Math 0290: Differential Equations
Instructor: Catalin Trenchea
Lectures: MWF 1:15-2:05PM,
630 William Pitt Union
or virtually via Zoom (meeting ID info on Canvas Announcements)
Tuesday and Thursday 2:00pm-3:00pm, and by appointment
(also via zoom)
Office: Thackeray 606
Phone: (412) 624-5681
Differential equations represent an important branch of mathematics.
Many of their properties have been understood mathematically and they have a history of being successfully applied to important problems
in all areas of science and engineering.
This course will introduce primarily linear, first-order, and second-order differential equations.
Solution techniques for separable equations and homogeneous and inhomogeneous equations as well as a range of
modeling-based applications arising in the context of engineering, physics and chemistry will be presented.
The application of Laplace transforms to differential equations, systems of linear differential equations, linearization of nonlinear systems,
and phase plane methods will be covered.
Fourier series, a useful tool in signal processing, will also be introduced, and we will discuss how the Fourier series arises in
solving the famous heat equation by separation of variables.
The idea of approximating and visualizing solutions using a computer, such as with Matlab, will be introduced early in the term and
students are expected to use Matlab as a resource in their work for this course.
The University has adopted the
Flex@Pittteaching model for this semester, and instruction will vary in form
depending on the University’s current operational posture. The bullet points below outline how this strategy will typically
be implemented in this course, but your instructor may choose to tailor the plan to fit your section,
so consult your instructor’s specific directions on Canvas.
Elevated Risk and High Risk postures, all instruction will be conducted remotely, and there will be no in-person class meetings. Typically this means your instructor will hold virtual class meetings through Zoom at the scheduled class time, and the links to join these synchronous meetings will be posted in Canvas. The class meetings will be recorded, uploaded to Panopto, and made available for viewing through Canvas.
In the Guarded Risk posture, students will have the option to participate remotely or attend in-person class meetings in their section’s assigned classroom at the scheduled class time. However, some sections may not have been assigned a classroom and will only be forced to meet remotely instead. Other sections may be assigned a classroom whose capacity with social distancing will permit only a portion of the students to attend on any given day. In that case, your instructor will divide the class into student cohorts, and each cohort will be assigned days that it is permitted to attend the class in person. No student will be required to attend the in-person meetings. Your instructor may choose to teach in-person, in which case the classroom will be recorded and connected to Zoom so that students participating remotely will be able to join the class meeting synchronously or watch the recorded session at a later time. Your instructor may also choose to teach remotely, in which case they will be connected to the classroom through Zoom, and students will be able to attend the class in-person (on their cohort’s assigned days) or remotely. Your instructor will communicate the details of their plan through Canvas.
During the week of August 19, 2020, all instruction will be conducted remotely, regardless of the University’s operational posture.
Polking, Boggess and Arnold, Differential Equations with Boundary Value Problems,
second edition, Pearson Prentice-Hall.
There is a link in Canvas which includes the purchase of the electronic version of the textbook onto your tuition statement if you do not `opt out'. This purchase offers more than what is necessary. The only requirement to this course is the textbook. Students may choose to use the first edition of the text or a used second edition, which may be available at a lower cost. If you wish to do that, you should choose the `opt out' option prior to the add/drop deadline and visit http://calculus.math.pitt.edu and click the Textbook information link.
Tutoring: The Mathematics Department offers a free tutoring service.
Math Assistance Center (MAC) is located on the second floor of the O’Hara Student Center.
Tutoring services and tutoring hours will be posted outside the MAC as well as on the web at MAC.
Your course grade will be determined as follows:
Two midterm exams 40% (20% each), Final exam 40%, Homework 20%.
Weekly homework assignments will be collect at the beginning of the lecture every Monday.
The assignment grade will be 20% of the course grade.
Midterm Exams: There will be two in class midterm examinations given. The second midterm will not be cumulative to the first. In other words, the second midterm will only cover course material not covered by first midterm exam. Each midterm exam grade will be 20%(x2) of the course grade.
Final Exam: The final exam grade will be 40% of the course grade and will take place during exams week. Your course grade will not exceed your final exam grade by more than one letter grade.
A/A-:90-100%, B/B±: 80-89%, C/C±: 70-79%, D/D+: 60-69%, F: < 60%
Some sections may deviate slightly from this recipe. Any deviations will be
announced by your instructor at the beginning of the term.
MATLAB component: The study of differential equations often uses computer algorithms to gain solutions to relevant problems in physics,
biology, chemistry, and engineering.
Several assignment problems will taken from the problem sets in the MATLAB supplemental textbook.
These problems will be of use to the student in both acquiring a visual sense of differential equations and their solutions,
as well as give an introduction into standard-practice techniques currently used in many disciplines.
Students are required to complete the homework problems; very few students can learn this material without constant practice.
Students are welcome to work together on homework.
However, each student must turn in his or her own assignments, and no copying from another student's work is permitted.
Deadline extensions for homework will not be given.
Students are encouraged to discuss with your professor about homework problems if you'd like additional feedback.
Final Exam Policy
All day sections will take a departmental Final Exam
12/1/2020, Tuesday at 8:00AM - 9:50AM, WEB based.
Since many assessments could be administered online, proctoring might be done via ZOOM and a video connection will be required.
Final Grade Policy
Your final grade should not exceed your final exam grade by more than
one letter grade.
Your instructor will announce his office hours.
Disability Resource Services
If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your
Disability Resources and Services (DRS),
140 William Pitt Union, 412-648-7890,
firstname.lastname@example.org, (412) 228-5347 for P3 ASL users, as early as possible in the term. DRS will verify your disability and determine reasonable accommodations for this course.
