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Tu+Th 9:30AM - 10:50AM FRENCH-W 4221 | File https://homepages.uc.edu/~brycwz/classes/2073/ revised 03/25/2025 23:57:33

Ordinary Differential Equations

Spring Semester 2025

Link to online lectures in Spring 2021

PDFs: Answer keys are posted in the module "Online Resources" on Canvas.

Instructor: Wlodek Bryc
Office: French Hall West, Room 4316 | Office Hours |
E-mail: brycwz@ucmail.uc.edu
Phone: (513) 556-4098 (leave a message)

Textbook:

Elementary Differential Equations by Boyce and DiPrima 12E (e-book may be accessed through WileyPlus) WileyPLUS video for student registration

Technology.
No books, notes, calculators and/or other electronic devices are allowed on in-class exams unless explicitly noted. To check your answers at home, you may 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.

Pre-requisites: Calculus: derivatives and integrals of functions of one real variable, sequences and series, partial derivatives of functions of two variables. Determinants of matrices.
Baccalaureate Competency:

CT Critical Thinking
QR Quantitative Reasoning

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; 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.
Reduce a system of two equations of order one to a single equation of second order and solve the system.

Exams and important dates. See also UC Academic Calendars

Cumulative Exams during class time. (No makeups!)
- Exam 1: Th, Feb 6
- Exam 2: Th, Feb 27
- Exam 3: Th, March 13
- Exam 4: Th, April 3
- Last day to withdraw: ??
Final Exam:Thursday, May 1 8:00 am-10:00 am

Technology and Calculators Policy on Exams: No books, notes, calculators and/or other electronic devices are allowed on in class exams and quizzes unless explicitly noted.

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:

Quizzes/Homework 20%
Exams 60%
Final 20%

Withdrawal policy: You will need to take at least one quiz/exam 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 14)

Sections covered: Ch 1, 2.1, 2.2, 2.3 SelfQuiz | (1.1) | (1.2) | 2.1/2.2| $y'(0)=?$ |

Suggested 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, 20, 21
    Sec. 2.2:   1-3, 6, 11, 12, 14, 21, 23, 25, 29, 31
    Sec. 2.3:   1,2, 3, 5, 6, 7, 12

Week 2 (Jan 21)

Sections covered: 2.3, 2.4, 2.5, SelfQuiz |(banking)| (2.3 all) |

Suggested Homework:

Sec. 2.3: 1, 3, 6, 7, 12, 15
Sec 2.4:  13, 14, 15
Sec 2.5: 1,2 (solve), 5, 8 (solve), 21, 22, 25 (solve), 27

Week 3 (Jan 28)
- Sections covered: 2.5, 2.6 SelfQuiz |(2.5) | (2.6 -exact) | Integrating factor $\mu(x)$ or $\mu(y)$ )|
- Suggested Homework:
```
Sec 2.6: 1-5, 7, 10, 12, 16, 18-21
    
```
Week 4 (Feb 4)
- Sections covered: Exam 1, 3.1 SelfQuiz| 3.1a | 3.1b|
- Suggested Homework:
```
Sec 3.1: 1, 5, 12, 13,  16, 17
      
```

Week 5 (Feb 11)

Sections covered: 3.2, 3.3, 3.4 SelfQuiz |3.2|3.2b|3.3 | 3.4|

Suggested Homework:

Sec 3.2:  4, 6, 7, 11, 17, 19, 23, 25, 27
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 note their behavior for increasing time $t$),  12, 18, 21, 26

Week 6 (Feb 18)
- Sections covered: 3.5, 3.6, damping demo SelfQuiz | 3.5 a| 3.5 b|3.7a| 3.7damped |
- Suggested Homework:
```
Sec 3.5: 1-15
Sec 3.6: 1, 5, 13, 24
    
```
Week 7 (Feb 25)
- Sections covered: 3.7. Exam 2 SelfQuiz |4.1| 4.2 |
- Suggested Homework:
```
Sec 3.7: 1, 2, 8
  
```

Week 8 (March 4)

Sections covered: 4.1, 4.2, 4.3 SelfQuiz | 4.3 | 4.4-B |

Suggested Homework:

Sec 4.1: 2, 6, 9, 16
Sec 4.2: 1, 3, 6, 9, 13, 14, 16, 20, 21, 22
Sec 4.3: 1-6, 8, 10-13

Week 9 (March 11)
- Sections covered: 4.4 , 5.1 Exam 3 SelfQuiz |5.1|
- Suggested Homework:
```
Sec 4.4:  3, 9, 10, 11
Sec 5.1:  2,  7,  10,   13, 15,  18, 19, 21, 22, 23
```
Spring Break: no classes March 17-21
Week 10 (March 25)
- Sections covered: 5.2, 5.3, SelfQuiz|5.2 |
- Videos: | $y'-y=0$ | $y''+y=0$ | $x^2 y''+xy'=e^x-1$ | $y''-x y=0$ |
- Suggested Homework:
```
Sec 5.1:  2,  7,  10,   13, 15,  18, 19, 21, 22, 23
Sec 5.2: 1, 3, 7,  9, 10, 11, 12a
Sec 5.3: 1,   8a, 10,  14, 15, 16
```
Course checkpoint. The topics below may need adjustment to match the actual pace of the course
Week 11 (April 1)
- Sections covered: 5.4, Exam 4 SelfQuiz|5.4|
- Suggested Homework:
```
Sec 5.4: 1, 3, 5, 9, 12, 15
```

Week 12 (April 8)

Sections covered: 6.1, 6.2, 6.3 SelfQuiz | 6.1/6.2 |6.3/6.4|

Suggested 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
Sec 6.3: 1, 2, 3, 5, 7, 13-16, 21, 23

Week 13 (Apr 15)

Sections covered: 6.4, 6.5, 6.6 SelfQuiz|6.4 |6.5|

Suggested Homework:

Sec 6.4: 1, 3, 6, 8, 9,  11(a,b,c), 13, 14
Sec 6.5: 1, 3, 5, 6, 7, 8,   13, 14
Sec 6.6: 4, 7, 8, 9, 12, 13, 14, 15

Week 14 (Apr 22)
- Sections covered: 3.7+3.8. Review. SelfQuiz |6.6| Final Exams: | 2018 [ans] | 2019 [ans] |
- Suggested Homework:
```
Sec 3.7: 20, 21 (use Laplace Transform)
Sec 3.8:  13, 14,  16 (use Laplace Transform)
```
Week 15 -- final exam week (April 28-May 2).

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.

Tutoring Students may schedule appointments online at the Learning Commons site: https://www.uc.edu/learningcommons.html or by contacting the Learning Commons at (513) 556-3244.

Drop-in tutoring is offered for this course by the Math and Science Support (MASS) Center. You can find the schedule and more information about the MASS Center at https://www.uc.edu/learningcommons/masscenter.html.

Safety

UC Night Ride is a student organization that provides any UC student, faculty, or staff member transportation to the neighborhoods around campus after dark. The phone number is 513-556-RIDE (7433)

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.

https://homepages.uc.edu/~brycwz/classes/2073/ revised 03/25/2025 23:57:33