Contact Information for the Instructor:
Instructor: Willard Miller
Office: Vincent Hall 513
Office Hours: 10:10-11:00 MW, 12:20-1:10
F, or by appointment
Phone: 612-624-7379
miller@ima.umn.edu, miller@math.umn.edu
www.ima.umn.edu/~miller/
Discussion Sections:
-021 10:10am-11:00am TTh, VinH 311 Matthew Dobson Phone: 5-5099, Office: VinH 420, dobson@math.umn.edu
-022 10:10am-11:00am TTh, VinH 211 Ji Hoon Ryoo, Phone: 5-8553, Office: VinH 422, jhryoo@math.umn.edu
-023 11:15am-12:05pm TTh, FolH 334
Matthew Dobson
Phone: 5-5099, Office: VinH 420,
dobson@math.umn.edu
-024
11:15am-12:05pm TTh, VinH 311
Ji Hoon
Ryoo Phone: 5-8553, Office: VinH 422,
jhryoo@math.umn.edu
Credit will not be granted if credit has been received for: MATH 2373, prereq 1272 or 1282 or 1372 or 1572, 4 credits |
|
Overview: The course is divided into
two somewhat related parts. Linear algebra: matrices and matrix operations, Gaussian elimination, matrix inverses, determinants, vector spaces and subspaces, dependence, Wronskian, dimension, eigenvalues, eigenvectors, diagonalization. ODE: Separable and first-order linear equations with applications, 2nd order linear equations with constant coefficients, method of undetermined coefficients, simple harmonic motion, 2x2 and 3x3 systems of linear ODE's with constant coefficients, solution by eigenvalue/eigenvectors, nonhomogenous linear systems; phase plane analysis of 2x2 nonlinear systems near equilibria. Audience: Part of the standard 2nd year calculus course for students outside of IT. Text: Farlow, Hall, McDill, West. Differential Equations and Linear Algebra We will cover Chapters 1-7 (up to Section 7.2) as well as Sections 8.1, 8.2 and 8.5. 4 credits. 3 lectures, 2 recitations per week. |
FINAL EXAM: 1:30 - 4:30
pm, Thursday, December 16
"All students must have their official University I.D. Card with them at the time of the final exam and must show it to one of the proctors when handing in their exam. The proctor will NOT accept a final exam from a student without an I.D. Card."
Syllabus and Suggested
Homework
Date
Lecture
Suggested Homework Problems
Wednesday, September
8 |
Section 1.1 Dynamical
Systems, Modeling |
#23-27 |
Friday, September
10 |
Section 1.2 Solutions
and Direction Fields |
#2,3,6,7,13-18,20,23,24,26,29,30 |
Monday, September
13 |
Section 1.3 Separation
of Variables: Quantitative Analysis |
#12,13,16-26,29,31,32,39,40,43-47,53,54 |
Wednesday, September
15 |
Section 1.4 Euler's
Method: Numerical Analysis |
#1,7-10,12 |
Friday, September
17 |
Section 1.5 Picard's
Theorem: Theoretical Analysis |
#2-4,7-12,21,23 |
Monday, September
20 |
Section 2.1 Linear
Equations: The Nature of Their Solutions |
#7-12 |
Wednesday, September
22 |
Section 2.2 Solving
the 1st-Order Linear ODE |
#1-6,9-15,19,20,25,26,30-35,45,46 |
Friday, September
24 |
Section 2.3 Growth
and Decay Phenomena |
#1-5,7,14,16,17,21,24,26,33 |
Monday, September
27 |
Review |
|
Tuesday, September
28 |
Midterm I |
|
Wednesday, September
29 |
Section 2.4 Linear
Models: Mixing and Cooling |
#2,4,7,8,11-13,17-19 |
Friday, October
1 |
Section 2.5 Nonlinear
Models: Logistic Equation |
#13-18,21-24 |
Monday, October
4 |
Section 2.6 Systems
of Differential Equations: A First Look |
#1-3,5-7,11,14-17,23 |
Wednesday, October
6 |
Section 3.1 Matrices:
Sums and Products |
#4,5,31-34,40,42,44-46,51,54,61 |
Friday, October
8 |
Section 3.2 Systems
of Linear Equations |
#5-10,29-33,35 |
Monday, October
11 |
Section 3.3 The
Inverse of a matrix |
#7-10,14,17,18,24,25 |
