MTH244 – Fall 2009 Differential Equations Instructor Gerry Ladas

The theory of differential equations constitutes a language that scientists and engineers use to make careful mathematical statements about the real world. MTH 244 is a lively and exciting course which is easily accessible to students who have had two semester of calculus.

Ever since Newton (1642-1727), Differential Equations have been the basis of the scientific understanding of Nature.

Differential equations are equations, which involve derivatives of unknown functions. Differential equations appear frequently in mathematical models that describe real-life situations. This a because many natural laws and hypotheses can be translated via mathematical language into equations involving derivatives. For example, derivatives appear in physics as velocities and accelerations, in geometry as slopes, in biology as rates of growth of populations, in psychology as rates of learning, in chemistry as reaction rates, in economics as rates of change of the cost of living, and in finance as rates of growth of investments.

This course is an introduction to the subject of differential equations involving one independent variable. Skills useful in solving differential equations will be developed. In addition, students will be exposed to techniques which use differential equations to model complex physical phenomena. The material in this course is basic for further study in applied mathematics, physics, engineering, chemistry, biology, and many other areas of science and the humanities.

INSTUCTOR: Professor Gerry Ladas

OFFICE: Lippitt 202H

TELEPHONE: 874-5592 (Office) 789-8105 (Home) 874-2709 (Department)


Instructor Office Hrs. and Special MTH 244 Tutors
M T W Th F

Prof Ladas Office Hrs

Lippitt 202H

12:00 - 1:00

10:45 - 11:15

10:45 - 11:15


Tutoring in Lippitt 206


1:00-3:00 11:45-12:45     12:00-1:00

Tutoring in Lippitt 206



Review Sessions for Exams will be available and will be announced here.

Review for exam 1

Review for exam 2


TEXT: Ordinary Differential Equations, 3rd Edition, by Finizio and Ladas,
Simon and Schuster

COURSE DESCRIPTION: We will cover most of the material in Chapters 1-7 but not necessarily in the order and way described in the text. You must attend classes and take notes and you are also expected to read thoroughly the material in the text. You need a programmable graphing calculator and you should learn on your own how to use MAPLE, MATHEMATICA, or some other program. In this course we will use the technology as a supplement to thought rather than a substitute for it.

TESTS: There will be two tests schedule on Tuesday, Oct. 20 and Thursday December 10 and a cumulative FINAL EXAM as scheduled by the Registrar. There will be regular Homeworks and irregular Quizzes. There will be no make-ups for homeworks and quizzes.

GRADING: Two Tests: 200 points possible
Quizzes: 100 points possible
Homework: 100 points possible
FINAL EXAM: 200 points possible
TOTAL: 600 points possible

You need 360 points to pass with a D and you need 560 points to receive an A in this class. You will also receive an A in the class if your total in the two tests and homework + quizzes is more than 380 points.




Links: Problem 1   Problem 1 hints Problem 2   Practice 1   Homework 3   Quiz1  Quiz 2   Existence and Uniqueness Theorem   Practice 2  Laplace Formulas   Quiz4




Only 2 problems from each “Homework Set”  will be graded, but you should submit complete solutions to all problems. Please print or type your solutions. Your homework should look neat and be stapled, otherwise it will not be graded. LATE HOMEWORK WILL NOT  BE ACCEPTED.

Section                        Homework

1.3                p. 28:             1,3,5,6,9, 18,19,20,23,24
                     Do problems 23, 24, and 37 by using MAPLE

1.4               p. 40:            3, 5, 11, 12, 19, 24, 25, 27, 37, 39

1.7                p. 61:             1, 2, 8, 9

                     p. 17:             1, 2, 3, 5, 6

1.8                p. 69:            2, 3, 4, 5

********************************************************** ***********


2.3              p. 98:             1, 2, 4, 5, 11

2.5              p. 112: 1, 2, 5, 6, 7, 8, 9, 10 ,20, 21



2.5               p. 112:            27, 28, 29,

2.5               Numerical Solutions of Differential Equations
                    READ SECTIONS: 2.2, 2.4, 2.6, 2.7, 2.8 and 2.10
                    Solve Problems 27, 28, 29 in Section 2.5 by using MAPLE



2.11            p. 144: 40, 41, 42,

                   Numerical Solutions of Differential Equations
                   APPLICATIONS: READ SECTIONS 2.1.1 AND 2.11.1
                   p. 84:
                   p. 113:33

                   p. 145: 48, 49


3.2              p. 183: 1, 2, 3, 5, 10, 11, 12, 13, 15



                   READ SECTIONS: 4.1 and 4.2
4.3              p. 222: 1, 3, 7, 9, 13, 37,38, 45
                   Numerical Solutions
                   Solve Problems 37, 38 and 45 in MAPLE


READ SECTIONS: 5.1, 5.2, 5.3, AND 5.5

5.4              p. 262: 1, 2, 3, 4, 9, 10



 The last homework is the practice final exam and is DUE 12/10/09

Illness Due to Flu
The H1N1 Flu Pandemic may impact classes this semester. 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 874-5592 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 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 a tissue when coughing or sneezing; frequently washing your hands to protect from germs; avoiding touching your eyes, nose and mouth; and staying home when you are sick. For more information, please view UrI information on the H1N1 will be posted on the URI website at, with links to the site.