Syllabus for Differential Equations Sean Yee csu mth 286




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Syllabus for Differential Equations Sean Yee

CSU MTH 286 syee@solonboe.org

Spring 2010 440-349-7757 ext 5429

Textbook:

Elementary Differential Equations, with ODE Architect CD, 8th Edition

by William E. Boyce, Richard C. DiPrima.


Course Description:

This is an introduction to Ordinary Differential Equations (ODE) with an emphasis on linear differential equations. Topics covered include:



  • Basic concepts and methods of solving 1st, 2nd, and higher order ODE’s including homogeneous equations with constant coefficients, method of underdetermined coefficients, and the method of variation of parameters.

  • Mathematical modeling with predetator/prey models, forced vibration modeling, and deducing boundary conditions from a given problem.

  • Basic theory of Systems of equations, linear independence and the Wronskian for 2nd order ODE’s, the characteristic equation, Eigenvalues, Eigenvectors, Fundamental Matrices.

  • Solving ODE’s using the Laplace Transform, especially with discontinuous forcing functions.

  • Elementary introduction to solving 2nd order ODE’s with Series and Sequences.


Attendance:

It is very important to be in class each day. Mathematics builds upon itself; therefore the more class time you miss, the more pressure you will put on yourself to get caught up with the class. Please make every effort to be in class everyday! If you are absent, it is your responsibility to get the assignments or assessments AND NOTES that you have missed. Assignments will be posted in the classroom and are available on my class webpage. It is advised that you get any missed notes from a classmate. Absence the day before an exam does not excuse you from taking the exam as no new material will be covered on review days. Be familiar with the make-up policy in the student handbook. If you are not in the room when the bell begins to ring, then you are tardy and will lose citizenship points.
Classroom Expectations:

  1. Respect others at all times this includes other students. Courtesy is expected.

  2. Be in class and ready to begin when the bell rings. Class is over when you are dismissed by the teacher.

  3. Listen to and follow directions the first time they are given.

  4. Participate in class discussions and group activities, take notes, and ask questions!

  5. Swearing, abusive or vulgar language is not appropriate and will not be tolerated.


Required Materials:

  1. Covered textbook (the textbook issued to you is your responsibility, including damage and theft)

  2. 3-ring binder and notebook paper

  3. Pencils with erasers and pens.

  4. Highlighter and Colored Pencils

  5. Graphing calculator-TI 83 or TI 84 models are recommended.


Assignments and Grading:

  1. Homework will be assigned almost everyday. Homework is an essential part of this class. It provides additional instruction, practice and reinforcement of newly acquired concepts.

  • TAKE PRIDE IN YOUR HOMEWORK! TURN IN EVERY ASSIGNMENT AS THE FINAL DRAFT OF A PAPER.

  • Assignments will be posted in the classroom. It is your responsibility to write them down.

  • Assignments are to be done in pencil only. They will not be accepted if done in pen.

  • Correct your homework in pen. This way, mistakes and weak areas will be easily identified.

  • Diagrams that accompany the exercises must be included on your homework for full credit.

  • Homework may be spot-checked in class for points without prior notice. Be prepared to share your solutions with the class.

  1. Exams will be given at the end of each unit of study and will always be announced in advance. Quizzes will be given periodically, and they may or may not be announced.

  2. I will not grade on a curve nor will grades be rounded. However, some extra credit assignments, citizenship points, and bonus questions will appear occasionally.

Consequences of misbehavior:

1st offense – verbal warning and loss of citizenship points

2nd offense – detention and loss of citizenship points

3rd offense – detention and loss of citizenship points and phone call home

4th offense – office referral
Internet Information:

My weekly lessons will be posted online. You will find the lesson (topic) for the day, homework, and upcoming tests and quizzes. To get to my page follow these steps:



  1. Go to the Solon Schools web page www.solonschools.org

  2. Choose Schools

  3. Choose Solon High

  4. Scroll down to my name (Sean Yee)

  5. Choose “Calendar of Events” from the bottom of the page

  6. Choose the appropriate class


Please email or call me with any questions or concerns!



