MTH 244/1
Differential Equations
Fall 2019/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 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, chemistry, 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 and computational 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, algebraic and analytic techniques to analyze and/or solve scalar differential equations and systems of differential equations, and to apply the obtained information in the study of basic mathematical models.

The quizzes and exams will reflect the variety of the homework problems 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 (separated variables, 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: TuTh: 12:30-2 and by appointment

Time: TuTh: 9:30 – 10:45 Room: Lippitt 204

### Syllabus

 Sections Homework Problems Exams/Events 1.1 4,5,7,8 1.2 2,5,7 2.1 1,3,7,8 2.2 2,5,7,8,14,20 3.1 1,5,11,20,28 3.2 1,7,12,19 3.3 3,7,12,14 3.4 1,4,5,7 3.5 2,7,8,10 3.6 1,7,8,11 3.7 5,7,11,19,32 3.8 2,5,7,14 Mathematica 1 4.1 7,11,19,31,37 Exam 1 4.2 5,7,10,11,14 4.3 1,2,4,7 5.1 1,2,7,10 5.2 5,7,8,11,19 5.3 1,4,5,7,16 5.4 4,5,7,8 5.5 1,2,5,7,19,20 5.6 1,2,4,7 6.1 1,2,5,7 Mathematica 2 6.7 2,4,5,7,11 Exam 2

Lectures on Differential Equations:

Mohamed Khamsi’s Lecures on Differential Equations

Paul’s Online Notes

Online Handbooks on Differential Equations:

Equation World

Wolfram Math World

Links for Differential Equations:

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).

Academic Enhancement Center (AEC):In addition to lecture and office hours, the Aca-demic Enhancement Center (AEC) offers extra academic help. For more information on AECservices, study tips, and SI session, visit the AEC website http://web.uri.edu/aec