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