AMTH 242 Section 1

AMTH 242 Section 1
Differential Equations
Fall 1998

Professor

Stephen C. King

Office

ADMN 201J

Telephone

641-3451; or leave message at 641-3446

e-mail

SteveK@usca.edu

Office Hours

M 12:20 – 12:50, 3:00 – 3:20; WF 3:30 – 4:30; TTh 3:30 - 4:30; other hours by mutual agreement. You may feel free to make an appointment to see me anytime, or just stop by my office. Outside of office hours, if I am busy I will schedule an appointment with you for a later time.

Class Hours

TTh 12:15 - 2:55 PM, ADMN 213

Prerequisite

Grade of C or better in AMTH 241.

Text

CALCULUS&MATHEMATICA by Bill Davis and Jerry Uhl, Book 5, DIFFERENTIAL EQUATIONS (installed on the computers in ADMN 213, and on 4 computers in ADMN 203 and 4 in the Math Lab).

Software

MATHEMATICA VERSION 3, installed on the computers in ADMN 213, and on 4 computers in ADMN 203 and 4 in the Math Lab.

Topics Covered

Linear equations, systems of linear equations, eigenvectors and eigenvalues, equilibrium points, linear oscillators, pendulum oscillator, linearization of non-linear systems, transient and steady state solutions, convolution integral methods, Dirac delta function, Laplace transforms, Fourier transforms.

Course Objectives

To learn the calculus and differential equations concepts and skills beyond those dealt with in AMTH 141, 142, and 241 which are needed for the successful study of upper-level science, mathematics, and engineering courses, including the ability to communicate using the language of mathematics, both symbolic and verbal.

Course Content

The emphasis will be on a modern balance between pencil and paper methods and methods accessible only through the use of technology. We will not study all of the traditional pencil and paper methods. No matter what the course includes, it cannot include every possible aspect of differential equations. If you learn the material in this course, you will have a strong foundation so that you will be able to study and learn any additional techniques or concepts that you might need later. If you are concerned about the course content, you may wish to go to the library and consult the Special Issue on Differential Equations of The College Mathematics Journal (November 1994) and the review of differential equations texts in the April 1998 issue of The American Mathematics Monthly (pp. 377 - 383) to see what recognized experts in differential equations say about appropriate content.

Expected student competencies to be acquired

The successful student at the end of this course will be able to produce well-written correct solutions for problems like those assigned for homework in this course, and will be able to use a computer algebra system to solve problems like those we study. This includes the ability to write problem solutions using clear and coherent arguments with correct standard English and correct mathematical notation and terminology. You will be graded on how your solutions are written as well as on the correctness of your final answers.

Class Structure

There are eight lessons. We will generally cover one section about every week and a half. Some weeks there will be lab experiments between lessons; see the Homework section below.

Teamwork

The class will be divided into two-person teams. In extenuating circumstances, other size teams are possible. Each team must designate 3 editors: a Mathematics Editor, a Mathematica Editor, and an English Editor, whose names are to be stated at the beginning each homework project. Each editor is responsible for what his or her title indicates.

Generally all team members get the same homework grade, but it is possible that an editor whose area pulls down the grade could lose more points than the other team members. Teams may be broken up and reformed at my discretion. Teams may vary the editorial duties at their discretion.

Homework

Homework assignments count 40% of your grade. The assignments will consist of computer problems from the "Give it a Try" sections of the text and pencil and paper problems from the literacy sheets. In addition, you will have some assignments based on data gathered using physical experiments; grades from this will be treated as part of your homework. Specific problems will be assigned roughly once a week and are due about a week later. The written work (Literacy sheets) will be 20% of your course grade and the Give it a Try problems will be 20% of your course grade.

Style

Late homework will not ordinarily be accepted. You will turn in assignments through the LAN. Keep a copy of your work on high density 3.5" disks in case it is lost. The format for your work is the Mathematica Notebook in a style similar to the Textbook. Each notebook should begin with the names and titles of the team members.

Help

You may seek help from other students but you must acknowledge this help in a credit statement at the beginning of the notebook just after your names. No homework will be read without a completed credit statement. If you help someone, point them in the right direction but don't do their work for them.

Literacy

You must demonstrate literate knowledge of the basic concepts of differential equations covered in this course on literacy tests. These tests will be "paper and pencil" tests. You may and should use Mathematica to check your work on these tests. There will be two or three literacy tests given throughout the semester, announced at least one week in advance. These tests count 30% of your grade.

Final Exam

A pencil and paper comprehensive final examination (on Tuesday December 15 at 11:00 AM) counts 30% of the total grade. You may and should use Mathematica to check your work on the final. The final will be graded upon your ability to apply the principles covered in this course.

Attendance

Class attendance is mandatory. You should consult with your professor if you must miss a class. Four unexcused absences or eight absences of any type may result in a grade of F. In addition to scheduled class hours you will need to spend many extra hours in the lab completing your homework assignments. How many extra hours will vary depending upon the individuals doing the work.

Special Notice

If you have a physical or learning disability which might affect Your performance in this class, please contact the Office of Disability Services as soon as possible. Once an evaluation has been made, appropriate accommodations will be determined.

