MATH 365 -- Differential Equations

Spring 2010

 

SYLLABUS

 

COLLEGE MISSION STATEMENT

Felician College is an independent co-educational Catholic/Franciscan College founded and sponsored by the Felician Sisters to educate a diverse population of students within the framework of a liberal arts tradition.  Its mission is to provide a full complement of learning experiences, reinforced with strong academic and student development programs designed to bring students to their highest potential and prepare them to meet the challenges of the new century with informed minds and understanding hearts.  The enduring purpose of Felician College is to promote a love for learning, a desire for God, self knowledge, service to others, and respect for all creation.

 

DIVISION OF ARTS AND SCIENCES MISSION STATEMENT

The mission of the Division of Arts and Sciences is to implement and manifest the Mission of Felician College in the Programs of the Division; the General Education Program, the Developmental Educational Program, and the Core by providing the highest quality of instruction at both the undergraduate and graduate level, encouraging students to develop to their fullest potential, to gain skills for life-long learning, and to produce graduates well-equipped to contribute to society. The division achieves the stated mission by using processes of continual improvement, based upon assessment of student learning at al levels, as well as the assessment of the administrative processes and mechanisms

 

DEPARTMENT OF MATHEMATICAL SCIENCES MISSION STATEMENT

The Department of Mathematical Sciences supports the mission of Felician College by providing the portion of students’ educational experiences dealing with quantitative literacy.  The Department supports the mission of Felician College to provide a strong academic program by providing rigorous mathematics courses to students in all majors at all levels.  The Department supports the mission of the Division of Arts and Sciences by providing a high quality of instruction in mathematics at both the college level and the developmental level.  The broad variety of courses offered by the Department of Mathematical Sciences helps bring students to their highest potential by providing theory and practice related to problem solving, logical reasoning, and analytical skills.  This will help prepare Felician College students to meet future challenges with informed mathematical minds.

 

DISCLAIMER

This syllabus is subject to change according to the needs of the class as deemed appropriate by the instructor.  In case of changes, students will be notified in class and a new syllabus will be distributed.

 

Division	Arts and Sciences
Department:	Mathematical Sciences
Course Number	MATH 365R
Course level:	Undergradute
Course Title:	Differential Equations
Instructor:	Dr. Michael Sanford, Ph.D.
Rank:	Associate Professor
Email:	sanfordm@felician.edu or msanfordphd@optonline.net
Phone:	201 559- 6000 ext. 3192
Office	Office: Room 3 Martin Hall Rutherford Campus, (or the Math Lab MH 4)

 

 

Course Description:

A course in ordinary differential equations with technical applications. Topics include differential equations of the first order, approximate methods, linear differential equations, nonhomogeneous equation, La Place transforms, systems of differential equations, power series methods and partial differential equations. (Spring)

Prerequisite: Calculus III - MT 364.

 

Course Objectives:

 

1.     Students will be able solve first order separable differential equations.

2.     Students will be able solve first order linear differential equations using the integrating factor method.

3.     Students will be able to program their own calculators  to solve first order differential equations using, Euler’s Method, Modified Euler’s method, Runge-Kutta Method.

4.     Students will be able to draw in 1-dimensional phase portraits, slope field, bifurcation diagrams, solutions of first order o.d.e.s from phase portraits.

5.     Student will be able to solve 2x2 linear systems.

6.     Students will be able to model, mixing problems, Newton’s Law of cooling problems, Spring problems, and exponential, radioactive decay and logarithmic growth problems and analyze competing and cooperative species problems, and predator prey problems.

7.     Students will be able to draw in 2-dimensional phase portraits, for both linear and non-linear systems, and graph solutions for each variable from the phase portraits.

 

Text Requirements:  Differential Equations, 3ed., by Blanchard, Devaney, and Hall. Published by Brooks/Cole Cengage Learning, 2006. ISBN-10: 0495012653, ISBN-13: 9780495012658. (Price Felician College Bookstore new $214)

 

Course Content:

	MONDAY	TUESDAY	WEDNESDAY	THURSDAY	FRIDAY
JAN.	18	19	20	21	22
					CH 1.1
	25	26	27	28	29
	CH 1.2		CH 1.2		CH 1.3
FEB.	1	2	3	4	5
	CH 1.4		CH 1.5		CH 1.6
	8	9	10	11	12
	CH 1.7		CH 1.8/1.9		CH 1.8/1.9
	15	16	17	18	19
	Prez Day		Review		EXAM I
			CHAPTER 1
			PROJECTS DUE
	22	23	24	25	26
	CH 2.1		CH 2.2		CH 2.3
MAR.	1	2	3	4	5
	CH 2.4		Lin. Alg.		Lin. Alg. Rev.
			Review		CHAPTER 2
					PROJECTS DUE
	8	9	10	11	12
	SPRING		BREAK
	15	16	17	18	19
	CH 3.1		CH 3.2		CH 3.3
MID-TERM	22	23	24	25	26
WEEK	CH 3.4		CH 3.5		CH 3.6
APR.	29	30	31	1	2
EASTER	REVIEW		EXAM II
BREAK	CHAPTER 3
	PROJECT DUE
	5	6	7	8	9
	CH 5.1		CH 5.2		CH 5.3
	12	13	14	15	16
	CH 5.4		CH 6.1		CH 6.2
					CHAPTER 5
					PROJECTS DUE
	19	20	21	22	23
	CH 6.3		Review		EXAM III
	26	27	28	29	30
	CH 8.1		CH 8.2		CH 8.3
MAY	3	4	5	6	7
	CH 8.4		REVIEW		REVIEW
	10	11	12	13	14
FINALS	FINALS		WEEK

