Differential Equations


handouts videos syllabus pdf flier photographs

Fall 2022

The classes will be held on the University City campus.
Class times and place: Wed 3:20–4:35 room TBA, Fri 3:20–4:35 pm in STC 147.

Office Hours

will be by appointment: email me and we will find a time for us to meet.


No textbook required. Handouts with new material and practice problems are available on my website for each topic.


Matlab will be used extensively. All students are also recommended to have a calculator.

Topics Covered

1. First order differential equations. Basic ideas and techniques.
2. Separable differential equations.
3. Linear differential equation.
4. Homogeneous diff. eq. Bernoulli diff. eq.
5. Exact equations.
6. Numerical solutions. Euler's method.
7. Autonomous differential equations.
8. Modeling with differential equations.
(Exam 1)

9. Second and higher order equations.
10. Solving homogeneous higher order linear equations.
11. Nonhomogeneous equations: variation of parameters.
12. Nonhomogeneous equations: the method of undetermined coefficients.
13. Applications of higher order equations.
(Exam 2)

14. The Laplace transform. Definition. Properties.
15. Inverse Laplace transform.
16. Solving linear systems with Laplace transforms.
17. Transforms of discontinuous and periodic functions.
18. Delta function. Convolution.
(Exam 3)

19. Systems of first order differential equations. Phase plane analysis
20. Nonlinear systems of differential equations.
21. Modeling with systems of differential equations. Steady states and stability.
(Final Exam)

Tentative exam dates

Exam 1: During the 4th week of classes
Exam 2: During the 8th week of classes
Exam 3: During the 11th week of classes
Final Exam: During the Finals week.


Exams 1, 2 and 318% each
Final Exam22%
Grades are computed according to the following system:
A+ A A- B+ B B- C+ C C- D+ D D- F
grade 97-100 93-96 90-92 87-89 83-86 80-82 77-79 73-76 70-72 67-69 63-66 60-62 0-59

Number of credits



Calculus 2 or the permission of instructor.


The class lectures will be delivered on campus (at the times listed above). Recordings of the lectures are available for students who miss some classes. To stay on track, it is highly recommended that students attend the classes and use the recordings just for reference.
Students are responsible for all material covered in class, even if attendance is not checked or assignments collected.


There will be three semester exams and a cumulative final exam. No makeup exam will be given unless the excuse for missing the scheduled exam is acceptable to the instructor. Any makeup exam must be taken before the next regularly scheduled exam. No exam grade will be dropped.

Assignments and Projects

There will be three assignments and three Matlab projects during the semester. There will be no makeup assignments. Assignments or projects turned in after their due date will receive an automatic reduction in grade. No assignment or project grade will be dropped.
The projects will focus on numerical solutions using Matlab and applications. Students will be able to install Matlab on their home computers or to use it from a web browser.

Response time

The assignments, projects and exams are typically graded in three days after they are turned in. Special circumstances like snow days, school closing or holidays, may occasionally delay the response time. Barring special circumstances, students’ emails are usually responded to within one working day.

Course Objectives

  • Solve differential equations using various techniques.
  • Identify situations that require the use of differential equations, develop mathematical models involving differential equations and justify their solutions.
  • Use appropriate technology to find and examine solutions of differential equations.

Learning outcomes

Students will:
  • demonstrate proficiency in solving differential equations,
  • develop understanding of various mathematical concepts and models involving differential equations,
  • develop understanding of modeling techniques required for successful application of mathematics,
  • demonstrate the use of differential equations in problem solving,
  • demonstrate proficiency in using mathematical software,
  • use appropriate technology to solve problems involving differential equations.

Academic integrity

Academic integrity is at the center of the educational experience at the SJU. Students are therefore expected to uphold the highest standards of academic integrity and not engage in nor tolerate academic dishonesty. Academic dishonesty includes, but is not limited to, fabrication, cheating or plagiarism, and unauthorized collaboration. Any violation of academic integrity will be investigated and, where warranted, the student will receive appropriate sanctions through the University's Student Conduct Process. Please familiarize yourself with the current Student Handbook. In particular, adherence to the Student Conduct Policy and Academic Integrity Policy will help to ensure that your learning and living experiences are founded on integrity.

Americans with Disabilities Act (ADA) Compliance Statement

SJU supports the educational endeavors of all students, including students with disabilities. ADA defines a disability as a mental or physical impairment that substantially limits one or more major life activities. If you believe that you have a disability that may impact your ability to fulfill your course or degree requirements, and you would like more information on applying for an accommodation under ADA, please contact the Program Coordinator of Student Accommodations who serves as 504 Coordinator.

Mental Health Wellness Statement

SJU encourages students to recognize that academic success requires students to be emotionally and physically well. If you are having difficulty coping with stress associated with the classroom or are experiencing other personal issues, please go to Student Health and Counseling (SHAC) located on the first floor of Whitecar Hall or call 215.596.8536. Additional emotional support is available 24/7 and can be obtained by contacting the National Suicide Prevention Hotline at 800.273.8255 or by texting “Go” to the Crisis Text Line 741-741. The services listed above are all free and confidential.

COVID-19 Syllabus Statement

As we continue to navigate the COVID-19 pandemic it is important to remember that:
· All individuals, regardless of vaccination status, are required to wear masks indoors on campus.
· SJU mandates that all students, faculty, and staff are vaccinated against COVID-19.
· Practice good hygiene by frequently washing hands.
· Conduct a daily health check before coming to campus.
Check the COVID-19 Return to Campus Guidelines regularly for updates. If we all follow the rules, we will help to ensure that our learning environment is as safe as possible.
Students who are ill, regardless of symptoms, vaccination status or or diagnosis, should not come to campus for classes or activities and should contact SHAC. If students are ill, but able to virtually participate in courses they may do so. Students should not contact the Office of Student Health for “sick notes.”
The COVID-19 pandemic has refocused the need for both mental and physical personal wellness. The University encourages students who are ill to take the time to focus on their health. Additionally, if needed students may reach out to their college dean’s office to inquire about leave of absence options including: short-term leave of absence (up to 10 business days), a personal leave of absence, or a medical leave absence. We firmly believe to learn you must be healthy.