# MA 320 Differential Equations

### Syllabus

handouts syllabus pdf flier photographs

## Office Hours

Monday 1-2, Thursday 4-5, Friday 1-3 (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 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 and mathematical software to solve problems involving differential equations.