Teaching/Learning Strategies

·       Class lectures, demonstrations, and discussions

·       Small group work and discussions

·       Study and homework groups

·       Individual problem solving

 

Grading Policies:

1. Weekly Quizzes (except those weeks in which an exam is given): 10 each will be give each Thursday. The best 10 will be counted for total of 100 points.

 

2. Exams: 100 points each. There will three in class exams during the semester.

 

 

 

 

3. Projects: 20 points each. There will be seven projects due throughout the semester. Write up: Type- use equation to get the symbols in your write up.

 

 

4. Final Exam: 200 points, Comprehensive, date: when the registrar’s office informs us.

 

COURSE GRADE: There 700 points possible the following describe how much you need to get each grade.

 

 

 

 

GRADING RUBRIC:

Quizzes/Exams

The student gets 100% of the credit for an exam question only if the answer is correct, all work is shown, and the work shown leads to the correct answer. Partial credit is given under the following circumstances:

• If the work is substantially correct but there is a minor error in arithmetic, the student will get close to full credit (99%-75% of the credit).
• If there are some mistakes but the student has shown an understanding of at least some of the math, the student will get credit proportional to the amount of understanding demonstrated (74%-1% of the credit).
• No credit (0%) for work that is nonexistent or unrelated

Projects:

 

Point Value	Logic and Reasoning	Computation	Communication
20-18	-Arguments are correct with logical order. −Solution strategy appropriate and comparable to that used by an experienced mathematician. −May suggest alternative approaches	−Computations are completed accurately and efficiently −May suggest alternative approaches	−Problem, hypothesis, and conclusion clearly stated −Project is written in complete sentences with no errors in grammar or spelling −Goes beyond the obvious and includes creative and enlightened answers and comments. -Includes diagram. Graphs, and illustrations. -Typed
17-16	−Arguments are correct, but awkward in order −Solution strategy appropriate	−Computations are completed accurately	−Problem, hypothesis, and conclusion stated −Project is written with minor errors in grammar or spelling −Some extraneous information present Includes diagram. Graphs, and illustrations but may contain minor flaws. -Typed
15-14	−Some flaws in arguments −Solution strategy appropriate, but not implemented correctly	−Some minor flaws in computations	−Problem, hypothesis, or conclusion not stated −Project is written without complete sentences or other errors in grammar or spelling -Not  typed
13-12	−Arguments are incorrect −Solution strategy inappropriate or not apparent	−Flawed Computations	−Problem not stated −Hypothesis and conclusion not stated −Project is written without complete sentences and other errors in grammar and spelling are present -Not Typed
11-0	−Work is nonexistent or unrelated	−Work is nonexistent or unrelated	−Work is non-existent or unrelated -Not Typed

 

 

 

Course Policies:

 

Missed quizzes, I’ll try to more than 10 so make-ups are not necessary but if you want make arrangements with me to do it outside of class time.

 

Missed exams, will not be made up unless there is an extreme need. Otherwise you final will become a 300 point final if you need to miss. If you do not talk with me about missing the exam in person I will assume you skipped and expect a 0.

 

Late projects you lose 10 points every week it is late. Working In groups is acceptable and expected.

 

In class behavior, I expect you to act as the adult you are and respect your classmates and myself which means the golden rule applies.

 

Calculators you’re nuts if you don’t have a good one. I hope you have the TI-89. Graphing and programmable is expected. We will be doing some programming.

 

Academic dishonesty, you are expected to work on your own unless otherwise directed. Quizzes will occasionally be a group effort.

 

 

Note: College Wide Policies can be found in the College Catalog.

 

 

	Monday	Tuesday	Wednesday	Thursday	Friday
9:20-9:50	OFFICE	OFFICE	OFFICE	OFFICE	OFFICE
	HOUR	HOUR	HOUR	HOUR	HOUR
9:50-11:05	MATH231R	OFFICE	MATH332R	MATH231R	MATH332R
	GEOMETRY I	HOUR	HIST. of MATH	GEOMETRY I	HIST. of MATH
	SM 37		SM 37	SM 37	SM 37
11:20-12:40	MATH365R	MATH122R1	MATH365R	MATH122R1	MATH365R
	DIFF. EQ.	STATISTICS I	DIFF. EQ.	STATISTICS I	DIFF. EQ.
	SM 37	SM 37	SM 37	SM 37	SM 37
1:00-2:15	Office Hour	MATH122R2	Office Hour	MATH122R2	Office Hour
	provided	STATISTICS I	provided	STATISTICS I	provided
	I have no	SM 37	I have no	SM 37	I have no
2:30-3:00	meeting	OFFICE	meeting		meeting
		HOUR