Ordinary Differential Equations  
                  Math 20750
                  Spring 2022 

Course Information -- information.pdf

> The text book will be "Elementary Differential Equations and Boundary Value Problems, 11th edition", by Boyce, DiPrima, & Meade, published by Wiley. However the 10th edition is fine as well for most of the material, however the homework problem numbering is different in different editions. Thus if you use an older edition, you will need to borrow the 11th edition to compare difference in numbering for the homework.

> Your instructor is Prof. Katrina Barron: E-mail: kbarron@nd.edu.

> Class is held MWF 12:50pm--1:40pm in DBRT 317.
Note! Here is our current mask policy: The COVID-19 levels in the community are very low now, but are rising. There have been students and faculty on campus who have had COVID cases that are not being reported on the ND dashboard and some of these are severe. It is currently highly recommended that you wear a mask. If cases continue at this pace or rise, we will reinstitute a mandatory (rather than recommended) in class mask policy.

Resources

> Office Hours will be Monday and Wednesday, 2:00pm - 3:00pm in my office, 276C Hurley, Monday 7:00pm-8:00pm on Zoom via our class Zoom link if reserved by appointment prior, and MWF in our classroom before class, 12:25pm-12:45pm, or by appointment. Questions via email are also welcomed.

> The Math Help Rooms and the Math Bunker will by running this semester. More information is available here: Math Help Rooms/Math Bunker

The Math Bunker is running starting Sunday, January 16th in the basement of Hayes-Healy, and is open for drop in help Sunday-Thursday 7pm-9pm with an extra hour (9pm-10pm) on Wednesdays.

Course Updates and Announcements

> Current mask policy: For now masks are optional but highly recommended. If you are feeling ill at all though or think you may have been exposed to an airborne disease such as COVID or the flu, please get tested and wear your mask or stay home and ask for a recording of class. The COVID-19 levels in the community are very low now, but are rising. There have been students and faculty on campus who have had COVID cases that are not being reported on the ND dashboard and some of these are severe. It is currently highly recommended that you wear a mask. If cases continue at this pace or rise, we will reinstitute a mandatory (rather than recommended) in class mask policy.

> We will have extra office hours during the reading period before Final Exams. Please let me know what times might be best.

Schedule and Homework -- Homework is to be turned in at the beginning of class on the day it is due.

Course Schedule, and Reading and Homework Assignments


Date Reading, Watching & Topics Assignment Due Date
M   1/10 Read the information sheet linked above.
Read Sections 1.1-1.3:
Review from Calc II & Classification of Diff Eqs
Section 1.1, p. 8: #1, 2.
Section 1.2, p. 15: #1.
Section 1.3, p. 22: #1, 4, 5, 8, 9, 11, 12, 15.
HW 1: F   1/21
W   1/12 Section 2.1:
Linear ODEs & Integrating Factors
Section 2.1, pp. 31-32: #1c, 5c, 7c, 9, 11, 12, 13, 21, 23. HW 1: F   1/21
F   1/14 Section 2.2:
Separable ODEs
Section 2.2, p. 38: #1, 2, 4, 5, 9ac, 11ac, 15ac, 16ac, 19. HW 1: F   1/21
M   1/17 MLK Day No Class None
W   1/19 Examples from Sections 2.1 & 2.2, &
Section 2.3
Modeling with 1st order ODEs
Section 2.3, pp. 47--49: #2, 3, 6, 7, 12, 15, 16. HW 2: F   1/28
F   1/21 Section 2.3
Activity 1 on Modeling
Work on Activity 1 on Modeling in class.
Continue to work on problems assigned for Section 2.3.
HW 1 due
HW 2: F   1/28
M   1/24 More on Activity 1 &
Start Section 2.4
Existence & Uniqueness for
Lin. v. Nonlin. 1st order ODEs
Work more on Activity 1 in class. Extra info given: T(1) = 81.5 degrees Fahrenheit for Part II, murder mystery.
Section 2.4, p. 57: #1, 2.
HW 2: F   1/28
W   1/26 Section 2.4
Existence & Uniqueness
Section 2.4, pp. 57--58: #5, 6, 8, 9, 11, 17, 18, 19. HW 3: F   2/4
F   1/28 Sections 2.4 & 2.5
Existence & Uniqueness, &
Autonomous ODEs
Section 2.5, pp. 67-68: #2, 4, 5, 6, 8, 15, 18.
HW 2 due, and Activity 1 due.
HW 3: F   2/4
M   1/31 Sections 2.5
Autonomous ODEs
Continue to work on the Homework from Sections 2.4 and 2.5. HW 3: F   2/4
W   2/2 No class. HAPPY SNOW DAY!! None.
F   2/4 Section 2.6
Exact Equations &
Integrating Factors &
In class Quiz
Section 2.6, p. 75: #1, 3, 4, 6, 7, 9, 11, 15, 18, 20, 21.
We will have a short in class Quiz focusing on HW 1-2, Sections 1.1-1.3, & 2.1-2.4 (first part -- Theorem 2.4.1).
HW 3 is due.
HW 4: F   2/18
M   2/7 Section 2.6
Integrating Factors for Non-Exact Equations
Continue to work on homework assigned for Section 2.6.
HW 4: F   2/18
W   2/9 In class will be a
non-mandatory Q&A on Exam I
Exam I will focus on material from HW 1--3, up through and including Section 2.5.
Class time will be for questions and answers on the exam material. The exam will be scheduled outside of class time on Thursday.
None.
Th   2/10 Exam I
3:30-5:15pm DBRT 318
6:00-8:15pm Hayes-Healy 117
Exam I will focus on material from HW 1--3, up through and including Section 2.5.
You may come at any time to either session, and may stay for up to 1 hour and 45 minutes if you wish.
None.
F   2/11 Activity 3 &
Section 3.1
2nd Order Linear Homogeneous ODEs
with Constant Coefficients
We will have an in class activity on the epidemiology of small pox.

