May 25th
May 25th
Differential Equations and Linear Algebra for Engineering
Supplementary instruction.
Free tutoring is available at the Math /Writing Center, 540B Nightingale, phone:
617-373-2438, at the following
times: Mon–Wed 12-8PM and Thurs 12-3PM.
Homework.
Exercises will be assigned at the end of every class and will be collected
weekly. I will go over the solution
of some, but not all of these at the beginning of the next class. If you have a
lot of of questions on the
homework, it is therefore essential that you go to tutoring or come to my office
hours.
Exercises assigned on Monday and Tuesday of any given week, and Wednesday and
Thursday of the previous
week, will be collected on Thursday of the given week. Late homework will not be
accepted. I will grade
3 exercises and give each a grade from 0 to 2.5. 2.5 extra points will be given
for completeness.
Students may work jointly on the homework but the write-ups of these must be
done separately.
Computer labs.
There will be four required computer labs. These are an essential component of
the course: some important
concepts will be introduced and explored, both visually and numerically. Late
labs will not be accepted.
The packet of labs is bundled with your textbook, and is also available on the
Web. It is expected that students
will work on the labs together; however, the write-ups of the labs be done
separately. The Mathematics
Dept. Computer Lab is in 553 Lake Hall; the DIFFS package for MATLAB is on the
computers there.
Grading.
There will be no curving of grades .
Homework. The homework make up 30% of the course grade. The lowest homework
score will be dropped.
This policy applies even if a student has a perfectly justifiable excuse not to
hand in a homework. Should that
be the case, that homework will be one to be dropped.
Computer labs. The computer labs make up 10 % of the course grade.
1 hour exams. There will be two one–hour exams on Thursday, May 22 and Thursday,
June 12. Each will
count as 15 % of the course grade.
Final exam. The two hour, common final exam will take place on Monday, June 23.
This exam will count
as 30% of the course grade. Please refer to for the room and building in
which the exam will be held. All students without legitimate conflicts (approved
by the instructor) must take
the exam at the scheduled time. Do not make travel plans that conflict with it.
Material allowed during exams. No course material, notes or summary cards will
be allowed during the
hour long and final exams. The use of a calculator will not be allowed during
the hour–long and final exam.
Course grades.
The course letter grades will be obtained from the numerical grades as follows:
0.5 and more will be rounded up to 1, 0 to 0.49 to 0.
Concerns and Conflicts.
In case of concerns about the course, or the instructor that cannot be re solved
by speaking with the instructor,
contact the Undergraduate Director:
Professor A. Martsinkovsky
471 Lake Hall (LA)
phone: (617) 373 55 10
It is the University policy that no grade, including an incomplete, can be
changed after one year . Exceptions
may be authorised by the Academic Standing Committee.
Course schedule
| Week |
Dates |
Topic |
Section |
Assignment |
| 1. |
May 6 |
Begin computer lab 2 (Euler’s Numerical Method) |
|
1,2,3,4 |
| May 5–11 |
|
Separable equations and applications
Linear First – Order Equations |
1.4
1.5 |
3-6,8-11,19-22,40-42
3,5,13,20,37 |
| 2. |
May 13 |
Computer lab 2 due |
|
1,2,3,4 |
| |
|
Substitution Methods and Exact Equations
Population models
Equilibrium Solutions and Stability
Accele ration -Velocity Models
Second-Order Linear Equations
General solutions of Linear Equation |
1.6
2.1
2.2
2.3
5.1
5.2 |
3,7,21,22
10,11,13,24
1,4,7,9 (no explicit soln.)
1-5
1,9,11
discussion only |
| |
May 14 |
Begin computer lab 3 (The Runge–Kutta Method) |
|
1,2,3,4 |
| May 12–18 |
|
May 16: last day to drop a Summer 1 class without
a W grade |
|
|
| 3. |
|
May 20: last day to file a Final Exam Conflict
Form |
|
|
| |
May 21 |
Computer lab 3 due |
|
1,2,3,4 |
| |
|
Homogeneous Equations with Constant
Coefficients
Mechanical Vibrations
Nonhomogeneous Equations and Unde termined Coefficients
Forced oscillations and resonance |
5.3
5.4
5.5
5.6 |
1,3,5,7,19,21,23,25,27
1,3,15,17,20
1,2,3,9,12,13,31,32
2,8,23 |
| |
|
May 22: 1 hour exam |
|
|
| May 19–25 |
May 22 |
Begin computer lab 5 (MATLAB for Differential
Equations ) |
|
1,2,3,4 |
| 4. |
|
May 26: Memorial day, no classes |
|
|
| |
|
Laplace Transform
Transformation of Initial Value Problems
Translation and Partial Fractions
Derivatives, Integrals and Products of Transforms |
10.1
10.2
10.3
10.4 |
1,3,5,7,9,13,15,16
1,3,5,7,9,10
11,13,15,17,29
1,2,7,8,15,16,29 |
| |
May 28 |
Computer lab 5 due |
|
1,2,3,4 |
| May 26–Jun. 1 |
May 29 |
Begin computer lab 4 (MATLAB for Linear Algebraic
Systems) |
|
1,2,3 |
| 5. |
|
Periodic Input Functions
Impulses and Delta Functions
Matrices and Gaussian Elimination
Reduced Row -Echelon Matrices
Matrix Operations |
10.5
10.6
3.2
3.3
3.4 |
1,3,11,12,13,33
1,2,4,5
1,11,15,20
5-8
1,9,10,19 |
| Jun. 2–8 |
|
June 6: last day to drop a Summer 1 class with a
W grade |
|
|
| 6. |
Jun. 9 |
Computer lab 4 due |
|
1,2,3 |
| |
|
Inverses of Matrices
Determinants
The Vector Space R3
The Vector Space Rn and Subspaces
Linear Combinations and Independence
Bases and Dimension for Vector Spaces |
3.5
3.6
4.1
4.2
4.3
4.4 |
1,7,9,19,23
1,3,5,33
1,5,11,17
1,4,5,7,12
11,13,15
1,4,7,15,19 |
| Jun. 9–15 |
|
Jun. 12: 1 hour exam |
|
|
| 7. Jun. 16–22 |
|
Eigenvalues and Eigenvectors
First-Order Systems
Matrices and Linear Systems
Eigenvalue Method for Linear Systems |
6.1
7.1
7.2
7.3 |
1,3,9,13,17
1,3
3-5
1,5,11,17 |
| |
|
Summer I classes end |
|
|
8.
Jun. 23–29 |
|
Monday, Jun. 23, 1–3 PM: Final exam |
|
|
This syllabus.
The instructor reserves the right to alter this syllabus according to the needs
which may arise during the
semester. It is each student’s responsability to be aware of any such changes
which are announced in class,
whether or not that student is present at the time of the announcement.
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