Differential Equations


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Fall 2023

The classes will be held on the University City campus.
Class times and place: Tue and Th 11:00–12:15 pm in STC 147.

Office Hours

Tue and Th 3:15 pm or at other times by appointment – email me and we will find a time for us to meet. I will be glad to answer all of your questions about the course material, go over some problems together with you, check your assignment work, review together for an exam, or simply discuss course content you may have questions about.


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 9th week of classes
Exam 3: During the 12th 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- B+ B B- C+ C C- D+ D F
grade 93-100 90-92 87-89 83-86 80-82 77-79 73-76 70-72 67-69 60-66 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

Saint Joseph’s University encourages the free and open pursuit of knowledge; we consider this to be a fundamental principle and strength of a democratic people. To this end, SJU expects its students, its faculty, its administrators, and its staff to uphold the highest standards of academic integrity. The University expects all members of the University community to both honor and protect one another’s individual and collective rights.

Student with Disabilities Statement

Reasonable academic accommodations may be provided to students who submit appropriate documentation of their disability. If students have need of assistance or questions with this issue, they are encouraged to contact the Office of Student Disability Services (SDS) at sds@sju.edu or by phone at 610.660.1774. The Office of SDS also provides an appeal/grievance procedure for complaints regarding requested or offered reasonable accommodations. More information can be found at: www.sju.edu/sds.

Health and Wellness Statement

Saint Joseph's University recognizes that physical and mental health strongly impact one's ability to do well in school and in life. As a result, there are many helpful campus resources designed to help students to care for their physical, mental, and spiritual health. Students may experience stressors that can impact both their academic experience and their personal well-being. These may include academic pressure and challenges associated with relationships, mental health, alcohol or other drugs, identities, finances, etc. All of us benefit from support during times of struggle and challenges. If you are experiencing concerns, seeking assistance sooner rather than later is a courageous thing to do for yourself and those who care about you. The resources at https://sites.sju.edu/counseling/ can help you to cope with stress and to achieve your academic and personal goals.