﻿ mth244spring2010-kulenovic/uri

MTH 244/2
Differential Equations
Spring 2016/URI

TextAn Introduction to Differential Equations, by Stanley Farlow, Dover Pubs, 1994

Exams and Grading: Your grade will be based on two tests, a final exam, quizzes and Mathematica projects as follows:

 Two tests at 150 points each 300 points Final exam 200 points Quizzes 100 points Two Mathematica Projects 100 points Total 700 points

Calculators and Computers: As in Calculus Courses you will need a programmable graphing calculator. We recommend TI89. You are encouraged to use the CAS (computer algebra system) such as Mathematica and Scientific Notebook and online programs that can be found on Internet. We will give a brief introduction to such resources. All Mathematica notebooks needed will be provided in SAKAI and demonstrated in the class.

Course Description: In MTH 244 we study ordinary differential equations in greater details than in the calculus courses. This subject has wide applications in the physical sciences, engineering, bio-medical sciences, and economics.  Ordinary Differential Equations lead to many advanced areas of mathematics itself. Ordinary Differential Equations  may be considered as the ultimate mastery of topics in calculus. You will find that there are new algebraic ideas to master.

The homework problems are the core of this course. An important purpose of the problems is to make you think through and master the ideas of the subject so that you can confidently apply your knowledge in new situations. You will learn a great deal from honest hard work on a problem, even if you don't succeed in solving it. Read the text material before working on the problems. In SAKAI you will be provided by numerous solved problems.

Objectives: At the end of the course you will be able to use numerical, graphical, analytic techniques to analyze and/or solve scalar and systems of differential equations, and to apply these concepts in the study of basic mathematical models.

The exams will reflect the variety of the homework problems, quizzes and problems solved in the class. It is important that you give these problems adequate time and effort.

The topics that will be covered are:

Exact solutions of first order differential equations (homogeneous, linear, Bernoulli, differential equations with total differential)

Existence and uniqueness theorems for differential equations

Linear differential equations – general theory

Solving linear differential equations with method of series

Laplace transform and applications in solving linear differential equations

Systems of linear differential equations

Online information: www.math.uri.edu/courses and  www.math.uri.edu/~kulenm

Instructor: Dr. M. Kulenovic,   Lippitt 202D,  Ph. 44436,                            e-mail: mkulenovic@ uri.edu

Office hours: M, F:10-11,   W: 1-2     Time: MWF: 12 - 12:50          Room: Quinn Hall 314

### Syllabus

 Sections Homework Problems Exams/Events 1.1 3,5,7,8 1.2 2,3,5,7 2.1 1-3,7,8 2.2 2,5,7,8,16,20 3.1 1,4,5,11,20,28 3.2 1,5,7,11,19 3.3 2,3,7,12,14 3.4 1,2,4,5,7 3.5 2,5,7,8,11 3.6 1,4,7,8,11 3.7 5,7,8,11,19 3.8 2,5,7,11,14 Mathematica 1 4.1 7,11,19,23,31,37 Exam 1 4.2 5,7,10,11,14 4.3 1,2,5,7 5.1 1,2,5,7,10 5.2 5,7,8,14,16,19 5.3 1,4,5,8,16 5.4 2,4,5,7,8 5.5 1,2,5,8,20 5.6 1,2,4,5,7 6.1 1,2,4,5,7 Mathematica 2 6.7 2,4,5,8,11 Exam 2

Illness Due to Flu

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 at 874-xxxx or xxx@uri.edu 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 www.cdc.gov/flu or flu.gov .  URI Health Services web page, www.health.uri.edu , will carry advice and local updates.

Lectures on Differential Equations:

Online Handbooks on Differential Equations:

Wolfram Math World

Interesting Java applets for Differential Equations

Interactive Differential Equations set of applets for Differential Equations

Disability Any student with a documented disability is welcome to contact me as early in the semester as possible so that we may arrange reasonable accommodations (contact Disability Services for Students Office at 330 Memorial Union 401-874-2098).