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y: University of North Georgia
College of Science and Mathematics
Mathematics Department
Mathematics 3000, Differential Equations
Semester: Fall 2017
Instructor: Dr. Piotr Hebda
Office: Gainesville Campus, Watkins Bld., Room 125
Office Phone: (678) 717-3758
E-Mail: piotr.hebda@ung.edu
Office Hours: Will be provided as a separate document
Important dates: 1. Course changes and late registration until: 08/25
2. Mid-Semester Drop Date: 10/13. Dropping a course after this date means an automatic WF, unless the Dean gives specific approval. Prior to this date, a W will be awarded.
3. Final Exam: Monday, 12/11, 12:40pm-2:40pm, regular classroom
Text and Other Materials:
Required Text: Wiliam F. Trench Elementary Differential Equations (at the level of Zill, A First Course in Differential Equations with Modeling Applications, 10th Ed., Brooks/Cole, 2012.) Free download from Shared Files.
2. Supplementary Text: Wiliam F. Trench Student Solutions Manual for Elementary Differential Equations. Free download from Shared Files.
3. Library Resources:
Birkhoff, Ordinary differential equations, Wiley, 1989.
Differential Equations Models in Biology, Epidemiology, and Ecology, Lectuer Notes in Biomathematics, Springer-Verlag, New York, 1991.
Dunham, The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities, Wiley & Sons, New York, 1994.
Hubbard and West, Differential Equations, a Dynamical Systems Approach, Springer-Verlag, New York, 1991.
King, Differential Equations: linear, nonlinear, ordinary, partial, Cambridge, 2003.
Spiegel, Applied Differential Equations, 2nd edition, Prentice-Hall, Englewood Cliffs, NJ, 1967.
Sterrett, 101 careers in mathematics, MAA, 1996.
Vladimirov, Equations of Mathematical Physics, M. Dekker, New York, 1971.
Women, Minorities and Persons with Disabilities in Science and Engineering, National Science Foundation, 1999 (NS 1.49).
Yount, A to Z of women in science and math, Facts on File, 1999.
4. Web-based Resources:
Alpha - HYPERLINK "http://www.wolframalpha.com/" http://www.wolframalpha.com/
Association for Women in Mathematics - HYPERLINK "http://www.awm-math.org" http://www.awm-math.org
The Math Forum - HYPERLINK "http://mathforum.org/" http://mathforum.org/
Waterloo Maples Student Center - HYPERLINK "http://www.maplesoft.com/academic/students/index.aspx" http://www.maplesoft.com/academic/students/index.aspx
Eric Weissteins World of Mathematics (Encyclopedia of Mathematics) - HYPERLINK "http://mathworld.wolfram.com/" http://mathworld.wolfram.com
Math Nerds HYPERLINK "http://www.mathnerds.com/" www.mathnerds.com
SOS Mathematics HYPERLINK "http://www.sosmath.com/" www.sosmath.com
Math Moments - HYPERLINK "http://www.ams.org/mathmoments/" http://www.ams.org/mathmoments/
Project Interactivate - HYPERLINK "http://www.shodor.org/interactivate" www.shodor.org/interactivate
Multicultural Pavilion - HYPERLINK "http://www.edchange.org/multicultural" www.edchange.org/multicultural
Careers in mathematics - HYPERLINK "http://www.ams.org/early-careers/" http://www.ams.org/early-careers/
5. Technology Resources: Maple.
Course Description: This course is an introduction to the study of ordinary differential equations. Topics included in this course are first and second order differential equations, higher order linear equations, mathematical models, Laplace transforms and the Laplace transform method for solving initial-value problems. Credit: 3 hours. Prerequisite: Grade of C or above in Math 2460 or approval of the department head.
Course Objectives: After completion of the course the student will be able to:
Determine an appropriate method of solution of a first or second order differential equation.
Solve first and second order differential equations by methods developed in the course.
Determine the existence and uniqueness of solutions to an initial-value problem.
Model an applied problem by setting up an initial-value problem.
Interpret the solution of an applied problem in the context of the situation.
Determine the long-term behavior of solutions of differential equations.
Solve mass on spring problems involving free-undamped, free-damped, and forced motion.
Classify the damped mass on spring motion as underdamped, critically damped, or overdamped.
Solve differential equations which are non-routine by using the problem-solving approaches employed during the course.
Use the correct notation and terminology when communicating results in the area of differential equations.
