Math 319 (Spring 2018)
Techniques in Ordinary Differential Equations
Techniques in Ordinary Differential Equations
Announcements
Lu Wang's office hours for the week beginning on May 7: Tuesday 4PM-6PM in 809 Van Vleck Hall.
Lu Wang's office hours for the week beginning on April 9: Monday 4:30PM-5:30PM and Tuesday 11AM-Noon in 809 Van Vleck Hall.
The new final exam time is May 10, 10:05AM-12:05PM.
Lu Wang's office hours for the week beginning on Feb. 26: Monday 4:30PM-5:30PM and Tuesday 11AM-12PM in 809 Van Vleck Hall.
Lectures
Time: Tuesday and Thursday, 2:30PM-3:45PM
Location: 272 Bascom Hall
Instructor
Lu Wang
Office: 809 Van Vleck Hall
Phone: (608) 262-3220
E-mail: luwang@math.wisc.edu
TAs
Jiyuan Han
Office: 522 Van Vleck Hall
E-mail: jiyuan@math.wisc.edu
Dae Han Kang
Office: 420 Van Vleck Hall
E-mail: kang@math.wisc.edu
Office Hours
Lu Wang: Tuesday and Thursday, 1:30PM-2:30PM, 809 Van Vleck Hall, or by appointment
Jiyuan Han: Tuesday, 6PM-8PM, 522 Van Vleck Hall
Dae Han Kang: Tuesday, Noon-2PM, 420 Van Vleck Hall
Textbook
Title: Elementary Differential Equations and Boundary Value Problems (10th Edition)
Authors: William Boyce, Richard DiPrima
Publisher: Wiley
Year: 2012
ISBN-13: 9780470458310
Syllabus
We will cover most materials of Chapters 2-3, 5-7, 9, and small parts of Chapters 10-11 (if time permitted).
For more details, click here.
Homework
Unless specified, homework will be assigned here every Thursday and collected on Thursday next week at the beginning of lecture. The graded ones will be returned to your discussion section.
No late homework will be accepted, but we will drop the lowest two homework scores.
Students are encouraged to collaborate on homework problems; however, submitted assignments must be the work of the individual submitting the assignment.
HW#1 (due Feb. 1): 2.1: #14, 18, 30, 40; 2.2: #2, 6, 22, 30(a)-(e); 2.3: #4, 20
HW#2 (due Feb. 8): 2.4: #2, 7, 16, 29, 32; 2.5: #3, 4, 18, 28
HW#3 (due Feb. 15): 2.6: #5, 14, 16, 22, 26; 3.1: #4, 14, 20, 24, 26
HW#4 (due Feb. 22): 3.2: #5, 17, 25, 31, 34; 3.3: #3, 10, 25, 36, 44
HW#5 (due Mar. 8): 3.4: #12, 18, 28, 34; 3.5: #10, 20, 30, 36; 3.6: #10, 14, 30, 32
HW#6 (due Mar. 15): 3.7: #5, 18, 24, 30; 3.8: #5, 7, 15, 17
HW#7 (due Mar. 22): 5.1: #9, 10, 13, 14; 5.2: #4, 12, 21; 5.3: #6, 8, 10
HW#8 (due Apr. 5): 5.4: #2, 13, 36, 38; 6.1: #5, 7, 11, 16, 23
HW#9 (due Apr. 19): 6.2: #4, 15, 36; 6.3: #10, 14, 22, 28; 6.4: #2, 4, 16
HW#10 (due Apr. 26): 7.2: #2, 4, 12, 22; 7.3: #8, 14, 18, 22; 7.4: #2, 4, 6, 8
HW#11 (not turn in): 7.5: #2, 8, 15; 7.6: #2, 10, 14; 7.8: #2, 8, 15; 9.1: #4, 6, 14
Quizzes
There will be three short quizzes based on the materials of previous homework. No make-up quizzes will be provided, but we will drop the lowest quiz score.
Quiz 1: Feb. 14, in the discussion section (based on HW#1&2)
Quiz 2: Mar. 21, in the discussion section (based on HW#5&6)
Quiz 3: May 2, in the discussion section (based on HW#9&10)
Exams
Make-up exams will be scheduled only with the instructor's (not with the TAs') consent, and only in case of illness, academic conflicts, or family emergencies. There will be no early finals given for any reason.
All exams are closed-book. No calculators or other electronic devices will be allowed during exams. Please bring your student ID to exams.
If you are a McBurney student, bring your voucher as soon as possible so we make exam arrangements.
Midterm I: Tuesday, Feb. 27, in class (based on HW#1-4)
Midterm II: Tuesday, April 10, in class (based on HW#5-8)
Final: cumulative, Thursday, May 10, 10:05AM-12: 05PM, in B130 Van Vleck
Grades
Homework & Quizzes: 20%
Midterm I: 20%
Midterm II: 20%
Final: 40%
We will use the following cutoffs to assign letter grade:
A: 90+
AB: 86+
B: 77+
BC: 72+
C: 60+
D: 48+
F: 0+
These cutoffs are approximate, tentative, and subject to change.
Lecture Schedule
The following will be updated through the semester.
Week of Jan. 22
Introduction
Mathematical models: 1.1, 2.3
Integrating factor method: 2.1
Week of Jan. 29
Separable equations: 2.2
Linear vs Nonlinear equations: 2.4
Week of Feb. 5
Autonomous equations: 2.5
Exact equations: 2.6
Week of Feb. 12
Second order homogeneous constant coefficient equations (two real roots): 3.1
Linearity and the Wronskian: 3.2
Week of Feb. 19
Second order Homogeneous constant coefficient equations (complex roots): 3.3
Second order Homogeneous constant coefficient equations (repeated roots): 3.4
Week of Feb. 26
Midterm I, Feb. 27, in class
Second order non-homogeneous constant coefficient equations (undetermined coefficients): 3.5
Week of Mar. 5
Second order non-homogeneous constant coefficient equations (Variation of Parameters): 3.6
Analyzing mechanical and electrical vibrations (free vibrations): 3.7
Week of Mar. 12
Analyzing mechanical and electrical vibrations (forced vibrations): 3.8
Review of power series: 5.1
Series solutions near an ordinary point: 5.2
Week of Mar. 19
Series solutions near a singular point: 5.3
Euler equations: 5.4
Week of Mar. 26
No class due to spring break
Week of Apr. 2
Laplace transform: 6.1
Initial value problems: 6.2
Week of Apr. 9
Midterm II, Apr. 10, in class
Step functions: 6.3
Week of Apr. 16
Differential equations with discontinuous forces: 6.4
Review of Linear algebra: 7.2
Week of Apr. 23
Review of Linear algebra: 7.3
Basic theory for linear systems: 7.4
Homogeneous linear systems with constant coefficients: 7.5-7.6, 7.8
Week of Apr. 30
Phase plane: 9.1
Final Review
Week of May 7
Final, May 10, 10:05AM-12:05PM, in B130 Van Vleck