The University of Pittsburgh Academic Integrity Code is available at https://www.provost.pitt.edu/faculty/academic-integrity-freedom/academic-integrity-guidelines.
The code states that
" A student has an obligation to exhibit honesty and to respect the ethical standards of the academy in carrying out his or her academic assignments."
The website lists examples of actions that violate this code. Students are expected to adhere to the Academic Integrity Code, and violations of the code will be dealt with seriously.
On homework, you may work with other students or use library resources,
but each student must write up his or her solutions independently.
Copying solutions from other students will be considered cheating,
and handled accordingly.
This is especially notable during this Flex period. Cheating/plagiarism will not be tolerated.
Students suspected of violating the University of Pittsburgh Policy on Academic Integrity will incur a minimum sanction of a
zero score for the quiz, exam or paper in question.
Additional sanctions may be imposed, depending on the severity of the infraction.
Please note, in particular, that Pitt has a data sharing arrangement with Chegg.com that enables us to identify in- stances in which Chegg.com has been used to cheat on assessments. Consequences of being caught in this academic integrity violation have included zero scores on assessments and F grades for the course.
Health and Safety
In the midst of this pandemic, it is extremely important that you abide by public health regulations and
University of Pittsburgh health standards and guidelines.
While in class, at a minimum this means that you must wear a face covering and comply with physical distancing requirements;
other requirements may be added by the University during the semester.
These rules have been developed to protect the health and safety of all community members.
Failure to comply with these requirements will result in you not being permitted to attend class in person and could
result in a Student Conduct violation. For the most up-to-date information and guidance, please visit
coronavirus.pitt.edu and check your Pitt email for updates before each class.
Diversity and Inclusion
The University of Pittsburgh does not tolerate any form of discrimination, harassment,
or retaliation based on disability, race, color, religion, national origin, ancestry, genetic information, marital status,
familial status, sex, age, sexual orientation, veteran status or gender identity or other factors as stated in the
Title IX policy.
The University is committed to taking prompt action to end a hostile environment that interferes with the University’s mission.
For more information about policies, procedures, and practices, see:
To ensure the free and open discussion of ideas, students may not record classroom lectures, discussion and/or activities not already recorded by the instructor, without the advance written permission of the instructor, and any such recording properly approved in advance can be used solely for the student’s own private use.
Lectures will be recorded by the instructor, and this may include student participation. Students are not required to participate in the recorded conversation. The recorded lecture may be used by the faculty member and the registered students only for internal class purposes and only during the term in which the course is being offered.
Recorded lectures will be uploaded and shared with students through Canvas.
Some of the materials in this course may be protected by copyright.
United States copyright law, 17 USC section 101, et seq., in addition to University policy and procedures,
prohibit unauthorized duplication or retransmission of course materials.
See the Library of Congress Copyright Office
University Copyright Policy.
Schedule and practice problems
Approximate schedule for lectures. References of the form a.b refer to sections in the main textbook.
(For midterms and final exams from previous years, please look at
Eugene Trofimov's webpage.)
Introduction to Differential Equations (DE)
Number 1-11. Homework: 1,2,5,7,11
Number 1-6, 12-15. Homework: 1,3,5,12,13,15
and computer tools including Matlab
Number 1-5 Homework: 3,5
Number 1-9. Homework: 5, 23
6.3 Number 1-6, 11-13.
Modeling, linear first-order equations
Number 1-22, 23-29, 33-35 Homework: 3,5,9,33
Number 1-10 Homework: 9
Number 1-21 Homework: 5,15,19
Modeling (cont.), second order equations
Number 1-7, 9-10 Homework: 5, 9b
Number 1-19 Homework: 1,3,5,7,11
Number 1-20, 26-30 Homework: 1,3,9,17
Second order equations (cont.), harmonic motions
Number 1-36 Homework: 1,9
4.3 (cont) Number 1-36 Homework: 17,35
Number 1-12, 14-16, 18 Homework: 1,7
Inhomogeneous second order equations
Number 1-29 Homework: 1,5,11
4.5 (cont.) Number 1-29 Homework: 15,19
Number 1-10 Homework: 1,3,5
Forced harmonic motion,
Midterm 1, Laplace Transform
Number 3-11 Homework: 3,11
Number 1-29 Homework: 7,13,15,29
Laplace Transform (cont.)
Number 1-41 Homework: 5,11,19,29
Number 1-36 Homework: 3,7,11,19
Number 1-26 Homework: 7,11,21
Laplace Transform (cont.)
Number 1-25 Homework: 1,3,11,17
Wednesday: Student Self-Care Day (no classes)
Number 1-9 Homework: 2,3,5,7
Laplace Transform (cont.), Systems of differential equations
Number 4-24 Homework: 6,8,10
Number 1-16 Homework: 5,7,13,15
Number 1-6, 13-16 Homework: 11,13,15 (use pplane.jar)
Systems of differential equations, Constant coefficient homogeneous 2x2 systems
Number 1-6 Homework: 1,3,5
Number 1-8, 16-23 Homework: 3,5,17,19
Number 1-27, 58-61 Homework: 3,13,15,59
Midterm 2, nonlinear systems
Number 20-23 Homework: 21
Number 1-16 Homework: 3,7,15
Number 1-22 Homework: 5,7,13,17
Number 1-32 Homework: 3,7,19,31
Number 1-11 Homework: 3
Separation of variables for the Heat equation, Review
13.2 Number 1-18