Course Syllabus
General Information:Spring 2016 (Piloted and tested beginning Summer 1999 and always being improved)
Course title and number: Differential Equations Mathematics 206 (Allegany College of Maryland number, this may vary at other schools.)
Required text: A First Course in Differential Equations 8th ed. Dennis G. Zill * (check with instructor before buying!)
Go here for a cheap copy.
Instructor’s name: Donald P. Robinson (Professor)
Office hours/location: H-23 M 2-4 PM, W 2:20-3:20 PM
Work email: drobinson@allegany.edu Work phone: 1-301-784-5237 (Maryland)
Fax number: 301-784-5060 Skype name: Odonata5237
Class meeting time: For this class, it is free form. You are required to follow the posted schedule, roughly three sections of the web material weekly with understanding. Exams will be scheduled with this in mind. Expect to spend at least 12 hours weekly on the lectures and the homework.
*Please note: The instructor reserves the right to change ANY course provisions or requirements during the course of the semester.
I. Purpose
A. Catalog description
Includes solution of equations of order one with elementary applications; linear differential equations--homogeneous and non-homogeneous equations; variation of parameters; inverse differential operators; and Laplace transforms. Prerequisite : Math 203 (ACM Calculus III)
(Note, strong Calc II students can take this class, I will give permission.)
B. Course objectives:
Students will study the items listed under the course outline.
C. The following General Education Goals are covered in the course:
Scientific and Quantitative Reasoning
Critical Analysis and Reasoning
II. Class Policies
A. Attendance
Attendance is required. This means that the information in the web must be browsed carefully. It won’t always match what is in the text, and I will have different sample problems worked out there. (Often problems from the assignment set. You should take notes just as you would in a regular class, and email, fax or have a web conference (several options here, see student requirements link on main page) questions. I am hoping that all students have access to Skype which is free and will allow us to talk to each other as well as share information.
B. Class routine
This is a web-based course. The routine is for the student to use a browser such as Microsoft’s Explorer or Netscape with the Windows Media Player (all of these are free downloads) to get lecture material and examples of solved problems from the web, including the instructor’s narration in Real Audio format. It is easier on the student to use the browser's print feature to print the page, then look at it during the lecture. The lectures are shorter than a typical class, since there is no time for interaction. This occurs via email and/or conferencing. The student will also spend a good portion of the 'lecture' time with the audio paused and working out problems.
C. Grades:
At the current time, there will be six regular exams, each counting as 100 points for a total of 600 points. This will be accomplished by the instructor mailing the exams to exam centers, and the students will take them in the exam center. This will be done at the student's remote site or in the Allegany College testing lab for local students. A picture ID must be shown to the lab. Collected assignments and or projects may count as part of an exam on any particular unit as the instructor sees fit, but never more than 20% of the exam total. Grades will be based on the correctness and completeness of exams and projects which will be emailed, faxed, or snail-mailed to the instructor:
Don Robinson
Allegany College of Maryland
12401 Willowbrook Road
Cumberland, MD 21502
Grading scale will be no more severe than:
540-600 points = A
480-539 points = B
420-479 points = C
360-419 points = D
below360 points = F
D. Extra credit: Not given in this course.
E. Tutoring:
Every attempt at mentoring will be made by the instructor. This will be done through email. These conferences must be made at mutually agreeable times based on EST of the USA. The use of the telephone system (no overseas calls on my account!) is possible, but expensive and will only be used if absolutely necessary and at the student’s expense. The option of peer tutoring may be available on some campuses.
F. Assignments:
Must be completed, else expect exams scores to be very low. If you miss a question (answers are provided in the back of the book or on the website), you can scan your work (include the question), type it as a .doc or a mathcad file and email it to me. I will try to respond within 1 work day.
H. Cheating:
of any kind will not be tolerated. I don’t mind presenting information to a group situation, but assignments must be individual. It will be up to the discretion of the instructor to determine whether or not such cheating has occurred and will force a large portion of the grade to be a monitored final examination for the class or any student that the instructor shall name.
I. When are assignments due?
Unless prior permission is obtained, nothing will be accepted late. Assignments will have clearly given due dates via email. A general guide is on the website.
