# Differential Equations with Linear Algebra for Engineering

# Differential Equations with Linear Algebra for Engineering

**TEXT: **Edwards and Penney, Differential Equations
and Linear Algebra - A Custom Edition for Northeastern

University (with a bundled lab packet)

**COURSE ORGANIZATION: **The summer semesters are very
intense; to make it easier for you, the class will

be divided into two halves . In the first 50 minutes we will do differential
equations, in the second half linear algebra.

Doing it this way will make it seem like you are taking two regular math courses
instead of one intense course, so

you will have more time to digest the important topics in the course. As the
course goes along, you will see the

many interesting connections between linear differential equations and linear
algebra , which is why we do both topics

together.

**HOMEWORK AND QUIZZES:** Homework will be assigned
daily, will be collected the next class. To make sure

that students are keeping up with the course, there will be a short quiz at the
beginning of class each Thursday.

Each quiz will consist of 1-3 problems.

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.

The problems will test your knowledge of differential and
integral calculus. If you’re shaky with the techniques

from these areas, then review or tutorial support is recommended.

**TUTORS: **The Math Dept. provides tutors to help you
with this course. You can find a tutor in 540B Nightingale,

starting Wednesday May 6. This is walk-in tutoring; no appointment is necessary.

**HOUR EXAMS AND FINAL EXAMS:** There will be three
hour exams, and a final exam in this course. The

hour exams will be on be on Mondays–May 18, June 1, June 15. The final exam is
on June 23 at 8AM Check for

exam schedule conflicts as soon as possible.

**COMPUTER LABS: **There will be five 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 at the

course BlackBoard site. 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.

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

• Final exam: 40%

• Hour exams: 30%

• Computer labs: 5% (1% each).

• Quizzes: 15%.

• Homework 10%

**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 Department,

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

**Homework for MTH 2341:
Summer I 2009**

**Week 1: May 5-7:**

Strand 1: ODEs

• Separable Equations. Section 1.4 (review): #3, 4, 11, 12, 20, 33, 37, 45, 47

• Begin Lab 2, exercises 1 and 2.

• 1st Order Linear Equations. Section 1.5: #3, 5, 13, 20, 33, 37

• Homogeneous and Bernoulli Equations. Section 1.6: #3, 7, 21, 22, 69

Strand 2: Linear algebra

• Introduction to Linear Systems . Section 3.1: discussion # 1, 3, 6, 23, 25, 31

• Matrices and Gaussian Elimination . Section 3.2: # 1, 11, 15, 20, 23, 25

**Week 2: May 11-14:**

Strand 1: ODEs

• Turn in Lab 2, exercises 1 and 2, on Wednesday, May 13.

• 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), 19, 20, 23

• Velocity-Acceleration Models. Section 2.3: #1-5, 9

Strand 2: Linear algebra

• Reduced Row -Echelon Matrices. Section 3.3: # 5-8, 32, 35, 36

• Matrix Operations . Section 3.4: 1, 9, 10, 19, 21

• Begin Lab 4, exercises 1, 2, and 3.

• Inverses of Matrices. Section 3.5: # 1, 7, 9, 19, 23, 32, 33

Friday, May 15: Last day to drop without a “W”.

**Week 3: May 18-21:**

May 19 Last day to file a final exam conflict form for
Summer 1 and Full Summer classes

• First hour exam: Monday May 18–during the second hour

Strand 1: ODEs

• Turn in Lab 3, exercises 1, 2, 3, and 4, on Wednesday, May 20

• 2nd Order Linear Equations. Section 5.1: #1, 9, 11, 13. Section 5.2:
discussion. Section 5.3: #1, 3, 5, 7, 9, 21,

23.

Strand 2: Linear algebra

• Determinants. Section 3.6: # 1, 3, 5, 33

• Turn in Lab 4, exercises 1, 2, and 3, on Thursday, May 21.

• The Vector Space R3. Section 4.1: # 1, 5, 11, 17, 19, 25, 29, 30, 33-36

**Week 4: May 25-28:**

May 25 Memorial Day observed, no classes

Strand 1: ODEs

• 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

Strand 2: Linear algebra

• The Vector Space Rn and Subspaces. Section 4.2: #1, 4, 5, 7, 12, 15, 19

• Linear Combinations and Independence of Vectors. Section 4.3: # 1, 3, 11, 13,
15, 17, 23

**Week 5: June 1-4:**

Hour exam 2: Monday June 1, first hour

Strand 1: ODEs

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

• Turn in Lab 5, exercises 1, 2, and 3 on Wednesday June 3.

• Laplace Transforms and Inverse Transforms. Section 10.1: #1, 3, 7, 9, 13, 15,
16

Strand 2: Linear algebra

• 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

Friday, June 5: Last day to drop a class with a “W” grade

**Week 6: June. 8-11:**

Strand 1: ODEs

• 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

Strand 2: Linear algebra

• 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, 3, 5, 11, 17, 27

• Begin Lab 6, exercises 1, 2, 3, and 4.

**Week 7: June 15-18:**

Hour exam 3 Monday June 15 second hour

Strand 1: ODEs

• 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

• Impulses and Delta Functions. Section 10.6: # 1, 2, 4, 5

• Turn in Lab 6, exercises 1, 2, 3, and 4 on Wednesday June 17.

Strand 2: Linear algebra

• Review

FINAL EXAM 06/23 8 AM

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