M 274 Intro to Differential Equations Summer 2018

Textbook:  Fundamentals of Differential Equations by Nagle, Saff, and Snider, 9th Edition

Note, if you have the 8th Edition, it will work but will be slightly inconvenient.

• Section 1: May Start - Rob Malo - Wilson 1-144
• Section 2: May Start - Ryan Grady - Wilson 1-134

Prerequisite: M 172 or M 182

Schedule:The tentative schedule is available here - Last updated 9 May.

Solutions:Solutions to in-class work, collected homework, quizzes, and exams can be found here.

Grades: Your percentage in the course will computed from the following.

• Collected Homework (10%)
• Quizzes (10%)
• Exam 1 (20%) - Monday 21 May, 9-10:45.
• Exam 2 (20%) - Tuesday 29 May, 9-10:45.
• Exam 3 (20%)  - Monday 04 June, 9-10:45.
• Final Exam (20%) - Thursday 07 June, 2-3:45.

Your overall percentage will be converted to a letter grade by the following chart. 

Homework:  Homework problems will be assigned daily and collected at the beginning of the next morning session. Late homework will not be accepted.

Suggested Exercises:   It is HIGHLY RECOMMENDED that you do all the suggested exercises. This course moves fast, and the best way to learn the material is to practice the problems. To incentivize doing the suggested exercises, we will give you back missed points, up to 20% of the value of the associated homework assignment, if you attach a complete set of ORGANIZED AND NEATLY WRITTEN suggested exercises for the section(s).  Incomplete and/or disorganized work will receive an arbitrary value between 0% and 20%.  Suggested Exercises are listed below.

Quizzes:  There will be quizzes given most days at the beginning of the afternoon session, see the tentative schedule.  The lowest score will be dropped.

Exam policies:

• You are responsible for all prerequisite information, this is a partial list.
• No electronic devices allowed.
• No outside notes allowed.  An equation sheet may be provided.

Accommodations:

• If you need special accommodations, please contact your instructor as soon as possible.

Expectations:

• Attendance & Engagement
  • Plan for 40 hours of work per week for a 4-credit class. Take only one class at a time.
  • Missing one class will be equivalent to missing a week’s worth of material. Demanding work or family commitments as well as travel or vacation plans that limit your attendance will greatly hinder your ability to succeed. We want you to do well! If you can’t commit to every class session, consider that the 4-week session won’t work for you.
• Working Session (The time formerly known as lunch)
  
  • During the three hours between sessions, we expect that you will be doing the following (in addition to taking a lunch break):
  • Reviewing your returned homework;
  • Preparing for the afternoon quiz;
  • Stopping by office hours if you have questions;
  • Working on the new homework assignment;
  • Reading the textbook to prepare for the afternoon lecture; and
  • Working/Reviewing with your peers.
• Productive Study Habits
  • Keep up with assigned work and reading. The course pace will cover a week in each day.
  • Be on time for class.
  • Use weekends to practice problems and think about concepts from the entire past week.
  • Take advantage of your instructor’s office hours.
  • Redo problems from returned homework and quizzes that you missed, and talk to your instructor about them.
  • Trade contact information with classmates. Arrange homework and study groups before and after class.
• Illness
  • What to do in the case of illness? Contact your instructor right away. In some cases, we can make an attendance recovery plan. University policy allows for W and I grades in other circumstances.

MLC:  The Math Learning Center will have the following schedule. Be aware that the majority of the tutors will not have experience with M 274. Your first stops for help should be your peers or instructor. MLC hours are as follows:

• Mondays – Thursdays: 3-7pm
• Fridays: 9am-4pm
• Saturdays: Closed
• Sundays: 11am-6pm (closed 5/27)

Academic Misconduct: Cheating and other forms of misconduct will be taken seriously, see University policy regarding misconduct.

Suggested Exercises: This is a minimal suggested list, if you are having problems, you should be doing additional exercises.  Homework is listed for both versions of the text.  Note that many of the odd problems in the 9th Edition were even problems in the 8th Edition.

Learning Outcomes.

Upon completion of the course students will have demonstrated an understanding of the following:

1. Classifications of ordinary and partial differential equations, linear and nonlinear differential equations.

2. Solutions of differential equations and initial value problems, and the concepts of existence and uniqueness of a solution to an initial value problem.

3. Using direction fields and the method of isoclines as qualitative techniques for analyzing the asymptotic behavior of solutions of first order differential equations.

4. Using the phase line to characterize the asymptotic behavior of solutions for autonomous first order differential equations.

5. Classification of the stability properties of equilibrium solutions of autonomous first order differential equations.

6. Separable, linear and exact first order differential equations.

7. Substitution and transformation techniques for first order linear differential equations of special forms. These include Bernoulli and homogeneous equations.

8. Mathematical modeling applications of first and second order differential equations.

9. Methods for solving second order, linear, constant coefficient differential equations. (includes both homogeneous and nonhomogeneous equations)

10. Some techniques for solving second order, linear, variable coefficient differential equations. (includes Variation of Parameters, Reduction of Order and Variable Substitutions for Euler equations)

11. The principal of superposition for linear differential equations.

12. Basic theory of nth order linear, constant coefficient ordinary differential equations.

13. The method of Laplace Transforms for solving first and second order, linear ordinary differential equations.

14. Using Unit Step (Heaviside) and Dirac Delta functions to model discontinuous, periodic and impulse forcing functions for first and second order, linear ordinary differential equations.

15. Using Laplace Transforms to solve linear differential equations containing Unit Step (Heaviside) and Dirac Delta functions.

16. Basic matrix methods for linear systems of ordinary differential equations.
    Phase planes for linear systems of ordinary differential equations.

17. Existence and uniqueness of solutions for initial value problems taking the form of linear systems of ordinary differential equations and corresponding initial conditions.