III. Course Requirements
A. Course outline:
Unit I
Learning objectives: Students will learn common terminology, definitions, and classification of differential equations, solve appropriate algebra and trig equations to solve initial value problems, construct differential equations as models for real life situations, solve differential equations by separation of variables, including all required algegra skills, solve exact equations utilizing appropriate calculus skills, solve linear first order differential equations by constructing an integrating factor, and make appropriate substitutions mto solve bernoulli equations as well as other types.
Introduction to differential equations
1.1 Definitions and terminology
1.2 Initial value problems
1.3 Differential equations as mathematical models
First order differential equations
2.2 Separable variables
2.4 Exact equations
2.3 Linear First Order equations
2.5 Solution by substitution and Bernoulli equations
Unit II
Learning Objectives:
Students will model real world problems with differential equations, some of which will be linear, some non-linear and some will need to be modelled with systems of equations. As a prelude to the next unit, students will also learn about solutions of equations both linear and higher order, and how to construct solutions based on solutions to homogeneous equations added to particular solutioins. Boundary value problems will be solved, the Wronskian is introduced, as well as differential operators.
Modelling with first order differential equations
3.1 Linear differential equations
3.2 Non-linear equations (students will create models of real life examples that are non-linear differential equations)
3.3 Systems of linear and non-linear equations (students will create models of real life examples that aresystems of equations)
Linear differential equations of higher order
4.1 Preliminary theory for linear equations of higher order
4.1.1 Initial value/Boundary value problems
4.1.2 Homogeneous equations
4.1.3 Non-homogeneous equations
Unit III
Learning Objectives:
Studnes will solve differential equations of higher order by 'undetermined coefficients', 'annihilators', and 'variation of parameters', including Cauchy - Euler equations. Linear initial value problems and boundary problems are modelled and are solved, including eigenfunction solutions.
Differential equations of higher order
4.2 Reduction of order
4.3 Homogeneous equation with constant coefficients
4.4 Undetermined coefficients -superposition approach
4.5 Undetermined coefficients -annihilator approach
4.6 Variation of parameters
4.7 Cauchy - Euler equation
Modeling with higher order equations
5.1 Linear equations: initial value problems
5.2 Linear equations: boundary value problems
Unit IV
Systems of differential equations
Learning Objectives: Students will be solving systems of differential equations using operators, and using matrix methods, including finding eigenvalues and eigenvectors of matrrices. This is a good introduction to some linear algebra skills. The matrix exponential and variation of parameters methods are used to solve non-homogeneous systems.
4.8 Systems of linear differential equations
8.1 Preliminary theory
8.2 Homogeneous systems with constant coefficients
8.2.1 Real eigenvalues
8.2.2 Repeated eigenvalues
8.2.3 Complex eigenvalues
8.3 Undetermined Coefficients, Variation of parameters
8.4 Matrix exponential
Unit V
Learning Objectives:
The students will learn the definition of Laplace transform, find several transforms of common functions and then ultimately solve initial value problems as well as systems of IVP using the method of laplace transform.
Laplace transform
7.1 Definition of Laplace transform
7.2 Inverse transform
7.3 Translation theorems, derivatives of a transform
7.2, 7.4 Transforms of derivatives, integrals, and periodic functions
Applications to differential equations
7.6 Systems of differential equations by Laplace transform
Unit VI
Learning Objectives:
The first part of this unit, the students will solve differential equations (linear and at least the concept of non-linear) graphically and numerically, as these might be the only usable options in some real life situations. Other methods, including solution of equations by power series methods are explored.
Numerical methods
2.1 Direction fields
2.5, 9.1 Euler methods
9.2 Runge-Kutta methods
Series solution to differential equations
Non-Linear Equations
4.9 Non-linear equations
Review of power series
6.1 Solutions about ordinary points
B. Assignments:
Made from each web lesson.
C. Required reading:
Each noted section of the textbook as well as all of the web material. Any text on Ordinary Differential Equations could be valuable reading.
D. Recommended reading assignments:
See above.
E. Supplemental learning resources:
A Computer Algebra System such as MathCad or Derive would be valuable, but not necessary. A Graphing Calculator with matrix operations would be a minimal requirement. Another reasonable option is the TI-89 or TI-92 calculator, but you have a computer already, so it seems you could use software instead.
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