MTH 244/1
Differential Equations
Fall 2020/URI

Text:  Elementary Differential Equations, Brooks/Cole Thomson Learning, 2001. by William F. Trench.

This book is freely available. You can downloaded it from Trinity University site and it will be also available in Brightspace contents. 

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 will use CAS (computer algebra system)   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 Brightspace 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 Brightspace 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 a method of series

Laplace transform and applications in solving linear differential equations

Systems of linear differential equations

 

Brightspace Help

 

To access Brightspace go to https://brightspace.uri.edu. The Brightspace resource

page can be found at https://web.uri.edu/brightspace/.

 

Getting Started

 

This is a fully online course. We will use Brightspace as our virtual classroom. After

you log into Brightspace, click on the link to our section. Then click on Content,

followed by Start Here. In there you will find the introductory content for this course

(including this syllabus!), and a video introducing you to the course and explaining how

to navigate it in the weeks ahead.

 

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: By appointment

Syllabus

Sections

 Suggested Homework Problems

Exams/Events

1.1

4,5,7,8

1.2

2,5,7

1.3

1,3,7,8

2.1

2,5,7,8,14,20

2.2

1,5,11,20,28

2.3

1,7,12,19

2.4

3,7,12,14

2.5

1,4,5,7

2.6

2,7,8,10

4.1

1,4,7,8

Mathematica 1

4.2

5,7,11,19,32

4.3

2,5,7,14

5.1

7,11,19,31,37

 

5.2

5,7,10,11,14

5.3

1,2,4,7

5.4

1,2,7,10

5.5

5,7,8,11,19

5.6

1,4,5,7,16

Mathematica 2

5.7

4,5,7,8

Exam 1

6.1

1,2,5,7,19,20

6.2

1,2,4,7

7.1

1,2,5,7

 

7.2

2,4,5,7,11

 

7.3

2,4,6,7

8.1

1,5,7,9

Mathematica 3

8.2

2,3,5,7

 

8.3

1,11,15,16

 

8.4

2,5,7,10

 

8.5

1,3,4,7,8

 

10.1

2,3,5,7,11

Exam 2

Handout

 

Mathematica 4

 

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

Americans With Disabilities Act Statement Any personal learning accommodations that may be needed by a student covered by the Americans with Disabilities Act must be made known to the university as soon as possible. This is the student's responsibility. Information about services, academic modifications and documentation requirements can be obtained from the Office of Affirmative Action, Equal Opportunity and Diversity (AAEOD). https://web.uri.edu/affirmativeaction/

Any student with a documented disability is welcome to contact me early in the

semester so that we may work out reasonable accommodations to support your success

in this course. Students should also contact Disability Services for Students, Office of

Student Life, 330 Memorial Union, 401-874-2098.

From the University Manual: 6.40.10 and 6.40.11 Accommodations for Qualified Stu-

dents With Disabilities. Students are expected to notify faculty at the onset of the

semester if any special considerations are required in the classroom. If any special con-

siderations are required for examinations, it is expected the student will notify the faculty

a week before the examination with the appropriate paperwork.

 

 

Brightspace modules and dynamics of learning:

1.   Book: This module contains the publisher’s textbook and file with solutions of all textbook problems.

2.   Lectures: This module contains the videos of all sections in the book. They must be watched first. They are clearly labeled as m244Lec.1.1&12.2, m244Lec.2.3 etc.

3.   Quizzes: This module contains some solved quizzes from previous semesters, which will be clearly labeled like m244f2019Q1.pdf and some practice quizzes labeled like m244f2020Q1Pr.pdf and some solved quizzes labeled like m244f2020Q1Sol.pdf. As soon as you are done with the theory from Lectures module you should look at these quizzes.

4.   Exams: This module contains some solved exams from previous semesters as well as some practice exams prepared for this course.

5.   Mathematica: This module contains Mathematica Notebooks that will be used in Lectures module as well in module on Mathematica Lectures. We will have some Mathematica assignments in this course.

6.   Mathematica Lectures: This module contains video lectures on Mathematica Notebooks from Mathematica module.

7.   Solutions: This module contains solved quizzes and exams from this course.

The proposed dynamics of learning in this course: First listen to video lectures from Lectures module in order given in the above table. Then take look at the Mathematica Lecture and check corresponding Mathematica notebook. Then go to Quizzes and/or Exams and see corresponding solved problems. Then try to solve problems from Practice quizzes and/or exams. After that you might try to solve some of the suggested homework problems. We will have 4 Mathematica assignments.