 Winter 2020
Syllabus Description:
General informationInstructor: Eli Shlizerman, shlizee@uw.edu Lectures: MWF 10:3011:20 in CSE2 G10 Office hours (LEW 230D): M 1:002:00 T 4:005:00
TA: Bea Stollnitz, bsto@uw.edu M 2:003:00 W 2:003:00 
Course description
An introductory survey of ordinary differential equations, linear and nonlinear equations, Taylor series, Laplace transforms, and linear systems of ODEs. Emphasizes formulation, solution, and interpretation of results. Examples drawn from physical and biological sciences and engineering.
Prerequisites
Proficiency in manipulation of algebraic equations and methods of differentiation and integration at the level of MATH 124 & 125 are required.
Textbook
W.E. Boyce & R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems.
The text is not required, but obtaining some edition of it is to use as a reference is strongly recommended.
Additional: Lecture Notes from a previous iteration of the course available here.
I will post my written notes after each lecture, see Course Schedule page.
Suggestion box
If you have a suggestion or any comments on anything related to the course that you do not feel comfortable bringing up with me in person, I have created an anonymous suggestion survey. I urge you to bring issues to my attention sooner rather than later. I'll do my best to address your concerns in a timely manner.
The survey can be accessed here.
Examinations
There will be three inclass examinations and a final, tentatively scheduled as follows:
 Exam 1: Friday, January 24 (week 3)
 Exam 2: Monday, February 10 (week 6+)
 Exam 3: Friday, February 28 (week 9)
 Final: Monday, March 16, 8:3010:20AM (finals week)
Each inclass exam will contain questions from every key skill previously covered in class, giving you multiple opportunities to demonstrate mastery. For example, if exam 1 covered skills 24, then exam 2 could have questions from skill 310 (skill 2 is only available through exam 1). The final will include questions from all key skills apart from skill 2.
In addition to the inclass examinations, I will also schedule weekly onehour sessions outofclass for you to attempt to demonstrate mastery. At the end of each week I will put up an optional poll where you can specify which key skills you would like to be tested on and choose from a list of possible times. I will select the time that works for most people and a room is available. There will be no testing sessions on the weeks when we already have inclass exams (weeks 3, 6, and 9).
No calculators, computers, collaboration, or cheat sheets will be allowed on exams.
Grades
In this course, we will use a masterybased approach. Associated with the class are 14 key skills. Successful students should demonstrate mastery of all of them by the end of the quarter. Your grade is determined by the number of key skills you master during the course.
Number of mastered skills  Grade 
14 
4.0 
13  3.9 
12  3.8 
11  3.7 
10  3.6 
9  3.4 
8  3.2 
7  3.0 
6  2.5 
5  2.0 
4 and below  0.0 
The examinations are your opportunity to demonstrate mastery of the skills. Problems on the examinations will be labeled with corresponding key skills. You need only demonstrate mastery in a particular area once. You may attempt to demonstrate mastery multiple times. You will not, in general, be penalized for when a skill is mastered.
Key skills

Homework
 Demonstrating mastery in this category requires earning a satisfactory grade on all homework assignments (see below for what constitutes a satisfactory grade).

Prerequisite knowledge (must be satisfied by or on the first exam)
 Derivatives: Students are able to differentiate common functions and combinations of common functions using the following techniques.
 Derivatives of common functions
 Product/quotient rule
 Chain rule
 Integration techniques: Given an integral, student is able to both identify the appropriate method and correctly apply the method to solve it. Students are expected to be familiar with the following methods.
 Antiderivatives of common functions
 (U) Substitution
 Integration by parts
 Partial fractions
 Students can perform algebraic manipulations (this includes properties of fractions, exponentials, radicals, and logarithms)
 Derivatives: Students are able to differentiate common functions and combinations of common functions using the following techniques.

