# Differential Equations

### Syllabus

handouts videos syllabus pdf flier photographs

## 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.

## Textbook

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

## Technology

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 3 18% each Final Exam 22% Assignments 12% Projects 12% TOTAL 100%
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

3

## Prerequisites

Calculus 2 or the permission of instructor.

## Attendance

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.

## Exams

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.