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University of North Carolina Math 383H Linear Algebra and Differential Equations Spring 2008
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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
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.