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MATH2073, Ordinary Differential Equations

Spring Semester 2021

Course Format: Online Synchronous M-W-F 9:05-10am on Webex

Instructor: Wlodek Bryc (Dr. Bryc, for short)
Office: French Hall West, Room 4316 | Office Hours |
E-mail:
Phone: (leave a message)

Textbook:

Elementary Differential Equations by Boyce and DiPrima 11th edition with WileyPLUS

Technology. We will use UC Canvas, Webex, and WileyPLUS. You may also want to use Symbolab Online ODE Solver or WolframAlpha

Course Overview, Description, Purpose

Study of first-order differential equations including linear, separable, homogenous, exact; linear differential equations of second order or higher with particular attention to equations with constant coefficients and Euler equations, including linear dependence for solutions of homogeneous equation and the Wronskians, the method of undetermined coefficients, the method of variation of parameters; the power series solution method (Froebenius) for solutions of homogenous differential equations of second order about ordinary points and regular singular points; Laplace transform and application to differential equations with discontinuous or impulse forcing functions. The material is covered by chapters 1-6 of the textbook.

Learning Outcomes

The successful Ordinary Differential Equations student should know topics described under course contents in the syllabus.

Recognize basic types of differential equations: order, linearity
Solve linear or nonlinear first-order differential equations: obtain analytic solutions to initial value problems by hand or using software; apply differential equations to describe and analyze simple models; use differential equations for qualitative analysis of long term behaviour
Second order equations: Use linear second-order differential equations to solve application problems ; Determine recursion for the coefficients of the power series solution of a differential equation and obtain solutions to initial value problems with non-constant coefficients by series expansions;
Find general solutions of the linear differential equations with constant coefficients of arbitrary order.
Perform operations with Laplace and inverse Laplace transforms to solve higher-order differential equations, including differential equations with discontinuous or impulse forcing functions.

Exams and important dates. See also UC Academic Calendars

Cumulative Exams during class time.
- Exam 1: Friday, Jan 22
- Exam 2: Friday, Feb 5
- Exam 3: Friday, Feb 19
- Exam 4: Friday, March 5
- Exam 5: Friday, March 19
- Last day to withdraw: Fri, April 2
- Exam 6: Friday, Apr 9
Final Exam: Thursday, April 22, 7:30-9:30 a.m.

Technology and Calculators Policy on Exams: You may use the book, notes, computers and calculators, including web-based calculators, on all online quizzes, and on all unproctored online exams.

Exam Proctoring: to be determined if/when need arises.

Assessment and Grading Policy

Grading scale: 93% A, 90% A-, 87%, B+, 83% B, 80% B-, etc. (70% C-, 60% D-)

Components of course grade:

Class Participation (Polls) 10%
Homework 10%
Exams 60%
Final 20%

Withdrawal policy: You will need to take at least one Poll to confirm your participation in the class.

Week-by-week

(The exact coverage dates may have to be adjusted. If necessary, some sections will be dropped or covered only lightly.)

Week 1 (Jan 11)

Sections covered: Ch 1, 2.1, 2.2, 2.3

Homework:

Sec. 1.1:   11-20
Sec. 1.2:   1, 2
Sec. 1.3:   1-4, 5, 7, 9
    Sec. 2.1:   1,8, 9, 12, 14
    Sec. 2.2:   1-3, 6, 11, 12, 14, 21, 23, 25, 29, 31
    Sec. 2.3:   1, 3, 6, 7, 12

Week 2 (Jan 20) No class on Monday
- Sections covered: 2.3, Exam 1
- Homework:
```
Sec. 2.3: 1, 3, 6, 7, 12 
```

Week 3 (Jan 25)

Sections covered: 2.5, 2.6, 3.1

Homework:

Sec 2.5: 1,2 (solve), 5, 8 (solve), 21, 22, 25 (solve), 27.
Sec 2.6: 1, 3, 5, 7, 10, 12, 18, 21
Sec 3.1: 1, 5, 12, 13,  16, 17

Week 4 (Feb 1)

Sections covered: 3.2, 3.2, Exam 2

Homework:

 Sec 3.2: 4, 6, 7,   17, 19,
 Sec 3.2:   11, 17, 19, 23, 25, 27

Week 5 (Feb 8)

Sections covered: 3.3, 3.4, 3.5

Homework:

Sec 3.3:  6,   13, (you do not need to graph the solutions, but discuss the behavior of the solution as time increases.)
Sec 3.4: 1-3, 9, 11  (for 9 and 11, you do not need to graph the solutions, but do address their behavior for increasing t),  12, 18, 21, 26
Sec 3.5: 1-15

