Mathematics

Math 321 - Differential Equations
Spring 2002

Course Description

(from the catalog)

Ordinary differential equations; series solutions for linear differential equations; linear operators. Prerequisite: grade of C or higher in 221. Offered as needed.

Text

H.S. Bear, Differential Equations, a concise course, Dover, New York, 1962.

Core (General Education) Skill Objectives:

1. Thinking Skills:

   (a)

   Students will use reasoned standards in solving problems and presenting arguments.

2. Communication Skills: Students will ...

   (a)

   ...read with comprehension and the ability to analyze and evaluate.

   (b)

   ...listen with an open mind and respond with respect.

   (c)

   ...access information and communicate using current technology.

3. Life Value Skills:

   (a)

   Students will analyze, evaluate and respond to ethical issues from an informed personal value system.

4. Cultural Skills: Students will ...

   (a)

   ...understand culture as an evolving set of world views with diverse historical roots that provides a framework for guiding, expressing, and interpreting human behavior.

   (b)

   ...demonstrate knowledge of the signs and symbols of another culture.

   (c)

   ...participate in activity that broadens their customary way of thinking.

5. Aesthetic Skills:

   (a)

   Students will develop an aesthetic sensitivity.

Specific Course Goals:

Those happen to coincide with some of the NCTM (National Council of Teachers of Mathematics) ``standards'' for mathematics education. We have:

The students shall ...

1. ...develop an appreciation of mathematics, its history and its applications.

2. ...become confident in their own ability to do mathematics.

3. ...become mathematical problem solvers.

4. ...learn to communicate mathematical content.

5. ...learn to reason mathematically.

General Education Course Objectives:

1. Thinking Skills: Students will ...

   (a)

   ...explore the problems that lead to differential equations;

   (b)

   ...learn to solve basic types of first order differential equations that can be done in closed form. Those include: separation of variables, Clairaut equations, homogeneous equations, equations with integrating factors.

   (c)

   ...learn to solve first order linear differential equation, and second order linear differential equation with constant coefficients.

   (d)

   ...Learn geometric interpretation of first order equations, and learn constructing the corresponding vector field.

   (e)

   ...learn Picard's method of solving differential equations numerically.

   (f)

   ...become familiar with basic existence and uniqueness theorems.

   (g)

   ...explore some more advanced techniques of solving differential equations such as, linear differential operators, method of undetermined coefficients, inverse operators, variation of parameter method.

   (h)

   ...study the use of Laplace transform in solving differential equations.

   (i)

   ...explore solving of systems of first order differential equations.

2. Communication Skills: Students will ...
   • ...justify their reasoning, provide precise, rigorous explanations for their work.

   • ... learn how to typeset the solutions to their homework; learn to use L^ATEX
   • ...learn to use the Internet resources and present the findings in class.

   • ...learn to model a real life problem.

   • ...learn how to interpret a solution of an ODE and apply it in a real life problem.

   • ...learn how to prove some theorems.

3. Life Value Skills: Students will ...

   (a)

   ...develop an appreciation for the intellectual honesty of deductive reasoning.

   (b)

   ...listen with an open mind and respond with respect.

   (c)

   ...understand the need to do one's own work, to honestly challenge oneself to master the material.

4. Cultural Skills: Students will explore the importance of differential equations in sciences and various applications, as well as become familiar with some elements of the historical development of the field.

5. Aesthetic Skills: Students will ...

   (a)

   ...develop an appreciation for the austere intellectual beauty of deductive reasoning.

   (b)

   ...develop an appreciation for mathematical elegance.

Content:

This course is aimed at the Math and Science majors with the idea of introducing to them some standard, most basic, topics and techniques in the field of differential equations.

Course Philosophy and Procedure

Two key components of a success in the course are regular attendance and a fair amount of constant, every-day study. You should try to make sure that your total study time per week at least triples the time spent in class.

This course will introduce you to one of the key tools of applied mathematics. In addition to applications of differential equations in solving a variety of problems, you will be able to see some of the mathematical subtleties involved, and thus further develop your mathematical maturity. Also, I hope that through exploring various advanced techniques in solving differential equations, you will see some of the ways how attempts to solve difficult differential equations problems generate development of new mathematics.

Above all, this course provides an excellent opportunity to master the basic tools of Calculus, that is, differentiation and integration.

Grading will be based on two in-class exams ( points each), a cumulative final exam ( points), class participation, take-home problems, projects, group practice exams and portfolios.

My grading scale is

A=90%, AB=87%, B=80%, BC=77%, C=70%, CD=67%, D=60%.

Americans with Disability Act:

If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me and Wayne Wojciechowski in Murphy Center Room 320 (796-3085) within ten days to discuss your accommodation needs.

This syllabus is tentative and may be adjusted during the semester.

Important dates: