URL MATH 2073-003 DIFFERENTIAL EQNS MoWeFr 1:25 - 2:20 FRENCH-W 4221 MATH 2073-004 DIFFERENTIAL EQNS MoWeFr 2:30 - 3:25 FRENCH-W 4221

Ordinary Differential Equations

Fall Semester 2025

DL version (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:
Phone: (leave a message)

Textbook:

Elementary Differential Equations by Boyce and DiPrima 12E. Use WileyPlus resources link on Canvas to access e-book. WileyPLUS video explains student registration process.

Technology.
No books, notes, calculators and/or other electronic devices are allowed on in-class exams unless explicitly noted. Free programs like Symbolab Online ODE Solver or WolframAlpha are useful to check answers on your homework.

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: Fri, Sept 12
- Exam 2: We, Oct 8
- Exam 3: Fri, Oct 24
- Exam 4: Fri, Nov 7
- Last day to withdraw: Fri, November 21
Final Exam:
see Exam Schedule
- Section 2073-003 Wednesday, December 10 12:30 pm - 2:30 pm
- Section 2073-004 Friday, December 12 12:30 pm - 2:30 pm

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%

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 (Aug 25)

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 (Sept 3) No class on Sept 1.
- 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 (Sept 8)
- Sections covered: 2.5, 2.6, Exam 1 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 (Sept 15)
- Sections covered: 3.1, 3.2, 3.3 SelfQuiz| 3.1a | 3.1b|
- Suggested Homework:
```
Sec 3.1: 1, 5, 12, 13,  16, 17
      
```

Week 5 (Sept 22)

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 (Sep 29)
- 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 (Oct 6) No class Oct 10
- Sections covered: 3.7. Exam 2 SelfQuiz |4.1| 4.2 |
- Suggested Homework:
```
Sec 3.7: 1, 2, 8
  
```

Week 8 (Oct 13)

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 (Oct 20)
- 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
```
Week 10 (Oct 27)
- 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
```
Week 11 (Nov 3)
- Sections covered: 5.4, Exam 4 SelfQuiz|5.4|
- Suggested Homework:
```
Sec 5.4: 1, 3, 5, 9, 12, 15
```

Week 12 (Nov 10)

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 (Nov 17)

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 (Nov 24) No class Nov 28

Sections covered: 3.7, 3.8 (by Laplace transform)

Suggested Homework:

      Sec 3.7: 1, 2, 8,
       Sec 3.7: 20, 21 (use Laplace Transform)
      Sec 3.8: 1, 2, 6, 8, 11
      Sec 3.8:  13, 14,  16 (use Laplace Transform)

Week 15 (Dec 1):
- Sections covered: 6.6, Ch. 7, Review
- Suggested Homework:
```
    Sec 6.6: 4, 5, 7-9, 12-15
    Sect 7.1: 7-9
```
Week 16 (Dec 8) Final Exams week
- Final Exams: | 2018 [ans] | 2019 [ans] |

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

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

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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.