Differential Equations - Math 238 South Seattle College
Fall 2014
Rick Downs, PhD
Office: RS 180 Phone: 934-6890 Email: [email protected] Office Hours: Monday – Friday: 9:00 – 9:50 am
Course Website: https://canvas.southseattle.edu/login Prerequisite
You must have completed Math& 152 with a grade of 2.0 or higher; Math& 153 is strongly recommended.
TEXT: Introduction to Differential Equations by Boyce, published by Wiley Custom Learning Solutions, ISBN: 978-1-11991-649-9. The material in this book is from Elementary Differential Equations and Boundary Value Problems, 10th edition by Boyce and DiPrima.
Course Material:
Chapter 1 – Introduction to Differential Equations Chapter 2 – First Order Differential Equations Chapter 3 – Second Order Differential Equations Chapter 6 – The Laplace Transform
Calculator
You are required to have a graphing calculator. If you do not own one, the TI-89 is a good choice. All homework, in-class instruction, and exams will assume you have and can use a graphing calculator.
Overview
This course is an introduction to ordinary differential equations. There are three main aspects we will be concerned with: 1) how to solve them, 2) how to interpret the solutions, and 3) how to use them to solve real world problems.
General Course Objectives
1. Learn to recognize and classify various types of ordinary differential equations. 2. Get used to thinking about and working with functions as “variables”.
3. Understand the qualitative nature of solutions to certain classes of differential equations. 4. Learn to solve certain types of elementary differential equations analytically, with an emphasis on first order and second order differential equations.
5. Develop skill in formulating differential equation models to address problems arising in engineering, physics, and other applied areas.
Learning Outcomes
1. Students will be able to model physical phenomena with first-order differential equations, to solve such equations using analytic, graphical, or numerical methods, and to analyze and communicate the results. Students will display proficiency in this area by demonstrating the following competencies:
a) Identify the order of an ordinary differential equation and determine whether it is linear or nonlinear.
b) Sketch a slope field for a first-order differential equation and sketch solution curves on the slope field.
c) Identify a separable first-order equation and find a family of solutions; find singular solutions.
d) Identify a first-order linear equation and find the general solution using an integrating factor.
e) Solve initial-value problems involving first-order separable, linear, and nonlinear differential equations.
f) Solve application problems involving first-order equations.
g) Use Euler’s Method to approximate the solution of first-order differential equations. 2. Students will be able to model physical phenomena with second-order differential equations, to solve such equations using analytic methods and to analyze and communicate the results. Students will display proficiency by demonstrating the following competencies:
a) Solve a second-order linear homogeneous equation with constant coefficients using the characteristic equation and solve an associated initial-value problem.
b) Solve a second-order linear nonhomogeneous equation with constant coefficients using the method of undetermined coefficients; solve an associated initial-value problem. c) Solve application problems involving second-order equations, including mass-spring
problems.
d) Analyze solutions in terms of steady-state and transient parts and identify solutions demonstrating resonance.
e) Compute the Laplace transform of a function.
f) Use step functions to represent a piecewise-continuous function. g) Solve a linear differential equation using Laplace transforms.
South Seattle College General Education Outcomes Computation
Use arithmetic and other basic mathematical operations as required by program of study Apply quantitative skills for academic and career purposes.
Critical Thinking & Problem-Solving
Think critically in evaluating information, solving problems and making decisions. Technology
Select and use appropriate technological tools for academic and career tasks. Method of Instruction
The method of instruction for this class will be in a format called a flipped classroom. What this means is that for most class periods, you will be required to watch a video before coming to class that will go over the new material that you need to know. When you are watching the video, you need to be sure to write down any questions you have regarding the new material. The scheduled class time will include time to discuss questions arising from the video, active learning activities, and problem solving sessions.
Video Lecture: Watching the video lecture before each class is a fundamental part of the course; you will be responsible for material presented in the video regardless of whether it is discussed in the textbook or in class.
Reading: Reading the sections of the textbook corresponding to material covered in class and the assigned homework exercises is considered part of the homework assignment; you will be responsible for material in the assigned sections regardless of whether it is discussed in the video or in class.
Homework
The homework problems for the class are listed in the Homework document that is on the course website. Homework assignments should be done daily on material covered that day in class. When working out homework problems, be sure to include the section number on the top of each page, and list the problem number of the problem you are working on. Be sure to show all of your work. Your homework is to be turned in on the day of the test for that chapter. Since the purpose of the worksheets and homework is to help you understand the material, if you do not understand a topic after completing the homework, be sure to ask for help.
Specific Homework Policies:
Homework assignments are due in class at 11:00 am on the day assigned. Two points will be deducted if the homework is late. No homework will be accepted after one day past the due date.
