MATH 46 – Differential Equations

Winter 2006

Professor: Dr. Janet Vassilev
Office: Surge 233  Office Hours:  T 10-11 am, MF 12-1 pm and by appointment.
Telephone: (951) 827-3020
email: jvassil@ucr.edu webpage: http://math.ucr.edu/~jvassil

Text :  Elementary Differential Equations, by W.F. Trench. Read it! We will cover chapters 1 through 6, in addition to chapter 8.

Course Meetings:  The course lectures will be held in Spieth Hall 1307 on Monday, Wednesday and Friday at 3:10 -4:00 pm. Discussion sessions will be held on Tuesday evening with Felix. You are expected to attend both the lectures and the discussion sessions as per Math Department decree. To encourage attendance, there will be unannounced quizzes in either discussion or lecture at least once a week.

Tips for Success: * Come to class! It is amazing how much you can learn by being attentive in class.  * Collaborative learning is encouraged but remember that only YOU will be taking the quizzes and exams... * Like all mathematics, differential equations is not a spectator sport; you will learn only by doing!  You will find that a consistent effort will be rewarded. * Be organized.   Have a notebook or binder for Differential Equations alone to keep your class notes, homework, quizzes and exams in order.  * No question you have should be left unanswered.  Ask your questions in class, discussion session or take advantage of office hours.

Homework (100 points):  Homework will be assigned daily and the starred problems will be collected the following Wednesday at the beginning of class. No late homework will be accepted. There will also be no make up quizzes. Homework will not be graded unless it is written in order and labeled appropriately. An answer alone will get 0 points. Make sure to justify every answer. Each week, 2-3 homework problems will be graded and a score will be assigned out of 10 points. The quizzes will have 1 problem and they will be graded out of 10 points. Do not avoid word problems because they will appear regularly on quizzes and tests. Your lowest homework and quiz will be dropped and the remaining homework and quizzes will be averaged to get a score out of 100.

Exams (300 points):  I will give one midterm (100 points) and a final (200 points). An ID is required to take all exams and it will be checked when you turn in your exam. There are no make up exams. If a test is missed, notify me as soon as possible on the day of the exam. For the midterm only, if you have a legitimate and documented excuse, your grade will be recalculated without that test. The Midterm is tentatively scheduled for Friday, February 10, 2006. The Final is on Saturday, March 25, 8-11 am.

Grades:  General guidelines for letter grades (subject to change; but they won't get any more strict): 90-100% - A; 80-89% - B; 70-79% - C; 60-69% - D; below 60% - F.  In assigning Final Grades for the course, I will compare your grade on all course work and your grade on the Final Exam. You will receive the better of the two grades.

Calculator Policy:  It is the Math Department’s policy to forbid the use of calculators on both exams and quizzes.

Tentative Schedule (for Dr. Vassilev’s Differential Equations):

Date	Section	Topic
1/6	1.1-1.2	Examples	1.2 *1, 2(b, c, *e), 3(a, c, d, i), 4(*a, b, h), 5(a, b), 6a, *7
1/9	1.3, 2.1	Direction fields, Linear homogeneous first order equations	1.3 *1, 4, 9, *16, 19; 2.1 2-5, *7, 8-10
1/11	2.1	Linear non-homogeneous first order equations, The Existence and Uniqueness Theorem	2.1*12, 16, *19, 20, 24, 30, *32, 33, 44, 46
1/13	2.2-2.3	Separable Variables	2.2 2, *3, 4, 6, *11, 27, *28, 35; 2.3 7, *8, 18
1/18	2.4	Bernoulli’s Equation, Homogeneous Equations	2.4 2, 3, *4, 8, *9, 16, *17, *23, 26
1/20	2.5	Exact Equations	2.5 *1, 2, *5, 13, *16, *20, 29a, 30c, *34
1/23	2.6	Integrating Factor	2.6 *2, *6, 9, 14, *19, 20, 23
1/25	2.6	Integrating Factors cont.	No Assignment today
1/27	4.1	Exponential Growth and Decay	4.1 2, *3, 5, *7, 8, *9, *11, *12, 15, 19
1/30	4.2	Cooling and Mixing	4.2 1, *2, 4, 5, *7, 8, *11, 13, 18
2/1	4.3	Applications to Mechanics	4.3 2, *5, 7, *10, 15a, *16a
2/3	4.3	Escape Velocity	4.3 17, *18
2/6	4.5, 5.1	Orthogonal Trajectories	4.5 1, 6, 8, 11, 25, 27, 29
2/8		Review	Practice Midterm Solutions
2/10		Midterm
2/13	5.1	Second order linear homogeneous equations	5.1 2, *3, 5(b,e), *7, 8, 11, *14, *29
2/15	5.2	Constant coefficient homogenous equations	5.2 1, *3, *4, 15, 23, 24, *25
2/17	5.2	Complex numbers, exponential solutions	5.2 *2, 5, *9, 11, 27
2/22	5.3	Second order linear non-homogeneous equations	5.3 *2, 4, 9, *10, 17, *34
2/24	5.4	The method of undetermined coefficients	5.4 1, *4, 6, *8, 12, *18, *27
2/27	5.5	The method of undetermined coefficients: trig functions	5.5 *1, 2, *4, 7, *10, 12, *28, 29
3/1	5.6	Reduction of order	5.6 1, *2, 4, *7, 10, 17, 19, 28, *31
3/3	5.7	Variation of parameters	5.7 *2, 3, 7, *11, 14, 17, *22, 31
3/6	6.1	Harmonic Motion, Spring Problems	6.1 2,*6, *10, *14, *17, 19, 20
3/8	6.2	Spring Problems	6.2 1, *5, 7, *8, 10, 13, *17, 20,21
3/10	6.3, 8.1	RLC circuits/Laplace Transforms	6.3 1, *2, *5
3/13	8.2	Laplace Transforms	8.2 1(a, d, e), 2(b, e, h), 3(b, c, f), 4(a, b, f), 5(b, c), 7a, 8b
3/15	8.3	Laplace Transforms	8.3 1, 2, 7, 21, 25, 27, 31
3/17		Review	Practice Final Solutions
3/25		Final