## Math 215 - DIFFERENTIAL EQUATIONS

### HOMEWORK:

 Date Assignment Sep 26 HW1 Sep 30 HW2 Oct 3 HW3 Oct 8 HW4 Oct 10 HW5 Oct 13 HW6 Oct 20 HW7 Oct 24 HW8 Oct 29 HW9 Nov 12 HW10 Nov 14 HW11 Nov 19 HW12 Nov 21 HW13

## SYLLABUS

Math 215 DIFFERENTIAL EQUATIONS
TR 1:30-3:10
SH C173

#### Instructor:

Gary Brookfield
Office: Simpson Tower 210
Office Hours: MTWR 12:00-1:30 or by appointment.
Phone: (323) 343-2164
Email: gbrookf@calstatela.edu

Prerequisites: Math 209.

Textbook: Subramanian and Hendrata, Lecture Notes on Ordinary Differential Equations, 3rd ed. You can buy a paper version of the book from the bookstore or from lulu.com. The price from lulu.com is \$13.99 plus shipping.

Topical outline: Ordinary differential equations with concentration on methods of finding solutions; applications in science and engineering.

Student learning outcomes: Students who successfully complete this course will be able to:

• Use symbolic methods to find general and particular solutions of separable differential equations and first order linear differential equations.
• Construct direction fields and phase lines, and use them, along with the existence-uniqueness theorem, to perform qualitative analysis of first order autonomous differential equations.
• Find explicit general and particular solutions of second order (and possibly higher order), linear, homogeneous differential equations with constant coefficients.
• Use the superposition principle and the method of undetermined coefficients, (or instead, the method of variation of parameters) to find general and particular solutions of second (and possibly higher) order linear, nonhomogeneous differential equations with constant coefficients.
• Use first and second order techniques to analyze classical applications (such as velocity-acceleration models, population models, mixing models; mechanical vibrations, electrical circuits, etc.).
• Use differential operators to solve first order linear homogeneous systems with constant coefficients.
• Use Laplace transforms to solve first and second order initial value problems.
• Use power series to construct the approximate solution of a simple nonlinear differential equation near an ordinary point.

Homework/Quizzes: I will assign homework regularly, but it will not be collected or graded. Instead, most Tuesdays, there will be a 15 minute quiz on the homework from the previous week. Homework and homework solutions will be posted on the web, liked to this page.

Course Material:

• Chapter 1: Preliminaries
• Chapter 2: First Order Linear Equations
• Chapter 3: Higher Order Homogeneous Linear Equations
• Chapter 4: Non-homogeneous Higher Order Linear Equations
• Chapter 5: Linear Equations with Variable Coefficients
• Chapter 6: Power Series Solutions
• Chapter 7: Systems of Linear Equations

Exams: As well as the quizzes, there will be a midterm exam and a final exam:

• Midterm: Tuesday, November 5.
• Final: Tuesday, December 10, 1:30-4:00pm

Grades: Your final grade will be determined from the quizzes and final exam with the following weights:
Quizzes: 25%
Midterm: 25%
Final exam: 50%

ADA statement: Reasonable accommodation will be provided to any student who is registered with the Office of Students with Disabilities and requests needed accommodation.

Academic honesty statement: Students are expected to do their own work. Copying the work of others, cheating on exams, and similar violations will be reported to the University Discipline Officer, who has the authority to take disciplinary actions against students who violate the standards of academic honesty.

Student responsibilities: Students are responsible for being aware of all announcements that are made in class, such as changes in exam dates, due dates of homework and papers, and cancellation of class due to instructor's absence. Students are responsible for announcements made on days that they are absent. Students must check their CSULA email account regularly for information from the instructor and the Department. Failure to do so may result in missed deadlines or other consequences that might adversely affect students. Note that you can forward this email account to any other account of your choosing.