Boyce and Diprima, 8th edition Elementary Differential Equations, with ODE Architect CD, 8th Edition

Differential Equations Pacing Guide

Homework Problems

Section Covered and Topic

NGC=No Graphing Calculator, EE=Exploratory Exercises, *=Challenging, JSU=Just Set Up, CAS= Computer Aided Software allowed

1.1 Basic Mathematical Models, Direction Fields

#3,4,7,12,15,17,18,20,21,22,26,29

1.2 Solutions of Some Diff Eq's

#1,3,**5,8,14,15,18,17a,b

1.3 Classifying Diff Eq's

#1-6,8,12,14,15,17,19,21,22,23,26,27

2.1 Linear Equations, Integrating Factors

#2,15,20,26,31,38,39

2.2 Separable Equations

#1,4,5,6,10,12,18,22,25 no need to find max

2.3 Modeling with 1st order Diff Eq's

#9,13,32 Brachistochone Problem

2.4 Differences between linear and nonlinear Diff Eq's

#2,3,6,8,14,22,27

2.5 Autonomous Equations and population dynamics

#1,3,7,8,12,18,25

2.6 Exact Equations and Integrating Factors

#2,3,10,14,22,26,

2.7 Numerical Approximation:Euler Method

#3,5,6,8 CAS,*20

2.8 Existence/Uniqueness Theorem

#1,3

3.1 Homogeneoud Equations with Constant Coeff

#2,6,10,13,17,23

3.2 Fundamental Soln's of Linear Homogeneous Eqn's

#1,5,8,14,23,25,28,29,Read #33

3.3 Linear Independence of FUNCTIONS and Wronskian

#3,6,14,17,20,24,27

3.4 Complex Roots of Characteristic Equation

#4,6,20,25,29,(38 if time.)

3.5 Nonhomogeneous Eqns'; Method of Undetermined Coeff

#2,3,9,10,15,**20,25,26,33,35,38

3.6 Variation of Parameters

#6,9,13,23,24,29 also may use taylor series

3.7 Mechanical and Electrical Vibrations

#1,10,17,18,**27 convolution integral,28,32

3.8 Forced Vibrations

#5,10,12JSU, 28

4.1 General Theory of nth degree linear ODE's.

#5,7,16,19,***20,24

4.2 Homogeneous Eqn's with Constant Coeff (Higher Degree)

#7,8,11,18,27,35,38

4.3 Method of Undetermined Coeff (Higher Degree)

#4,11,17,18,21

4.4 Method of Variation of Parameters (Higher Degree)

#1,11,13

5.1 Power Series

#1,4,7,9,12,13,14,21,25

5.2 Series Solutions near an ordinary point I

#7,12 (16 & 26 Feel free to use computer)

5.3 Series Solutions near an ordinary point II

#1,3,7,10,11,12

5.4 Regular Singular Points

#3,14,15,19

5.5 Euler Equation

#1,5,10,13,18,21

5.6 Series Solutions near a Regular Singular Point

#3,6

6.1 Definition of Laplace Transform

#1,2,3,5,18,21,23 **integrate (sint)/t from 0 to infinity.

6.2 Solution of Initial Value Problem (IVP)

#4,7,11,22, **27

6.3 Step Functions

#1,3,8,15, **28

6.4 Diff Eq's with Discontinuous Forcing Function

#9 CAS

6.5 Impulse Function/Dirac Measure/Delta Function

Just discuss Dirac Measure/Delta Function

6.6 The convolution integral

#9,13,15

7.1 Intro to Systems of 1st order linear ODE's.

#1,3,4,5,7,8,17

7.2 Review of Matrices

#4,8,9,11,12,20,23

7.3 Linear Algebraic Eqn's: Eigenvalues, Eigenvectors

#1CAS,2CAS,3,6,7,16,21,26,28,30

7.4 Basic Theory of Systems of 1st order linear ODE's.

# *2,4,5,6

7.5 Homogeneous Linear Systems with Constant Coeff

#1,7,19,20,24,29

7.6 Complex Eigenvalues

#1,2,9,11,24

7.7 Fundamental Matrices

#1,3,11,**16

7.8 Repeated Eigenvalues

#1,2,**17


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