Copy the problem in its original form from the book; for long word problems, summarize the problem in your own words.
Provide the solution to the problem. If you are having difficulty with a problem, make sure you get help before the due date. If you still can't complete the problem, do as much as you can.
Staple your pages together and cut off any messy edges. Failure to do so will result in a one-point reduction.
Write neatly!! Project:
The project for this class will be completed in groups of two and will consist of using differential equations to analyze a problem. You and your partner are to pick a topic from a list that I will provide. Each group will present the results of their work with a poster presentation on Dec 2 or Dec 3. Each poster presentation will be peer-reviewed by your fellow students using a rubric that I will provide.
Quiz
There will be one quiz during the quarter. It will cover the material in Chapter 1. Testing
You will be allowed one page (8.5x11 inches, both sides) of handwritten notes to refer to during the exam, which you must turn in with your exam. No calculators, electronic devices, or other assistance will be allowed during the exam. Unless you have a very serious, well documented, and compelling reason to miss an exam, there will be no makeup exams, for any reason.
You may not listen to music during an exam. If you are caught plagiarizing, you will, at a minimum get a zero for the test, and I will write a memo to the dean documenting the case. The dean may assess further penalties such as disciplinary probation, dismissal from this class, or dismissal from South Seattle College.
Grading
Your grade for the course will be based on the following:
Homework 70 points
MATLAB Assignments 40 points
Group Project 80 points
Quiz 80 points
Tests (best 2 out of 3) 200 points
Final Exam 120 points
GPA = 0.08 * P - 3.6
where P is the percentage of the total points that you received. Percentage Numerical Grade
100% 4.0
90% 3.6
80% 2.8
70% 2.0
60% 1.2
58% 1.0
<58% 0
No Credit (NC) Grade:
If you wish to receive an NC (no credit) for the class, you must inform me in writing before the last day of class. An NC or No Credit grade indicates that the student did not fulfill the requirements for receiving a numerical grade in the course. An "NC" does not affect a student's GPA.
The District policy is that if a student in good standing (attending and passing the class) has something unexpected happen towards the end of the quarter that does not allow them to continue with school, they may request an "NC" grade from the instructor prior to the final examination. An NC grade is granted at the instructor's discretion. An NC grade will not be given to protect a student’s GPA. After an "NC" is issued, the course may be repeated no more than one more time.
Course Withdrawal
It is your responsibility to withdraw from the class if you are unable to attend for the quarter. You can do this by filling out a Drop Form and turning it into the Registration Office. If you withdraw before Oct 4, no record of taking the class will be on your transcript. The last day to withdraw from a class is Nov 15 and a W will show in place of a grade for the class on your transcript. The W will have no effect on your grade point average.
Class Policies
In class I expect you to be considerate of your fellow students by not talking when I am lecturing. If you don't understand something, ask a question so everyone can hear your question. If a topic is confusing to you, there are probably other people in class who also do not understand it. Food and drinks are not permitted in the classroom. Spilled drinks are very messy to clean up and it can be very distracting to hear someone eating in class. Classroom Behavior
You should be aware of the Student Conduct Code regarding student behavior in class. This code states that students need to act in a manner that maintains an appropriate learning environment. Those who fail to adhere to such behavioral standards are subject to discipline. Disruptive behavior, as applied to the academic setting, means behavior that a reasonable faculty member would view as interfering with normal academic functions. Examples include, but are not limited to: persistently speaking without being recognized or interrupting other speakers; behavior that distracts the class from the subject matter or discussion; or in extreme cases, physical threats, harassing behavior or personal insults, or refusal to comply with faculty direction. Instructors may ask disruptive students to leave the classroom.
A copy of the Student Conduct code is available on p. 41 – 43 in the Student Handbook. Student misconduct is also defined in Seattle College District Procedure 375.20 (WAC 132F-120-110). Attention is called to paragraphs (d) and (e) which identify the intentional obstruction or disruption of teaching and physical and/or verbal abuse of any person on campus premises as misconduct. Disciplinary sanctions for misconduct may include dismissal from the campus. By Procedure 375.40.4 an instructor has the authority to exclude a student from any class session in which the student is disorderly or disruptive. The Washington Administrative Code (WAC) is available online.
Special Needs
It is the policy of SSC to accommodate students with disabilities according to federal law, state law, and the College’s commitment to equal educational opportunities. Any student with a disability who needs accommodation should inform the instructor at the beginning of the course. Students with disabilities are encouraged to contact Disability Support Services, which is located in the Robert Smith Building, room RS 12 or phone 206-934-5137.
Cell Phones and Pagers
