# MA 320 Differential Equations

### Syllabus

handouts syllabus pdf flier photographs

## Office Hours

Monday 1-2, Thursday 4-5, Friday 2-4 (no appointment necessary). Feel free to make an appointment if you cannot come to my regular office hours.

## Textbook

No textbook required. Handouts with new material and practice problems will be distributed for each teaching unit.

## 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. Direction field.
4. Numerical solutions. Euler's method.
5. Linear differential equation.
6. Homogeneous diff. eq. Bernoulli diff. eq.
7. Autonomous differential equations.
8. Modeling with differential equations.
9. Exact equations.
(Exam 1)

10. Second and higher order equations.
11. Solving homogeneous higher order linear equations.
12. Nonhomogeneous equations: variation of parameters.
13. Nonhomogeneous equations: the method of undetermined coefficients.
(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 5th 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 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

3

## Prerequisites

Calculus 2 or the permission of instructor.

## Attendance

It is imperative that students attend all classes. 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.

## 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 the proficiency in solving differential equations,
• acquire knowledge of various mathematical concepts and models involving differential equations,
• acquire knowledge of modeling techniques required for successful application of mathematics,
• demonstrate the use of differential equations in problem solving,
• demonstrate a proficiency in using mathematical software,
• know how to use appropriate technology and mathematical software to solve problems involving differential equations.

Academic integrity is at the center of the educational experience at USciences. Students are therefore expected to uphold the highest standards of academic integrity and not engage in or 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 USciences Student Handbook. Adheren ce 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

USciences 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 Administrator of Student Accommodations at 215-596-8758.

## Mental Health Wellness Statement

USciences 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 USciences 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.