This page copyright © 1998-99, The Board of Trustees of the University of South Carolina.
Send comments to: stevek@usca.edu.
URL:http://www.usca.edu/math/~mathdept/sck/
This page has been accessed 99 times since November 2, 2001 . Last updated Friday, 28-Dec-2001 08:57:51 EST.

Professor	Stephen C. King
Office	ADMN 201J
Telephone	641-3451; or leave message at 641-3446
e-mail	SteveK@usca.edu
Office Hours	M 12:20 – 12:50, 3:00 – 3:20; WF 3:30 – 4:30; TTh 3:30 - 4:30; other hours by mutual agreement. You may feel free to make an appointment to see me anytime, or just stop by my office. Outside of office hours, if I am busy I will schedule an appointment with you for a later time.
Class Hours	TTh 12:15 - 2:55 PM, ADMN 213
Prerequisite	Grade of C or better in AMTH 241.
Text	CALCULUS&MATHEMATICA by Bill Davis and Jerry Uhl, Book 5, DIFFERENTIAL EQUATIONS (installed on the computers in ADMN 213, and on 4 computers in ADMN 203 and 4 in the Math Lab).
Software	MATHEMATICA VERSION 3, installed on the computers in ADMN 213, and on 4 computers in ADMN 203 and 4 in the Math Lab.
Topics Covered	Linear equations, systems of linear equations, eigenvectors and eigenvalues, equilibrium points, linear oscillators, pendulum oscillator, linearization of non-linear systems, transient and steady state solutions, convolution integral methods, Dirac delta function, Laplace transforms, Fourier transforms.
Course Objectives	To learn the calculus and differential equations concepts and skills beyond those dealt with in AMTH 141, 142, and 241 which are needed for the successful study of upper-level science, mathematics, and engineering courses, including the ability to communicate using the language of mathematics, both symbolic and verbal.
Course Content	The emphasis will be on a modern balance between pencil and paper methods and methods accessible only through the use of technology. We will not study all of the traditional pencil and paper methods. No matter what the course includes, it cannot include every possible aspect of differential equations. If you learn the material in this course, you will have a strong foundation so that you will be able to study and learn any additional techniques or concepts that you might need later. If you are concerned about the course content, you may wish to go to the library and consult the Special Issue on Differential Equations of The College Mathematics Journal (November 1994) and the review of differential equations texts in the April 1998 issue of The American Mathematics Monthly (pp. 377 - 383) to see what recognized experts in differential equations say about appropriate content.
Expected student competencies to be acquired	The successful student at the end of this course will be able to produce well-written correct solutions for problems like those assigned for homework in this course, and will be able to use a computer algebra system to solve problems like those we study. This includes the ability to write problem solutions using clear and coherent arguments with correct standard English and correct mathematical notation and terminology. You will be graded on how your solutions are written as well as on the correctness of your final answers.
Class Structure	There are eight lessons. We will generally cover one section about every week and a half. Some weeks there will be lab experiments between lessons; see the Homework section below.
Teamwork	The class will be divided into two-person teams. In extenuating circumstances, other size teams are possible. Each team must designate 3 editors: a Mathematics Editor, a Mathematica Editor, and an English Editor, whose names are to be stated at the beginning each homework project. Each editor is responsible for what his or her title indicates.
	Generally all team members get the same homework grade, but it is possible that an editor whose area pulls down the grade could lose more points than the other team members. Teams may be broken up and reformed at my discretion. Teams may vary the editorial duties at their discretion.
Homework	Homework assignments count 40% of your grade. The assignments will consist of computer problems from the "Give it a Try" sections of the text and pencil and paper problems from the literacy sheets. In addition, you will have some assignments based on data gathered using physical experiments; grades from this will be treated as part of your homework. Specific problems will be assigned roughly once a week and are due about a week later. The written work (Literacy sheets) will be 20% of your course grade and the Give it a Try problems will be 20% of your course grade.
Style	Late homework will not ordinarily be accepted. You will turn in assignments through the LAN. Keep a copy of your work on high density 3.5" disks in case it is lost. The format for your work is the Mathematica Notebook in a style similar to the Textbook. Each notebook should begin with the names and titles of the team members.
Help	You may seek help from other students but you must acknowledge this help in a credit statement at the beginning of the notebook just after your names. No homework will be read without a completed credit statement. If you help someone, point them in the right direction but don't do their work for them.
Literacy	You must demonstrate literate knowledge of the basic concepts of differential equations covered in this course on literacy tests. These tests will be "paper and pencil" tests. You may and should use Mathematica to check your work on these tests. There will be two or three literacy tests given throughout the semester, announced at least one week in advance. These tests count 30% of your grade.
Final Exam	A pencil and paper comprehensive final examination (on Tuesday December 15 at 11:00 AM) counts 30% of the total grade. You may and should use Mathematica to check your work on the final. The final will be graded upon your ability to apply the principles covered in this course.
Attendance	Class attendance is mandatory. You should consult with your professor if you must miss a class. Four unexcused absences or eight absences of any type may result in a grade of F. In addition to scheduled class hours you will need to spend many extra hours in the lab completing your homework assignments. How many extra hours will vary depending upon the individuals doing the work.
Special Notice	If you have a physical or learning disability which might affect Your performance in this class, please contact the Office of Disability Services as soon as possible. Once an evaluation has been made, appropriate accommodations will be determined.