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Differential Equations and Linear Algebra

The emphasis of this course is on understanding techniques for solving linear systems .
These ideas are introduced through examples.

Text: Edwards and Penney, Differential Equations and Linear Algebra - A Custom Edition
for Northeastern University (with a bundled lab packet)

HOMEWORK AND QUIZZES: Homework will be assigned daily, but will not be
collected. There will be a quiz at the beginning of class each Thursday (except for the
weeks of the hour exams). Each quiz will consist of one or two problems taken verbatim
from the homework assignments and other specific examples worked out in class from
the previous week . Material from the immediately preceding class will not be on each
Thursday's quiz. We will not be able to go over all homework problems in class. If
you have a lot of questions on the homework, it will be essential for you to attend the
recitations, or to come to my office hours, or make special appointments to see me.

ADDITIONAL RESOURCES : In addition to office hours the Mathematics Department
Tutoring Center is in Room 540B, Nightingale Hall. Tutoring should begin there
two weeks after the start of classes. The tentative schedule is 10am-9pm on Mondays,
Tuesdays, and Wednesdays; 10am-6pm on Thursdays; and 10am-1pm on Fridays. This is
walk-in tutoring; no appointment is necessary.

HOUR AND FINAL EXAMS: There will be two hour exams, and a final exam in
this course. The exams are 65-minute in-class exams; they will be on Feb 5, and on March
12. The final exam date is to be determined. Check for exam schedule conflicts
immediately. Late work will not be accepted.

COMPUTER LABS: There will be four required computer labs. Late labs will not
be accepted. The packet of labs should have been bundled with your textbook. It is
expected that students will work on the labs together; however, the write-ups of the labs
MUST be done separately. The Mathematics Dept. Computer Lab is in 553 Lake Hall;
the DIFFS package for MATLAB is on the computers there.

SNOW DAYS: If classes are cancelled due to snow, or for other official reasons, any
scheduled quiz, mid- term exam , or collection of a computer lab assignment will occur on
the next class meeting.

GRADING: The course grade will be determined as fol lows
•Final exam: 40%
•Hour exams: 30% (15% each).
•Computer labs: 4%
•Quizzes: 26%. I will drop your worst two quiz grades.

NOTES: On the hour exams and on the final exam, you may use one 8.5*11 in. sheet
of notes. You may not have a sheet of notes for the quizzes.

ISSUES WITH THE COURSE/INSTRUCTOR: If you have issues with this course
and/or instructor which you are not comfortable discussing with your instructor, you
should contact the Course Coordinator, Prof.

Week 1: Jan. 5-9:
Separable Equations. Section 1.4 (review): #3, 4, 11, 12, 20
Begin Lab 2 Ex 1,2. Turn in on Jan 14
1st Order Linear Equations. Section 1.5: #3, 5, 13, 20, 37

Week 2: Jan. 12-16:
Homogeneous and Bernoulli Equations. Section 1.6: #3, 7, 21, 22
Begin Lab 3 Ex 1,2,3,4 : Hand in Jan 21
Population Models. Section 2.1: #10, 11, 13, 24
Equilibrium Solutions and Stability. Section 2.2: #1, 4, 7, 9 (no explicit solutions)
Velocity-Accele ration Models . Section 2.3: #1-5, 9

Week 3: Jan. 19-23:
Monday, Jan. 19: Martin Luther King Jr. Day - no classes
Tuesday, Jan. 20: Last day to le a final exam conflict form.
•2nd Order Linear Equations. Section 5.1: #1, 9, 11. Section 5.2: discussion. Section
5.3: #1, 3, 5, 7, 21, 23.
Friday, Jan. 23: Last day to drop without a "W".

Week 4: Jan. 26- 30:
•Mechanical Vibrations. Section 5.4: #1, 3, 15, 17, 20
•Non-homogeneous Equations and Undetermined Coefficients . Section 5.5: #1, 2, 3,
9, 13, 31, 32
•Begin Lab 5 Ex 1,2,3: Hand in Feb 12

Week 5: Feb. 2 - 6:
•Forced Oscillations and Resonance. Section 5.6: #2, 8, 19, 23
•hour exam 1: Feb. 5

Week 6: Feb. 9-13:
•Laplace Transforms and Inverse Transforms. Section 10.1: #1, 3, 7, 9, 13, 15, 16
•Transformation of Initial Value Problems. Section 10.2: # 1, 3, 5, 7, 9, 10
•Translation and Partial Fractions . Section 10.3: # 11, 13, 15, 17, 29

Week 7: Feb. 16-20:
Monday, Feb. 16: President's Day - no classes
•Derivatives and Products of Transforms . Section 10.4: # 1, 2, 7, 8, 15, 16, 29 (hard)
•Piecewise Continuous Input Functions. Section 10.5: # 1, 3, 11, 12, 13, 33

Week 8: Feb. 23-27:
•Impulses and Delta Functions. Section 10.6: # 1, 2, 4, 5
•Introduction to Linear Systems. Section 3.1: discussion
•Matrices and Gaussian Elimination . Section 3.2: # 1, 11, 15, 20
Feb. 28 - March 8: Spring Break

Week 9: March 9-13:
•Reduced Row-Echelon Matrices. Section 3.3: # 5-8
Matrix Operations . Section 3.4: 1, 9, 10, 19
•Begin Lab 4 Ex 1,2,3 : Hand in March 18
•Hour exam 2: March 12

Week 10: March 16-20:
•Inverses of Matrices. Section 3.5: # 1, 7, 9, 19, 23
•Determinants. Section 3.6: # 1, 3, 5, 33
•The Vector Space R3. Section 4.1: # 1, 5, 11, 17

Week 11: March 23-27:
•The Vector Space Rn and Subspaces. Section 4.2: #1, 4, 5, 7, 12
•Linear Combinations and Independence of Vectors. Section 4.3: # 11, 13, 15
Friday, March 27: Last day to drop a class with a \W" grade

Week 12: March 30-April 3:
•Bases and Dimension for Vector Spaces. Section 4.4: # 1, 4, 7, 15, 19
•Introduction to Eigenvalues. Section 6.1: # 1, 3, 9, 13, 17

Week 13: April 6-10:
•1st Order Systems. Section 7.1: # 1, 3
•Matrices and Linear Systems. Section 7.2: # 3-5
•The Eigenvalue Method for Linear Systems. Section 7.3: # 1, 5, 11, 17

Week 14: April 13-14:
•Review
Wednesday, April 15: Reading Day
Final Exams: April 16-17
Monday, April 20: Patriot's Day - no exams
Final Exams: April 21-24

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