# Differential Equations with Line

# Differential Equations with Linear Algebra for Engineering

**OFFICE HOURS:**

Tuesdays and Wednesdays: 1:35-4:25pm

Other times : Drop in or by appointment

**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. To make sure that

students are keeping up with the homework, there will be a quiz at the beginning
of class each Thursday (except

for the weeks of the midst-term exams). Each quiz will consist of 1-3 problems
taken verbatim from the homework

assignments from the previous week . Homework questions from the immediately
preceding class will not be on each

Thursday's quiz.

The problems in this course tend to be long and involved, although not usually
outrageously difficult. We will

not be able to go over all homework problems in class, and even those that we do
go over may not get worked out

to the bitter end. Therefore, if you have a lot of questions on the homework, it
will be essential for you to come to

my office hours or make special appointments to see me.

**
MIDST-TERMS AND FINAL EXAMS:** There will be two midst-term exams, and a final
exam in this course.

The midst-term exams are 65-minute in-class exams; they will be on Thursday, Feb. 5 and Thursday, March 12. The

final exam is date is to be determined.

**Check for exam schedule conflicts as soon as possible.**

**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 should have been bundled with your textbook, and is also available on the Web. It is

accepted.

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, midst-term

exam, or collection of a computer lab assignment will occur on the next class meeting.

**GRADING**: The course grade will be determined as follows

•Final exam: 40%

•Midst-term exams: 30% (15% each).

•Computer labs: 4% (1% each).

•Quizzes: 26%. I will drop your worst two quiz grades.

**NOTES:**On the midst-term 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.

**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.

**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 Chair of the Mathematics Depart-

ment, Prof. McOwen: 505 Lake Hall, 617-373-5635

## Homework for MTH U343:

Spring 2009

**Week 1: Jan. 5-9:**

•Separable Equations. Section 1.4 (review): #3, 4, 11, 12, 20

•**Begin Lab 2, exercises 1 and 2.**

•1st Order Linear Equations. Section 1.5: #3, 5, 13, 20, 37

•Homogeneous and Bernoulli Equations. Section 1.6: #3, 7, 21, 22

Week 2: Jan. 12-16:

•**Turn in Lab 2, exercises 1 and 2, on Wednesday, Jan. 14.
**•

**Begin Lab 3, exercises 1, 2, 3, and 4.**

•Population Models. Section 2.1: #10, 11, 13, 24

•Equilibrium Solutions and Stability . Section 2.2: #1, 4, 7, 9 (no explicit solutions)

•Velocity-Acceleration 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**.

**•Turn in Lab 3, exercises 1, 2, 3, and 4, on Wednesday, Jan. 21.**

•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-Jan. 30:**

•Mechanical Vibrations. Section 5.4: #1, 3, 15, 17, 20

**•Begin Lab 5, exercises 1, 2, and 3.**

•Non-homogeneous Equations and Undetermined Coefficients . Section 5.5: #1, 2, 3, 9, 13, 31, 32

**Week 5: Feb. 2-6:**

•Forced Oscillations and Resonance. Section 5.6: #2, 8, 19, 23

**•Midst-term exam 1: Thursday, 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

**•Turn in Lab 5, exercises 1, 2, and 3, on Thursday, Feb. 12.**

**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, exercises 1, 2, and 3.
•Midst-term exam 2: Thursday, 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

**•Turn in Lab 4, exercises 1, 2, and 3, on Wednesday, March 18.**

•The Vector Space R

^{3}. Section 4.1: # 1, 5, 11, 17

**Week 11: March 23-27:**

•The Vector Space R

^{n}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

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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