## Math 215/255 Section 921 - Ordinary Differential Equations - Summer 2015 T1

Instructor: Malabika Pramanik
Office: 214 Mathematics Building
E-mail: malabika at math dot ubc dot ca
Lectures: Mon, Tue, Fri 1-3pm, Wed 1-2pm
Lecture venue: Room 100 Mathematics Building.
Office hours: Mon, Fri 3-4.
Weekly drop-in tutorials (led by Abenezer T/mariam) : Tue, Fri 11-12 in LSK 301 (math help centre).
TA info : Abenezer T/mariam (abenezer1993@yahoo.com), Christy Choi (munchichi.choi@gmail.com).

### Textbooks

• Required : Notes on Diffy Qs , a free online text by Jiri Lebl.
• Optional : Elementary differential equations and boundary value problems, by Boyce and DiPrima.

Piazza is an online discussion forum, where students can ask and answer questions, with some input from the instructors. Please use the following piazza links for this class as a supplement to traditional office hours. You will need a UBC email address to sign up for Piazza.

### In-class quiz info

• Quiz 1: Friday May 22, 2:20-2:50.
• Syllabus: Sections 0.2, 1.1, 1.2, 1.3, 1.4, 1.6, 1.7.
• Quiz 1 Solutions .
• Quiz 1 stats: Average = 20, 1st quartile = 12, 2nd quartile (median) = 19, 3rd quartile = 28.
• Quiz 2: Friday June 5, 2:20-2:50.
• Syllabus: Sections 2.1, 2.2, 2.4, 2.5, 2.6, 6.1, 6.2, 6.3, 6.4.
• Quiz 2 Solutions .
• Quiz 2 stats: 1st quartile = 15, 2nd quartile (median) = 22, 3rd quartile = 29.
• Quiz 3: Wednesday June 17, 1:10-1:50.
• Syllabus: Sections 3.1, 3.2, 3.3, 3.4, 3.5, 3.9, 8.1, 8.2, 8.3.
• Quiz 3 Solutions .
• Quiz 3 stats: 1st Quartile= 22, 2nd Quartile= 30, 3rd Quartile= 35.

### Final exam info

• The final exam will be held 8:30-11am on June 25 in ESB 1013.
• Review problem sheet .
• Solutions to the review problems.
• Some old exams from previoous offerings of the course. Solutions to these exams will not be posted, but I am happy to provide feedback on your solutions during office hours. Solutions to some of these exams are available at the UBC Wiki page. Some others may be bought from the math club.

### Homework Assignment and online Practice Problems

• Weekly homework assignments will be posted on Webwork . Our course identifier is MATH215-255-921_2015S1. Please pay careful attention to the opening/closing dates of each homework assignment and the maximum number of attempts. Solutions will be made available after the due date of the homework assignment.
• WebWork issues should be reported to the Webwork TA Christy Choi (contact information above).
• Weekly online practice problem sets will also appear on this same site. These are not for marks, but it is strongly recommended that you work through these to solidify your understanding of the material.

### Week-by-week lecture schedule

• This is a tentative schedule only, and will be updated each week as the course progresses. The syllabus for each quiz will be finalized depending on the material covered in lecture.
• The section numbers appearing below refer to those in the online text book. Each section has a set of exercises at the end. You are encouraged to work through these. In-class quizzes will be based on these exercises.
• Week 1 :
• Section 0.2: Introduction.
• Section 1.1: Integrals as solutions.
• Section 1.2: Slope fields.
• Section 1.3: Separable equations.
• Section 1.4: Linear equations and the integrating factor.
• Section 1.6: Autonomous equations.
• Section 1.7: Numerical methods: Euler's method.
• Clicker questions and in-class problem set: Wednesday May 13 , Friday May 15.
• Week 2 :
• Section 2.1: Second order linear ODEs.
• Existence and uniqueness of solutions of second order linear ODE-s
• Linear independence of solutions
• Wronskian
• Section 2.2: Constant coefficient second order linear ODEs.
• Characteristic equation
• Case of real and distinct roots
• Real repeated roots
• Case of complex roots
• Clicker questions and in-class problem set: Wednesday May 20.
• Week 3 :
• Section 2.4: Mechanical vibrations.
• Section 2.5: Nonhomogeneous equations.
• Section 2.6: Forced oscillations and resonance.
• Section 6.1: The Laplace transform.
• Section 6.2: Transforms of derivatives and ODEs.
• Clicker questions and in-class problem set: Wednesday May 27 and Friday May 29.
• Week 4 :
• Section 6.3: Convolution.
• Section 6.4: Dirac delta and impulse response.
• Section 3.1: Introduction to systems of ODEs.
• Section 3.2: Matrices and linear systems.
• Clicker questions and in-class problem set: Monday June 1 and Friday June 5.
• Week 5:
• Section 3.3: Linear systems of ODEs.
• Section 3.4: Eigenvalue method.
• Section 3.5: Two dimensional systems and their vector fields.
• Section 3.9: Nonhomogeneous systems.
• Section 8.1: Linearizations, critical points and equilibria.
• Clicker questions and in-class problem set: Tuesday June 9 and Friday June 12.
• Week 6:
• Section 8.2: Stability and classification of isolated critical points.
• Section 8.3: Applications of nonlinear systems.
• Review