Week 6 (Feb 15)
- Sections covered: 3.5, 3.6 Exam 3
- Homework:
```
Sec 3.5: 1-15 (continued)
Sec 3.6: 1, 5, 13, 24
    
```

Week 7 (Feb 22)

Sections covered: 3.7, 4.1, 4.2

Homework:

Sec 3.7: 1, 2, 8
Sec 4.1: 2, 6, 9, 16
Sec 4.2: 1, 3, 6, 9, 13, 14, 16, 20, 21, 22

Week 8 (March 1)

Sections covered: 4.3 , 4.4 Exam 4

Homework:

Sec 4.3: 1-6, 8, 10-13
Sec 4.4:  3, 9, 10, 11

Week 9 (March 8)

Sections covered: 5.1, 5.2, 5.3,
Videos: |$y'-y=0$ | $y''+y=0$ | $x^2 y''+xy'=e^x-1$ | $y''-x y=0$ |

Homework:

Sec 5.1:  2,  7,  10,   13, 15,  18, 19, 21, 22, 23
Sec 5.2: 1, 3, 7,  9, 10, 11, 12a, 20
Sec 5.3: 1,   6, 10,  14, 15, 16

Week 10 (March 15)
- Sections covered: 5.4, review, Exam 5
- Homework:
```
Sec 5.4: 1, 3, 5, 12, 15
```
Week 11 (March 22) No class Wednesday
- Sections covered: 6.1, 6.2.
- Homework:
```
Sec 6.1: 1, 3, 4(b,c), 7, 12, 13
Sec 6.2: 1-7, 8, 10, 12, 13, 14, 16, 17, 18
```
Week 12 (March 29) Withdrawal deadline is Friday, April 2
- Sections covered: 6.3, 6.4
- Homework:
```
Sec 6.3: 1, 2, 3, 5, 7, 13-16, 21, 23
Sec 6.4: 1, 3, 6, 8, 9,  11(a,b,c), 13, 14
```
Week 13 (Apr 5)
- Sections covered: 6.5, review, Exam 6
- Homework:
```
Sec 6.5: 1, 3, 5, 6, 7, 8,   13, 14
```

Week 14 (Apr 12)

Sections covered: 6.6, 3.7, 3.8

Homework:

Sec 6.6: 4, 7, 8, 9, 12, 13, 14, 15
Sec 3.7: 20, 21 (use Laplace Transform)
Sec 3.8:  13, 14,  16 (use Laplace Transform)

Week 15 (Apr 19) Review, Final Exam: on Thursday, Apr 22

Classroom Procedures/Policies

Communication is a bottle-neck in online classes. Use chat during Webex meetings. Use email, or leave a telephone message outside of class.

For Technology assistance, use Canvas support listed under their Help menu and there is separate WileyPLUS support. Contact the IT@UC Service Desk for general IT issues.

Academic Integrity Policy

The University Rules, including the Student Code of Conduct, and other documented policies of the department, college, and university related to academic integrity will be enforced. Any violation of these regulations, including acts of plagiarism or cheating, will be dealt with on an individual basis according to the severity of the misconduct.

Academic Integrity Policies for Spring 2021

Pandemic-adjusted policies for this section of the Differential Equations course.

Allowed

All assignments, homeworks, projects, exams, quizes are open book and open notes.

You may use computer software and computer search. If your solution is not a paper-and-pencil work, you must provide information about the software that you used.

You may discuss your homeworks or projects with other students, provided any help you received is described and acknowledged by name in your submission, and you did not merely copy their work.

Disallowed

You may not communicate with other people while taking online quizzes and exams.

You may not submit someone's work as your own.

Presenting some else work as your own, whether you paid for it, got it for free, or just found somewhere, is simply not acceptable. In particular, you may not hire others to take your exams for you, or to purchase your submissions. Submitting as your own a work done by a tutor also falls under plagiarism and is not acceptable.

Students are expected to review and follow the UC Faculty Senate policies on Attendance, Class Cancellation, Academic Integrity, Accessibility, Title IX , Counseling Services

Safety

For public health updates see https://uc.edu/publichealth.html

For weather closures, see UC Status page: http://www.uc.edu/alert.html

Syllabus is subject to change
This syllabus may be updated with additional information as it becomes available. Please refresh your browser to make sure that the updates are visible. Revision date appears at the top and at the bottom of this page.