Math 204 Syllabus

MATH 204

Differential Equations

Mon, Tues, Wed, and Thurs 2:00 to 3:05 AM

Room E100 5 UNITS

Instructor: Larry Green

Phone Number

Office: 541-4660 Extension 341

Internet e-mail:... DrLarryGreen@gmail.com

Home Page: http://www.ltcc.edu/depts/math/

Your Grades

Required Text Elementary Differential Equations ninth edition by William Boyce and Richard DiPrima

Course description This is a beginning course in ordinary differential equations, including traditional topics, series solutions, applications and Laplace transforms.

Prerequisite A grade of C or better in Math 107 or equivalent.

Grading Policy Your letter grade will be based on your percentage of possible points.

A 90 -- 100% C 70 -- 79%

B 80 -- 89% D 60 -- 69%

Homework: ........................................................….100 points

Poster Session: May 26, 12:00 to 2:00 PM ............100 points

Exam 1: May 6.......................................…...…......200 points

Exam 2: June 8....................................................…200 points

Final Exam: June 20........................................…....400 points

Exam Policy Students are to bring calculators, pencils or pens, and paper to each exam. Grading will based on the progress towards the final answer, and the demonstration of understanding of the concept that is being tested, therefore, work must be shown in detail. Any student who cannot make it to an exam may elect to take the exam up to two days before the exam is scheduled. If every homework since the prior exam is scored at least 6, then you may bring a 3" x 5" note card (front and back) to the exam.

Homework Policy Homework will be turned in during class immediately after the question and answer part of lecture. Homework that is turned in within one week of the due date will be counted as half credit. Homework may be turned later than one week after the due date, but points will not be awarded.

Extra Credit Any student who attends the CMC³ Tahoe conference and reports on it will have one of their homework assignments that has a score of at least a 5, become a 10.

Poster Project The project involves investigating an application of differential equations and physics. Exceptions will be made for students without a physics background. The display must be approximately 1 meter by 1.3 meters. You may write any equation by hand. You are encouraged to have a computer math program assist you in the project. Ideally you should work on the project with one partner, but an exception can be made under special circumstances. Your abstract is to be a one-paragraph description of your project. It will be due on May 19. Included in your abstract should be a set of references that you intend to use. From 12:00 to 2:00 on May 26 you will be expected to stand by your project and give a five minute presentation and field questions. The projected will be graded on both content and presentation.

Student Learning Outcomes

1. Apply ordinary differential equations to problems from physics, biology, and other scientific disciplines.
2. Employ the technique of transformations in finding solutions to ordinary differential equations.
3. Prove results from the field of differential equations.
4. Sketch direction fields for first-order ordinary differential equations.
5. Solve differential equations using sequences, series, and matrices.

Registration

In this class, it is your responsibility to drop the class in order to avoid an unwanted grade.

CALCULATORS: A TI 89 graphing calculator is required for this class.

Instructions on the TI 89 Calculator

LEARNING DISABILITIES: If you have a learning disability, be sure to discuss your special needs with Larry. Learning disabilities will be accommodated.

TUTORING: Tutors are available at no cost in A 201 (The Math Success Center).

A WORD ON HONESTY:

Cheating or copying will not be tolerated. People who cheat dilute the honest effort of the rest of us. If you cheat on a quiz or exam you will receive an F for the course, not merely for the test. Other college disciplinary action including expulsion might occur. Please don’t cheat in this class. If you are having difficulty with the course, please see me.

OFFICE HOURS:

Monday ............................. 10:40 to 11:40 AM MSC

Tuesday ............................. 1:00 to 2:00 PM A 210

Wednesday ..................... 1:00 to 2:00 PM A 210

Thursday ........................ 1:00 to 2:00 PM MSC

Friday .................................. 1:00 to 2:00 PM A210

CALCULATORS: A graphing calculator is required for this class. There are a variety of such calculators on the market. The instructor will be using a Texas Instruments-89.

Instructions on the TI 89 Calculator

LEARNING DISABILITIES: If you have a learning disability, be sure to discuss your special needs with Larry. Learning disabilities will be accommodated.