Find the Laplace transform or inverse Laplace transform of a given function.
Solve an initial-value problem by using Laplace transforms.
Explain mathematical proofs in the area of differential equations.
Describe real-world applications of differential equations.
Methods of Instruction: The methods of instruction are determined by the instructor; however, the instructor is encouraged to use a variety of methods. These methods may include, but are not limited to lecture; problem-solving sessions with informal assessment by the student or instructor; discussion; group projects; timely feedback from test, quiz, or project results (formative assessment); question and answer; computer or calculator based explorations; and student presentations. Students will be encouraged to assess and monitor their own problem-solving process to determine when an error has been made or a new strategy should be used.
Evaluation Methods: Formative assessment will be in the form of written tests, quizzes and summative assessment will be in the form of a final examination. Special projects and daily grades may be used at the discretion of the instructor. Final grades are determined by the percentage as follows: 90-100=A, 80-89=B, 70-79=C, 60-69=D and below 60=F.
Course Calendar: (Number of 50 minute lessons is approximate)
1. Basic definitions and terminology 3 days
2. Differential equations of the first order 8 days
3. Applications of first order equations 3 days
4. Higher order linear equations 12 days
5. Applications of higher order equations 3 days
6. Power series solutions about ordinary points 2 days
7. Laplace transforms 6 days
Make-up Information: Missing a test will result in the grade of 0 for the missed assignment. Make up tests will be given only in cases of serious, documented emergencies. Difficulties with transportation to campus will not, in general, be considered to be such emergencies.
One lowest test grade (possibly a 0 for a missed test) will be replaced by your final test grade, provided that the final test grade is higher.
Attendance Policy: Attendance is mandatory. Usually the roll will be taken at the beginning of each class. It is the responsibility of each tardy student to tell me about his/her presence during the break and make sure the absence was removed from my records. Each time a student is late or leaves early it counts as half of an absence.
Absences may be excused (removed) if they were results of a documented (in writing) emergency. The documentation must be provided at the first reasonable opportunity. Notes from parents will not be accepted. The instructor reserves the right to reject any excuse.
The first two absences will incur no penalty. For any absence above two will result in the final grade lowered by 3 points.
Any student with 5 or more unexcused absences may be dropped from class without warning. The grade will be a W or WF, depending on time of dropping (not the time of absence) and student performance.
Disruptive Behavior: Any Students who exhibit behaviors which are considered to obstruct or disrupt a class or its learning activities will be considered under the Board of Regents Policy on Disruptive Behavior. It is the right of the individual instructor to define his/her expectations for student behavior. Behaviors which may be considered by some instructors to be inappropriate in a classroom include sleeping, eating, coming in late, interrupting others, talking out of turn, inappropriate behavior during group work, verbal or nonverbal behavior that is disrespectful of other students or the teacher. Students who exhibit disruptive behavior will be given a verbal warning by the class teacher. If the disruption does not stop or is recurring, the student will be removed from the classroom. If the disruptive behavior persists, the student will be given a written warning in a meeting with the chair of the Department of Mathematics and Computer Science. Any further infractions would be referred to the Disciplinary Committee of the College.
Electronics: No electronic devices except an approved calculator are allowed during class. No communication device, even in a calculator mode, may be turned on. All cell phones, i-phones, and similar must be turned off and out of sight. A student trying to omit that rule may be asked to leave the classroom.
(Last Revised March 2016)
Students are expected to refer to the Supplemental Syllabus
http://ung.edu/academic-affairs/policies-and-guidelines/supplemental-syllabus.php
for the following information:
Academic Exchange
Academic Integrity Policy
Academic Success Plan Program
Class Evaluations
Course Grades and Withdrawal Process
Disruptive Behavior Policy
Inclement Weather
Smoking Policy
Students with Disabilities
MATH 3000 TESTS and GRADES:
Trench, free download
Test schedule:
1.2, 2.1 2.6 Test 1
5.1 - 5.7, 6.1, 6.2 Test 2
7.1 - 7.4, 8.1 - 8.3 Test 3
Comprehensive (covering all of the above) FINAL TEST
1. Final grades will be determined as follows:
Regular test weight 5
Final exam weight 10
Each homework assignment 1
2. Grade distribution: 90-100 A
80-89 B
70-79 C
60-69 D
Below 60 F
A graphical calculator required. TI-89 and similar allowed.
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