The image “http://jeff560.tripod.com/euler5.jpg” cannot be displayed, because it contains errors.

University of North Carolina

Math 383H
Linear Algebra and Differential Equations

Spring 2008



The photo above is of Swiss currency featuring L. Euler.  See http://jeff560.tripod.com/


Schedule / Assignments:

Note:  All assignments are due at the beginning of class (9:30am) on the specified day.  The section numbers, page numbers, and problem numbers correspond to those in the 4th edition of the textbook.

Please show all of your work.  A correct answer without proper supporting work is worth zero credit.


[1/10/08]

Intro to ODE (1.1), Existence and uniqueness (1.3), Separable equations (1.4).
[1/15/08]

Separable equations (1.4), First order linear equations (1.5)

Assignment 1:  Section 1.4 (p. 43-46) #28, 43, 62; Section 1.5 (p. 56-58) # 18.
Solutions
[1/17/08]

Substitution methods (1.6)

Assignment 2:  Section 1.5 (p. 56-58) #38; Section 1.6 (p. 74-75) #7, 25, 38
Solutions
[1/22/08]

Assignment 1 due

Substitution methods (1.6), Population models (2.1)

Assignment 3:  Section 1.6 (p. 74-75) #48, 52, 63; Section 2.1 (p. 87-90) #24
Solutions
[1/24/08]

Assignment 2 due

Population models (2.1), Equilibrium Solutions and Stability (2.2), Acceleration-Velocity Models (2.3)

Assignment 4:  Section 2.1 (p. 87-90) #34; Section 2.2 (p.98-100)  #10 (sketch the graph by hand), 24, 29
Solutions

[1/29/08]

Class canceled -- It's a girl!




[1/31/08]

Assignment 3,4 due

Acceleration-Velocity Models (2.3), Intro to 2nd order linear equations (3.1)

Assignment 5:  Section 2.3 (p. 108-109)  #10, 12, 19, 24
Solutions
[2/5/08]

Intro to 2nd order linear equations (3.1),  General solutions to linear equations (3.2)

Assignment 6:  Section 3.1 (p. 158-160) #19, 39, 51; Section 3.2 (p. 170-172) #40
Solutions
[2/7/08]

Assignment 5 due

General solutioins to linear equations (3.2), Homogeneous equations with constant coefficients (3.3)

Assignment 7:  Section 3.1 (p. 158-160) #32; Section 3.2 (p. 170-172) #12, 27; Section 3.3 (p. 183-184) #11
Solutions
[2/12/08]

Assignment 6 due

Homogeneous equations with constant coefficients (3.3),  Nonhomogeneous equations and undetermined coefficients (3.5)

Assignment 8:  Section 3.3 (p. 183-184) #19, 35; Section 3.5 (p. 210-211) #37, 59
Solutions
[2/14/08]

Assignment 7 due

Nonhomogeneous equations (3.5), Mechanical Vibrations (3.4)

No assignment -- due to the exam next Thursday
[2/19/08]

Assignment 8 due

Exam Review, Mechanical Vibrations (3.4), Forced Oscillations and Resonance (3.6)

Assignment 9:  Section 3.4 (p. 195-198) #8, 27, 29; Section 3.6 (p. 222-223) #20
Solutions
[2/21/08]

Exam 1

Linear algebra: matrices, matrix operations, matrix multiplication, row reduction
[2/26/08]

Assignment 9 due

Linear algebra: row reduction, span,

Assignment 10
Solutions

[2/28/08]

Linear algebra: linear independence, transpose, matrix inverses,

Assignment 11
Solutions
[3/4/08]

Assignment 10 due

Linear algebra: matrix inverses, invertible matrix theorem, determinants, linear transformations

Assignment 12
Solutions

[3/6/08]

Assignment 11 due

Linear algebra: linear transformations, eigenvalues and eigenvectors.  Linear systems of ODE.

Assignment 13
Solutions
[3/18/08]

Assignment 12 due

Eigenvalue method for homogeneous systems (5.2)

Assignment 14:  Section 5.2 (p. 316-317) #6 (solution only), 18, 32 (no graph is needed), 40
Solutions

[3/20/08]

Assignment 13 due

Eigenvalue method for homogeneous systems (5.2), Multiple Eigenvalue Solutions (5.4)

Assignment 15:   Section 5.4 (p. 345-347) # 8, 16, 20, 22
Solutions


[3/25/08]

Assignment 14 due

Multiple Eigenvalue Solutions (5.4), Second-Order Systems and Mechanical Applications (5.3)

No assignment - due to the exam on 4/1/08
[3/27/08]

Assignment 15 due

Review, Matrix Exponentials (5.5), Nonhomogeneous Linear Systems (5.6)

Assignment 16:   Section 5.3 (p. 328-330) # 17; Section 5.5 (p. 359-360) # 20, 30, 32
Solutions

[4/1/08]

Exam 2

Nonhomogeneous Linear Systems (5.6)
[4/3/08]

Assignment 16 due

Nonhomogeneous Linear Systems (5.6), Matrix diagonalization and applications to ODE

Assignment 17:   Section 5.5 (p.359-360) 24; Section 5.6 (p. 369-370) 10, 14, 21
Solutions
[4/8/08]

Matrix diagonalization and applications to ODE, Stability and the Phase Plane (6.1)

Assignment 18
Solutions
[4/10/08]

Assignment 17 due

Stability and the phase plane (6.1), Linear and almost linear systems (6.2)

Assignment 19:  Section 6.1 (p. 381-383)  18 (you can sketch the graphs by hand), 22, 27, 28
Solutions
[4/15/08]

Assignment 18 due

Linear and almost linear systems (6.2)

Assignment 20
:  Section 6.2 (p. 395-397) # 5, 10, 14, 16 (hand sketches for the graphs)
Solutions
[4/17/08]

Assignment 19 due

Linear and almost linear systems (6.2), Linear algebra: vector spaces

Assignment 21:  Section 6.2 (p. 395-397): #29-32 (hand sketches for the graphs)
Solutions
[4/22/08]

Assignment 20 due

Linear algebra: vector spaces, subspaces, null space, column space
[4/24/08]  Last lecture

Assignment 21 due

Linear algebra: vector spaces, bases, change of coordinates;  Review.

Other dates of interest:

3/10-3/14/08    - Spring break (no classes)

3/4/08        - Last Day to Drop
4/25/08      - Last day of lectures

2/21/08, 4/1/08 - Midterm exams
4/29/08       -
Final Exam, 8:00-11:00 am

Academic Calendar

Honor code:

The honor code will be strictly enforced on all assignments.   Acceptable collaboration on homework is limited to discussion among peers after which each individual must complete his or her assignment on his or her own.  I.e., when you are writing up your solutions, you should not be looking at any notes developed in discussion of the problems with another student.  Suspiciously similar assignments will be considered in violation of the honor code and treated accordingly.