Section 3.1, p. 109: #1, 4, 7, 9, 10, 13, 16, 17.
HW 4: F   2/18
M   2/14 Sections 3.1 & 3.2
Finding a complete set of solutions
Existence and Uniqueness Theorem
Finish Activity 3 for Wednesday.
Continue to work on Homework for Section 3.1.
HW 4: F   2/18
W   2/16 Section 3.2
The Wronskian
Section 3.2, p. 119: #1, 3, 4, 6, 7, 8, 11, 14, 17, 19, 20, 23, 25, 27, 29.
Activity 3 is due.
HW 5: F   2/25
F   2/18 Sections 3.2 & 3.3
Abel's Theorem &
Complex Roots
Section 3.3, pp. 125-126: #1, 2, 4, 5, 6, 9, 12, 13, 14, 21, 23.
HW 4 is due.
HW 5: F   2/25
M   2/21 Sections 3.2, 3.3, & 3.4
More on Abel's Thm. & Complex roots
& start Repeated roots.
Continue to work on Homework for Sections 3.2 & 3.3. HW 5: F   2/25
W   2/23 Sections 3.4 & 3.5
Repeated roots & Reduction of Order, &
Intro to Nonhomogen. Eqn.
Section 3.4, pp. 132-133: #1, 4, 6, 9, 10, 12, 14, 20, 21, 22. HW 6: F   3/4
F   2/25 Section 3.5
Nonhomog. Eqns. &
Method of Undetermined Coeffs.
Section 3.5, p. 141: #4, 5, 7, 8, 11, 13, 14, 16, 18.

