MTH 244 Section 02  Differential Equations Spring 2011

Department of Mathematics, University of Rhode Island

Calendar, Suggested Problems link






Orlando Merino,, 874-4442, Lippitt Hall 101C


Class Meets



Bliss Hall 205, MWF 12 - 12:50





Ordinary Differential Equations by Finizio and Ladas, Third Editio, Simon and Schuster or PWS Publishing Co.





MTH 243 or permission of the instructor




First order differential equations (separable, homogeneous, linear, exact).

Existence and uniqueness theorems for differential equations

Linear differential equations – general theory (homogeneous and nonhomogeneous, constant and variable coefficients, undetermined coefficients, variation of parameters.

Systems of linear differential equations

Laplace transform and applications to solving linear differential equations

Solving linear differential equations with the method of series

Numerical solutions of ordinary differential equations






Four tests 10 % each, Final Exam 30 %, CAS projects 12 %, Homework/quizzes 18 %.

The policy for late hw/projects will be announced in class.



About the Course


MTH 244 is the first course in Ordinary Differential Equations. We will study mathematical techniques involving differential equations used in the analysis of physical, biological and economic phenomena. Emphasis is placed on the use of established methods, rather than rigorous foundations.
We shall emphasize those methods that are capable of broad applications and that can be extended to various problems. The methods to be discussed include not only elementary analytical techniques that lead to exact solutions of certain classes of problems, but also include approximations based on numerical algorithms or series expansions, as well as qualitative or geometric methods.




We will use the software Mathematica, which is available at URI computer labs..


Electronic Devices


Unless explicitly stated by the instructor during class time, all electronic devices are forbidden. This includes cellular phones, ipods and alike, ipads and other tablets, calculators, netbooks, laptops.




Instructor's expectations

  • IN THE CLASSROOM Lecture time is at a premium, so it must be used efficiently. Expect to have material covered at a fast pace. We expect you to come prepared to class as detailed below.
  • OUTSIDE THE CLASSROOM You cannot be taught everything in the classroom. Much of your learning must take place outside the classroom. At a minimum you should plan on studying two or more hours outside the classroom for each hour in class. You should attempt all the homework that is assigned and try additional problems in areas where you feel weak.
  • THE TEXTBOOK You are expected to read the textbook for comprehension. It gives a detailed account of the material of the course. It also contains many examples of problems worked out, and these should be used to supplement those you see in the lecture. Use pencil and paper to work through the material and to fill in omitted steps. Read the appropriate section(s) of the book before the material is presented in lecture. Then the faster-pace lecture will make more sense. After the lecture carefully reread the textbook along with your lecture notes to cement your understanding of the material.
  • EXAMS Our intent is to determine how well you understand the basic principles underlying the methods and if you are able to apply these principles to novel as well as routine situations. Some problems on an exam may seem new, but all will be solvable using principles from the material on which you are being tested.
  • SOLUTIONS TO PROBLEMS It is your responsibility to communicate clearly in writing up solutions for homework, quizzes, and exams. Your results must display your understanding well and be written in a correct, complete, coherent, and well organized fashion. The rules of language still apply in mathematics, and apply even when symbols are used in formulas, equations, etc. Neatness counts!

[Based on: Zucker, S., Teaching at the University Level, AMS Notices (43), 1996, pp 863-865.]

Special Needs

Any student with a documented disability is welcome to contact me early in the semester so that we may work out reasonable accomodations to support your success in this course. Students should also contact Disability Services for Student, Office of Student Life, 330 Memorial Union, Kingston, 874-2098.

Academic Honesty

Students are expected to be honest in all academic work. A student's name on any written work shall be regarded as assurance that the work is the result of the student's own thought and study. Work should be stated in the student's own words, properly attributed to its source. Students have an obligation to know how to quote, paraphrase, summarize, or reference the work of others with integrity. The following are examples of academic dishonesty.

  • Using material from published sources (print or electronic) without appropriate citation
  • Claiming disproportionate credit for work not done independently
  • Unauthorized possession or access to exams
  • Unauthorized communication during exams
  • Unauthorized use of another's work or preparing work for another student
  • Taking an exam for another student
  • Altering or attempting to alter grades
  • The use of notes or electronic devices to gain an unauthorized advantage during exams
  • Fabricating or falsifying facts, data or references
  • Facilitating or aiding another's academic dishonesty
  • Submitting the same paper for more than one course without prior approval from the instructors.


If you become ill, notify me at 874-4442 or of your status, and we will communicate through the medium we have established for the class. We will work together to ensure that course instruction and work is completed. We will follow regulations as stated in the University Manual 8.51.1--8.51.14

Additional Information

The University Manual (See ) contains useful information: 8.39.10-12 (attendance); 8.51.11-14 (excused absences); 8.51.15 (examinations during the semester); 8.51.16 (final examinations); 8.27.16-19, 8.27.17-19, 8.27.10-15 (plagiarism-instructor's responsibilities, judicial action, and student's responsibilities); and 8.52.10 (grading criteria).

Civility Policy

The University of Rhode Island has adopted a civility policy regarding disruptive classroom behaviors. Disruptive behaviors are defined as behaviors that interfere with the learning and/or teaching process. Disruptive behaviors in the classroom include inappropriate talking during lectures or class discussions or in any manner interfering with other student's ability to have a quality learning experience. Students who engage in disruptive behavior will receive one warning without penalty. Continued incidents of disrupting the class will result in the initiation of removal procedures or the loss of a letter grade. Disruptive behaviors include cell phone and pager use. Cell phones and pagers must be turned off, silent, and out of sight during classes, and you should not be checking for calls or messages during class (including "texting"). Common sense and common courtesy should govern classroom civility.

"Incomplete" grade

I follow to the letter the URI regulations concerning incomplete grades, namely the following paragraphs taken from the university manual:

  • 8.53.20. A student shall receive a report of "Incomplete" in any course in which the course work has been passing up until the time of a documented precipitating incident or condition, but has not been completed because of illness or another reason which in the opinion of the instructor justifies the report. An instructor who issues a grade of "Incomplete" shall forward a written explanation to the student's academic dean.
  • 8.53.21. The student receiving "Incomplete" shall make necessary arrangement with the instructor or, in the instructor's absence, with the instructor's chairperson to remove the deficiency. This arrangement shall be made prior to the following midsemester for the undergraduate student and within one calendar year for the graduate student.