Prof. Vladimir Dobrushkin
Department of Mathematics

MTH244 (Differential Equations)

Vladimir A. Dobrushkin,Lippitt Hall 202C, 874-5095,

Math 244 will cover first order and second order ordinary differential equations, numerical methods, and Laplace transform.

MTH244, section 03, TR 2:00 - 3:15 pm, While Hall, 204

TEXTBOOK: "Applied Differential Equations. The Primary Course", by Vladimir Dobrushkin. CRC Press, 2015;

Course Objectives and Goals:
MTH 244 is the first course in Ordinary Differential Equations. We will study mathematical techniques involving differential equations used in the analysis of physical and biological 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.

By the end of the semester, students will be able to use numerical, graphical, and analytic techniques to analyze and/or solve scalar differential equations, and to apply these concepts in the study of basic mathematical models.

Prerequisite: MTH142 or equivalent. MTH 243 is recommended.

Homework will be assigned after each section. Each day we will spend time going over examples, quizzes, and homework problems. You are responsible for all problems assigned, see Course Calendar for a list of problems associated with each chapter. Quizzes will be given almost every class in the weeks without exams. Quiz problems are from homework problems and examples given in class with number changes. There are no makeup quizzes. I'll drop one quiz grade.

Because of the high level of knowledge that will be imparted and assessed during class time, attendance is highly recommended.

Technology will play an important role in this course and we will make extensive use of available solvers. The computer algebra system (CAS) Mathematica is available at university labs, as well as commercial software Matlab (its free version is Octave). Other software CASs such as Sage and SymPy (based on Python) are recommended. Online tutorial can be found here.

Mathematica Projects:
In this course we will use the Mathematica software, which is available in computer labs at URI. The Mathematica projects are created to help you learn new concepts. Mathematica is very useful in visualizing graphs and surfaces in two and three dimensions.

Help With Your studies and homework:
Tutors are available at both the Providence and Kingston campuses. Walk-in tutoring for math is located in Lippitt Hall. There is a no appointment needed in the Lippitt Hall tutoring center. It is a place where you can work with tutors and other students in this and other math courses. Support is provided for all math courses up to MTH 244. Be sure to bring your book, notes, and questions with you. The tutoring center is a great place to study with classmates and friends, prep for exams, and review the material covered in lecture. Check with them for specific hours. In addition, you can find help at the Academic Enhancement Center. For an updated schedule for Spring 2017 Math Walk-In Tutoring click here, and then select "Math Walk In Schedule" from the menu on the right (make sure you see which of the tutors can help you with MTH 244).

A no-cost resource is Paul's Online Notes , that in addition to notes also contain many completely solved examples.
Another resource is Mohamed Khamsi’s Lecures on Differential Equations , that in addition to notes also contains many completely solved examples.

Also, you can make individual appointments with me. For this, contact me by phone, e-mail, or ask me during class. I may help you with questions during office hours, or at other times by appointment. Also, I will try to answer questions sent by electronic mail as promptly as possible. Students who require accommodations and who have documentation from Disability Services (874-2098) should make arrangements with me as soon as possible.
The Academic Enhancement Center provides Weekly Tutoring Groups program that has replaced Supplemental Instruction.

The nation is experiencing widespread influenza-like illness. If any of us develop flu-like symptoms, we are being advised to stay home until the fever has subsided for 24 hours. So, if you exhibit such symptoms, please do not come to class. Notify me your instructor 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 for the semester.

The Centers for Disease Control and Prevention have posted simple methods to avoid transmission of illness. These include: covering your mouth and nose with tissue when coughing or sneezing; frequent washing or sanitizing your hands; avoiding touching your eyes, nose, and mouth; and staying home when you are sick. For more information please view or . URI Health Services web page, , will carry advice and local updates.

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.

Grading Incomplete (URI regulations): .

  • 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