Wednesday, October
13 |
Section 3.4 Determinants
and Cramer's Rule |
#1,4-7,11,12,16-18,20,23,29-32,34-36 |
Friday, October
15 |
Section 3.5 Vector
Spaces and Subspaces |
#2,4-6,8,9,12-14,16-20,22,23,25,26,34,36-38,43-51,56 |
Monday, October
18 |
Section 3.6 Basis
and Dimension |
|
Wednesday, October
20 |
Section 3.6 |
#1,2,5-8,11-14,16-18,20-22,26-32,38,39,42-45,47-50,54-58,64,65 |
Friday, October
22 |
Section 4.1 The
Harmonic Oscillator |
#4-6,8-10,14-16,21,22,25-28,31-39,49,52 |
Monday, October
25 |
Review |
|
Tuesday, October
26 |
Midterm II, Covers
material through Section 3.6 |
|
Wednesday, October
27 |
Section 4.2 Real
Characteristic Roots |
#16-24,28-30,35,38-41,43,47,55,56,59-62 |
Friday, October
29 |
Section 4.3 Complex
Characteristic Roots |
#13,15-28,34-36,41,42 |
Monday, November
1 |
Section 4.4 Undetermined
Coefficients |
#4-6,22-33,36,39,40 |
Wednesday, November
3 |
Section 4.5 Forced
Oscillations |
#4-13,15-17,20,22,23 |
Friday, November
5 |
Section 4.6 Conservation
and Conversion |
#1,2,8-13,17-20,32,33,40,41,44 |
Monday, November
8 |
Section 5.1 Linear
Transformations |
#6-10,13-15,17-29,33,34,37-43,47,59,61-63,65-67,70-73,78-80 |
Wednesday, November
10 |
Section 5.2 Properties
of Linear Transformations |
#2,3,6,7,10-14,23,30,34,35,38,39,44-47,50-52,55-61 |
Friday, November
12 |
Section 5.3 Eigenvalues
and Eigenfunctions |
#6-9,15,18,20,22,24,26-29,31,33-36,39-41,45-47 |
Monday, November
15 |
Section 5.4 Coordinates
and Diagonalization |
#1-3,7-9,13-15,20-23,27-33,39-41,43-44 |
Wednesday, November
17 |
Section 6.1 Theory
of Linear DE Systems |
#3,5,7,9,17-19,23-26,33-35 |
Friday, November
19 |
Section 6.2 Linear
Systems with Real Eigenvalues |
#15-23,28,31,39,40,43 |
Monday, November
22 |
Section 6.3 Linear
Systems with Nonreal Eigenvalues |
#14-17,23-27,30,33 |
Wednesday, November
24 |
Section 6.4 Decoupling
a Linear DE System |
#3-5,9-11,15,16 |
Monday, November
29 |
Section 6.5 Stability
and Linear Classification |
#1-12,14,15,17 |
Wednesday, December
1 |
Review |
|
Thursday, December
2 |
Midterm III, covers
material through Section 6.4 |
|
Friday, December
3 |
Section 7.1 Nonlinear
Systems |
#11,13,15,17,19,21,23,27-33,35,37 |
Monday, December
6 |
Section 7.2 Linearization |
#1-9,11-18,20-23 |
Wednesday, December
8 |
Section 8.1 Linear
Nonhomogeneous problems |
#3,5,11,13,15-17,24,25 |
Friday, December
10 |
Section 8.2 Variation
of Parameters |
#3-9,12-15,18,19 |
Monday, December
13 |
Section 8.5 Chaos
in Forced Nonlinear Systems |
didn't cover this |
Wednesday, December
15 |
Review |
|
Thursday, December
16 |
Final Exam 1:30-4:30
pm Sec. 021: VinH 113, |
Secs. 022-023:
MurphyH 130, Sec. 024: MurphyH
214 |
1. Solution of equation y'=t-3y from t=0 to t=1, with initial condition y(0)=1, step size h=.001
2. Solution of equation y'=y/t -1 from t=1 to t=2, with initial condition y(1)=1, step sizes h=0.1, h=0.01, h=0.001. According to theory, decreasing step size by a factor of 10 should decrease maximum discretization error by the same factor. However, decreasing step size by a factor of 10 may increase maximum roundoff error 10 times. In this example the total error, discretization and roundoff, is listed in the righthand column. For h=0.1 the maximum error is about 5 x 10-2 , for h=0.01 the maximum error is about 5 x 10-5 , while for for h=0.001 the maximum total error is 5 x 10-4 . Thus reducing step size improves accuracy initially, but eventually the increased roundoff error actually reduces the accuracy.