Also HW 5 is due.
HW 6: F   3/4
M   2/28 Section 3.6
Nonhomog. Eqns. &
Method of Variation of Parameters
Section 3.6, p. 146: #1, 3, 4, 6, 8, 9, 10, 12, 13. HW 6: F   3/4
W   3/2 Activity 5 on Change of Variables
In class Quiz.
We will have a short in class Quiz on HW 4 & 5, Sections 2.6, & 3.1-3.3.
We will also start an Activity on Change of Variables.
None.
F   3/4 More on Activity 5 We will finish most of Activity 5 in class. This activity will be due on Wed. 3/16.
Also HW 6 is due.
Act 5: W   3/16
M   3/7 Spring Break! No class! None.
W   3/9 Spring Break! No class! None.
F   3/11 Spring Break! No class! None.
M   3/14.159.... Section 3.7
Mechanical & Electrical Vibrations
Section 3.7, pp. 157-158: #1, 2, 3, 4, 6, 7, 12, 13, 14, 17. HW 7: F   3/25
W   3/16 Exam II Q&A in class Exam II will focus on material from HW 4--6, Sections 2.6, & 3.1-3.6. In class I will answer questions on the material.
In addition: Activity 5 is due.
None.
W   3/16 Exam II
6:00pm - 8:30pm
Hayes-Healy 129
You may come anytime during the blocks of time set aside to take Exam II on Wed and Thurs. Suggested amount of time you should budget for is 50 minutes to 1 hour and 45 minutes depending on how fast you want to work and how much you want to double check your work. None.
TH   3/17 Exam II
4:30pm - 7:00pm
Hayes-Healy 117
You may come anytime during the blocks of time set aside to take Exam II on Wed and Thurs. Suggested amount of time you should budget for is 50 minutes to 1 hour and 45 minutes depending on how fast you want to work and how much you want to double check your work. None.
F   3/18 Section 3.8
Forced Mechanical & Electrical Vibrations
Section 3.8, pp. 167-168: #1, 2, 4, 6, 7, 13, 14. HW 7: F   3/25
M   3/21 Video for Section 4.1
nth Order Linear ODEs
You are assigned the video for Section 4.1 on Sakai panopto. There is no in person class.
Section 4.1, pp. 173-174: #1, 2, 3, 5, 7, 8, 9, 10, 12, 14, 15.
HW 7: F   3/25
W   3/23 Video for Section 4.2
Homogeneous nth Order Lin. ODEs
with Constant Coefficients
You are assigned the video for Section 4.2 on Sakai. There is no in person class.
Section 4.2, pp. 180-181: #8, 14, 17, 20, 29.
HW 8: F   4/1
F   3/25 Video for Sections 4.3 & 4.4
Nonhomogeneous nth Order Lin. ODEs
Method of Undetermined Coefficients
& Variation of Parameters
You are assigned the video for Sections 4.2 & 4.3 on Sakai. There is no in person class.
Method of Undetermined Coefficients: Section 4.3, p. 184: #1, 2, 5, 10, 11, 12.
Method of Variation of Parameters: Section 4.4, p. 188: #1, 2, 3, 5, 9.
HW 7 due in Prof. Barron's Math Dept mailbox 255 Hurley by 2pm. Please put it in the pink plastic folder.
HW 8: F   4/1
M   3/28 Section 7.1
Intro to Systems of ODEs
We resume in person class. Please come with questions on Chapter 4 .
Section 7.1, pp. 284-285: #1, 2, 4, 6, 8.
HW 8: F   4/1
W   3/30 Sections 7.2, 7.3 & 7.4
Review of Linear Algebra &
Basic Theory of 1st Order Linear Systems
Section 7.2, pp. 293-294: #1, 9, 11, 12, 13, 14, 16, 17, 19.
Section 7.3, pp. 303-304: #1, 2, 5, 6, 8, 11, 13, 14, 15, 19.
HW 9: F   4/8
F   4/1 Sections 7.4 & 7.5
Basic Theory of 1st Order Lin. Systems
& Homogeneous with Constant Coeff. Intro
Section 7.4, pp 308-309: #1, 3, 5, 8(a)-(c), 9, 11, 12.
Note: There is a typo in the text in 5(d). You should let t = 2 not t = 0, so that x(2) = (1,2)^T.
HW 9: F   4/8
M   4/4 Sections 7.4 & 7.5
Basic Thry & Homogen. Constant Coeff.
Real Eigenvalues
Section 7.5, p. 318: #2b, 3b, 5b, 7, 10, 12, 18, 19. HW 9: F   4/8
W   4/6 Section 7.5
Basis of Real Eigenvalues
Quiz 6
We will have a shortquiz in class on HW 7-8, Sections 3.7, 3.8, Chapter 4, and Section 7.1. None.
F   4/8 Sections 7.6 & 7.7
Complex Eigenvalues & Fundamental Matrices
Section 7.6, pp. 327-329: #1b, 3b, 5, 7, 25(a)-(c). HW 10: F   4/22
M   4/11 Exam III Q & A
in class
Bring your questions on Exam III material to class.
Exam III will be offered outside of class time on Tuesday and Wednesday outside of class time. The exam will focus on HW 7--9, Sections 3.7, 3.8, Chapter 4, & Sections 7.1-7.5. Also, in addition to usual office hours 2pm-3pm today, there will be office hours on Zoom at 7pm, and office hours tomorrow (Tuesday) 1:30pm-2:30pm.
None.
T   4/12 Exam III
5:00pm - 7:00pm DBRT 318
Exam III will be offered today and Wednesday. The exam will focus on HW 7--9. The exam will focus on HW 7--9, Sections 3.7, 3.8, Chapter 4, & Sections 7.1-7.5. You may take as much as twice the 50 minute time for the exam during this time period. None.
W   4/13 Sections 7.6, & 7.7.
Nonhomeogeneous systems with Complex Eigenvalues & Fundamental Matrices
Section 7.7, p. 336: #1, 3, 4, 7, 9. HW 10: F   4/22
W   4/13 Exam III
5:30pm - 8:30pm DBRT 215
Exam III offered again. None.
F   4/15 Good Friday No class! None.
M   4/18 Easter Monday No class! None.
W   4/20 Sections 7.8
Generalized Eigenvectors & Nonhomogeneous Linear Systems
Section 7.8, pp. 342-344: #1, 2, 4, 9(a) and 9(c), 17(a)-(e). HW 11: T   4/26
F   4/22 Section 7.9
Nonhomogeneous Linear Systems
Section 7.9, pp. 351-352: #1, 4, 5, 6, 10.
Also HW 10 is due.
HW 11: T   4/26
M   4/25 Activity 7 We will have an in class activity on modeling of flow between reservoirs. Activity 7: T   4/26
T   4/26 More in class activities. Since MLK Day was added as a day when classes do not meet, the administration added this day as an extra day for MWF classes. So we will meet. Also HW 11 is due and we will finish Activity 7. None.
W   4/27 Extra Office Hours
2pm - 3pm
Drop in Office Hours 276C Hurley None
F   4/29 Extra Office Hours
1pm - 2pm
Drop in Office Hours 276C Hurley None
M   5/2 Extra Office Hours
2pm - 3pm
Drop in Office Hours 276C Hurley None
W   5/4 Final Exam
8:00am - 10:00am
DBRT 317
The final exam will cover all course material covered by homework assignments but will focus a little more on the material from HWs 10 & 11.
You will have the same sheet of formulas as you had for Exam III.
Also if you are doing any part of Extra Credit Activity 8, you should hand it in at the final exam or earlier in my Math Department mailbox.
None


Last updated April 29, 2022.