Fundamental ODE knowledge (mandatory)
 Student is able to identify ODEs and initial value problems
 Student is able to determine whether a given function is a solution of a differential equation
 Student can classify differential equations based on their linearity, coefficients, dimension, order, type (ordinary vs. partial), and homogeneity
 Student can distinguish between explicit and implicit solutions to ODEs

Direction field analysis
 Student is able to derive the direction filed formula for a first order ODE
 Student is able to compute the direction field for values of interest
 Student can interpret the direction field of a first order ODE
 Student can identify equilibrium points of a firstorder autonomous ODE and classify their stability
 Student is able to draw a qualitatively correct phase line diagram for firstorder autonomous ODE

Phase plane analysis
 Student is able to compute nullclines and equilibrium points for firstorder 2D autonomous ODE
 Student is able to draw a qualitatively correct phase plane diagram for a given 1O 2D ODE
 Student can identify directions of nullclines
 Student can qualitatively interpret the solution of 1O 2D ODE based on the phase plane

Solving firstorder ODEs
 Student can solve a first order ODE using one of the methods from class: method for separable equations, integrating factor, method for exact equations, or substitution

Secondorder linear equation theory
 Student is able to distinguish between homogeneous, particular, and general solutions to an ODE and explain the differences between them
 Student is able to explain the superposition principle and use it to find a general solution
 Student can determine whether or not two functions are linearly independent using the Wronskian or another technique
 Given one solution to a second order linear ODE, student is able to use Abel's theorem/reduction of order to obtain a second linearly independent solution

Systems of ODEs

Student can express highorder linear differential equations as a system of firstorder differential equations
 Student can solve systems of linear constantcoefficient ODEs.


Ansatz
 Student can use an ansatz to solve a differential equation

Variation of parameters
 Student can use variation of parameters to solve second order linear constant coefficient ODEs

Series solutions
 Student can identify ordinary points of an ODE
 Student can find a series solution for a given ODE

Laplace transform
 Student can use the Laplace transform and its fundamental properties to solve second order linear constant coefficient differential equations

Mathematical modeling
 Given a description of a physical system or phenomenon, student is able to construct a differential equation which models it

Identifying appropriate solution technique for ODEs
 Given an ODE, student is able to identify an applicable solution technique or recognize that none of the techniques discussed will work
The fine print:
 In order to obtain a passing grade, students must demonstrate mastery in skill 3, i.e. skill 3 is mandatory.
 Students will only be allowed to demonstrate mastery in skill 2 during the first three weeks of class (up to and including exam 1). Also homework 1, 2 that primarily focus on skill 2 will have a passing grade of 16/18pts. If you have difficulties with these assignments consider to fulfill the prerequisites first and take the course in the future.
Homework
Weekly homework assignments will allow students to practice the skills presented in class. Homework assignments will typically be assigned on Wednesdays and will be due a week later.
Homework must be submitted as a single PDF file , legible writing, and portrait mode on canvas.
Collaboration: Collaboration is encouraged, but every student must submit their own assignment consisting of their own work. Below is a reminder of the UW policy on academic misconduct. Please discuss with me or one of the TAs if you have concerns about what constitutes misconduct.
Late assignments: No late assignments will be accepted for any reason. In the rare event of an emergency, with sufficient documentation, a homework will be dropped.
Scoring: Each homework assignment will be graded for completeness, with a few problems selected at random to be graded for correctness. Students are urged to treat each problem seriously, as it is possible that any problem will be graded for correctness. Each homework is worth 18 points, and you need 132 points to earn skill 1, which is an average of 14.67 per homework.The TA will take completeness, presentation (showing work, clarity), approach and correctness of the final answer into account in grading your assignments.
Attendance
Attendance is not recorded nor taken into consideration in grades. However, it is highly recommended that students attend lecture to keep up with the material.
Policy on Academic Misconduct
It is essential that students in fulfillment of their academic requirements and in preparation to enter their profession shall adhere to the University of Washington’s Student Code of Conduct. Any student in this course suspected of academic misconduct (e.g., cheating, plagiarism, or falsification) will be reported to the University’s Office of Community Standards and Student conduct.
University of Washington Religious Accommodations Policy
Washington state law requires that UW develop a policy for accommodation of student absences or significant hardship due to reasons of faith or conscience, or for organized religious activities. The UW’s policy, including more information about how to request an accommodation, is available at Religious Accommodations Policy (https://registrar.washington.edu/staffandfaculty/religiousaccommodationspolicy/). Accommodations must be requested within the first two weeks of this course using the Religious Accommodations Request form (https://registrar.washington.edu/students/religiousaccommodationsrequest/).