|
|
|
B+ |
3.3-3.6 |
C+ |
2.3-2.6 |
D+ |
1.3-1.6 |
||
|
A |
3.8-4.0 |
B |
3.0-3.2 |
C |
2.0-2.2 |
D |
1.0-1.2 |
|
A- |
3.4-3.7 |
B- |
2.7-2.9 |
C- |
1.7-1.9 |
F |
0.0-0.9 |
A bonus topic worth 0.1 grade points will be included in each case study to allow students to make up for past or future point deductions.
Minimum examination grades
The midterm and final examinations serve as final verifications of the student's mastery of basic concepts and procedures. Subject matter from the midterm shall not be repeated in the final. A student must obtain at least 0.3 grade points in each examination. Each examination shall contain 8 questions from which the student may select 6 to answer. Of those selected, 50% must be answered correctly in order to pass. For students who do not obtain the minimum grade points in the midterm, 2 supplementary questions shall be available in the final to enable attainment of the minimum grade points. No additional time shall be allocated for the makeup questions during the final. There is no possibility for makeup of grade points from the final. Both examinations are structured so that 50% of the questions shall represent basic concepts while the balance shall treat more advanced techniques. A benefit of the case study bonus points is to makeup for any point deductions on the advanced techniques part of the examinations.
Course Texts
The following texts will be used during the course:
Partial Differential Equations for Scientists and Engineers (Dover Books on Advanced Mathematics) by Stanley J. Farlow, Dover Pubns; ISBN: 048667620X
Complex Analysis With Applications, by Richard Silverman, Dover Pubns; ISBN: 0486647625
The texts serve as convenient repositories of background material and basic techniques. Exercises from the texts shall be assigned on a regular basis as part of each case study.
Case studies
Motivation and framework
An important part of a student's training is the ability to apply theoretical knowledge to practical problems. The case study approach adopted in this course seeks to foster this aptitude. Each case study provides a framework for seeing how the mathematical developments presented in the course are relevant for real-world problems. There is a basic framework involved:
-
a problem is set forth
- mathematical theory is presented in class
- exercises from the texts are assigned to gain
familiarity with the mathematical techniques
- the techniques are applied to the more interesting
problems arising in the case study
- conclusions are drawn
Case study exercises
Each case study shall contain exercises from the course texts that should be solved. Students are expected to conscientiously solve these exercises since they are preparatory material for the case study computations, but solutions are not to be included in the case study report.
Case study reports
The case study reports are intended to document a student's progress and attainment of mathematical skills. They are also intended to instill habits of good note-keeping, report preparation and a critical view of the suitability of the techniques and approximations used. The reports are presented to the instructor in two stages. A first draft is presented at the end of the case study period allotted. Comments shall be made on each report and a preliminary grade is assigned. Final versions of reports 1-4 are due on March 4, before the mid-term examination.
The case study reports should be drafted with care, preferably on a computer, contain concise presentations of all relevant computations and results, and include analysis and comments. Complete and cogent sentences are expected. The reports should not be overly long. Quality is much more important than quantity. A page limit of 4 computer printed pages or 6 handwritten pages plus a maximum of 4 pages for graphical elements shall be imposed.
Case study grading
Grade points are assigned as follows:
0.05 - Statement of objectives, techniques used, and motivation.
0.05 - Correct transposition of the case study objectives into a mathematical problem
0.05 - Use of all applicable mathematical techniques presented in the course
0.05 - Correct computations
0.05 - Graphs of data and results. Graphs must be relevant, carefully drafted and properly labeled.
0.10 - Analysis and comments. Results must be analyzed:
-
are they what the student expected?
-
what errors might affect the results?
-
are the techniques used suitable descriptions?
-
do different techniques give similar results?
-
what practical implications for the problem studied arise from the obtained results?
0.05 - Overall quality: care in presentation, clear and concise language.
0.10 - Bonus topic. The bonus topic shall invite the student to consider the deeper issues inherent in the case study.