HOMEWORK ASSIGNMENTS

Lecture will always be geared towards an explanation of the topics that will be covered on the upcoming homework assignment.

Date Section Topic Exercises

4-4 Introductions

4-6 1.1 Direction Fields 4, 15-20, 24
1.2 Diff EQ Solutions 7, 9, 18

4-8     1.3    Classification                        2, 6, 11, 17, 20, 23, 27
          1.4     History                                Read Only
          2.1      Linear Equations                  6, 13, 16, 19, 27, 30, 33

4-11 2.2 Separable Equations 1, 8, 18, 26, 30, 33, 37

4-13 2.3 Modeling 1, 5, 10, 19, 26, 32

4-15 2.4 Linear vs. Nonlinear 3, 10, 16, 23, 27, 30, 33

4-18 2.5 Population Dynamics 2, 12, 15, 18, 21, 23, 24, 28

4-20 2.6 Exact Equations 8, 17, 22, 24, 27, 30

4-22 2.8 Existence & Uniqueness 2,11, 13, 14, 15, 16, 17, 18

4-25 2.9 Difference Equations 1, 4, 7, 10, 14, 16

4-27 3.1 Constant Coefficients 2, 7, 10, 15, 17, 21, 24, 27

4-29 3.2 Fundamental Solutions and The Wronskian 5, 12, 15, 25, 32, 35, 46, 49

5-2 3.3 Complex Roots 3, 7, 14, 20, 26, 43, 44

5-4 3.4 Repeated Roots 8, 13, 18, 19, 23 ,29, 32, 38

5-6 Exam I

5-9 3.5 UC Functions 3, 6, 14, 17, 33, 36

5-11 3.6 Variation of Parameters 1, 10, 16, 19, 22, 23, 28, 30

5-13    3.7      Vibrations                             4, 7, 11, 15, 21, 27, 30
           3.8      Forced Vibrations                  4, 10, 15, 16, 21
            An example of forced vibrations gone bad

5-16 4.1 n^th Order Equations 1, 8, 14, 23
4.2 Constant Coefficients 5, 17, 33, 39

5-18 4.3 UC Functions 1, 4, 9, 11, 16, 19, 20

5-20 4.4 Variation of Parameters 1, 6, 8, 11, 13, 14, 16

5-23 5.1 Power Series 5, 13, 18, 20, 21, 23, 28
5.2 Series Solutions I 3, 7, 14, 17, 21, 24

5-25 5.3 Series Solutions II 2, 7, 10, 14, 19, 26

5-26 Poster Session 12:00 to 2:00 PM

5-27 5.4 Euler Equations 4, 15, 19, 23, 43, 46
5.5 Regular Singular Points 4, 9, 13, 14, 16

5-30 Memorial Day

6-1 6.1 Laplace Transform 5, 10, 14, 18, 25, 26
6.2 Initial Value 4, 8, 14, 19, 25, 27, 37

6-3 6.3 Step Functions 3, 9, 16, 22, 25, 26, 31

6-6 6.4 Discontinuous Forcing 2, 8, 13, 18, 21

6-8 Exam II

6-10 7.2 Matrix Review 22, 25
7.3 Linear Algebra Review 1, 6, 10, 12, 18, 26, 32, 33

6-13 7.4 System of Diff Eqs. 2, 3, 4, 5, 6, 8, 9

6-15 7.5 Homogeneous Systems 4, 7, 12, 15, 20, 25, 29, 30

6-17 7.6 Complex Eigenvalues 4, 9, 12, 17, 24, 25, 28

6-20 Comprehensive Final Exam 2:00 PM - 3:50 PM

HOW TO SUCCEED IN A MATH CLASS

Come to every class meeting.
Arrive early, get yourself settled, spend a few minutes looking at your notes from the previous class meeting, and have you materials ready when class starts.
Read each section before it is discussed in class
Do some math every day.
Start preparing for the tests at least a week in advance.
Spend about half of your study time working with your classmates.
Take advantage of tutors and office hours, extra help can make a big difference.