of the cutoffs for that level for each exam or quiz.
Tentative quiz and exam schedule
- Quiz, Friday, August 31
- Hour exam, Tuesday, September 11
- Quiz, Friday, September 21
- Hour exam, Tuesday, October 2
- Quiz, Tuesday, October 16
- Hour exam, Friday, October 26
- Quiz, Tuesday, November 13
- Hour exam, Friday, November 30
- Cumulative final exam, the week of December 10 - 14
Sickness policy: If you are sick the day of an exam, you should contact
the instructor by phone on the day of the exam to arrange a timely make-up.
Students will find it useful to have a calculator for this class. I strongly urge students to use the TI-89 Titanium. This calculator has special features for differential equations, and examples in class will use this calculator. It is able to work algebraically many problems in the textbook. If you use this calculator you will be able to check your answers to many problems on tests. (Work must be shown, however, and credit for answer alone will not be given on tests.)
At a minimum, calculators should be capable of graphing functions and zooming in on the graphs. By far the best calculator for this course is the TI-89 Titanium. The TI-83 Plus, TI-84 Plus, TI-85, and TI-86 are also acceptable but lack features which are sometimes useful for this course.
You may bring your calculator to class and to quizzes and exams.
For help in using your calculator, see your manual or else use
web calculator help.
Khan Academy Differential Equations:
The Khan Academy includes a large number of short YouTube videos on many mathematical topics, from basic algebra through calculus and differential equations. All are free, and they take from 5 to 12 minutes each. A typical video works through one or two examples. In particular, there are lots of videos on Differential Equations. Often the order of topics differs from the order in Math 267.
For a full list of Khan Academy videos on differential equations, see
Khan Academy Differential Equations.
For a list of Khan Academy videos to review topics in calculus, see
Khan Academy Calculus.
Supplemental instruction (SI) is a free service run by the Academic Success Center in which a student who recently did very well in a course leads regularly scheduled review and help sessions in that course for other students currently taking that course. You can visit the SI session every time, or only occasionally. See Supplemental Instruction for detailed information about the program.
There is no supplemental instruction specifically geared to this particular section of Math 267. Nevertheless, students are welcome to attend supplemental instruction for other sections of Math 267. The subjects being stressed may be slightly non-synchronized with our section. Moreover, some sections will study chapters 5 and 9 before chapters 7 and 8, while this section will study chapters 7 and 8 before chapters 5 and 9.
There are three meetings of SI for Math 266/267 for Fall 2012. These are:
- Sunday, 7:10 pm in Pearson 2137
- Monday, 5:10 pm in Pearson 2137
- Thursday, 7:10 pm in Pearson 2137
The Mathematics Department runs a Help Room that is free to all students. The Help Room
is in 385 Carver. Its hours are
MTWRF 9:00 a.m. - 4:00 p.m.,
The Help Room begins Monday, August 27.
The following schedule marks by x each hour where a TA is present who feels particularly proficient in answering questions from students in Math 267.
Please address any special needs or special accommodations with me at the beginning of the semester or as soon as you become aware of your needs. Those seeking accommodations based on disabilities should obtain a Student Academic Accommodation Request (SAAR) form from the Disability Resources (DR) office (515-294-6624). DR is located on the main floor of the Student Services Building, Room 1076.
Information about the instructor: For more information about the
Last updated September 6, 2012.