Case study course material
Especially for the first 2 case studies, but in some measure for all, it is not possible to cover during the lectures given in the case study cycle all the techniques that are applicable. Nonetheless, students will be expected to make use of all available mathematical techniques from the course in each case study. The two-tier verification of case study work is intended to allow this. When the first draft is presented students will apply techniques covered in class up to that date. As the class progresses, additional techniques may be applicable and should be tried out and included in the final report. Good notekeeping is essential in order for students to successfully complete the case studies. It is recommended that each student keep notebooks with some 40-50 pages allocated to each case study for exercises, applications of new mathematical techniques as they arise during the course, annotations of results, thoughts that come along the way, and from which the case study reports may be conveniently prepared.
Case study schedule
|
Case no. |
Dates |
Topic |
Title |
Text |
|
1 |
1/7-1/16 |
Diffusion equation |
Of ice storms and warm places |
|
|
2 |
1/21-1/30 |
Linear wave equation |
The science of music |
|
|
3 |
2/4-2/13 |
Non-linear wave equation |
For no traffic jams, go the extra mile |
|
|
4 |
2/18-2/27 |
Reaction-diffusion |
How the leopard got its spots |
Case study honor code
Each case study report should represent independent work. Students are encouraged to discuss applicable techniques, work together on assigned exercises or computer programs. However, the case study reports are to be written independently. The variety of mathematical techniques that may be applied will lead to different transpositions of the case study objectives into mathematical problems, different computations and different conclusions. Any evident plagiarism will be referred to the Honor Court. All signed final case study reports are assumed to provide a pledge by the student that the work did not include unauthorized aid.
Homework
During the second part of course homework replaces the case study approach used in the first part. Each
|
Week |
Due |
Assignment |
|
3/18-3/25 |
3/25 |
Farlow, L33:2-5, L34: 1 (0.25 grade points) |
|
3/25-4/1 |
4/1 |
Farlow, L35 1-5 (0.25 grade points) |
|
4/1-4/8 |
4/8 |
Farlow L44, 1-4, L 45, 5 (0.25 grade points) |
|
4/8-4/15 |
4/15 |
Silverman, C2, p. 22: 20,21; C3, p. 32: 7, C4, p.43: 5,7,10 (0.30 grade points) |
|
4/15-4/22 |
4/22 |
Silverman, C4, p.44, 11,12,14,15,18 (0.25 grade points) |
Computer work
The case studies will involve symbolic and numeric computations. Students are expected to write their own programs. "Starter" programs that students can further develop to the requirements of the case study will be posted here, typically on the second Tuesday of each case study cycle.
The class will meet in the computer lab in Phillips 324 on the following dates:
1/14, 1/28, 2/11, 2/25, 3/25, 4/8, 4/22
|
Case no. |
Date |
Title |
Lab starter program |
|
1 |
1/14 |
Of ice storms and warm places |
|
|
2 |
1/28 |
The science of music |
|
|
3 |
2/11 |
For no traffic jams, go the extra mile |
|
|
4 |
2/25 |
How the leopard got its spots |
|
|
5 |
3/25 |
Life on the range |
|
|
6 |
4/8 |
How do I interact with thee? |
|
|
7 |
4/23 |
Tunneling through |
Mid-term examination
Mid-term examination is on Thursday, March 6, 12:30 PM, Phillips 224. The class on March 4 will be a review session in preparation for the mid-term examination. Reminder: a student must answer 50% of the questions correctly to pass the course. Makeup questions will be available during the final. Typical questions, representative of what students should expect in the midterm shall be posted here on February 27. The examination is "closed-book", no notes, books or aids are permitted. Any course material that may be needed to solve an examination question and can reasonably considered to mostly involve rote memorization will be included in the examination itself.
Mid-term solutions. (problems 1-8, the bonus question 9 can be submitted in the first week after Spring Break)
Final examination
Final examination is on Thursday, May 8, 2:00 PM, Phillips 224. The class on April 24 will be a review session in preparation for the final examination. Reminder: a student must answer 50% of the questions correctly to pass the course. Typical questions, representative of what students should expect in the final shall be posted here on April 22. The examination is "closed-book", no notes, books or aids are permitted. Any course material that may be needed to solve an examination question and can reasonably considered to mostly involve rote memorization will be included in the examination itself.