Math 255 Differential Equations (2012-13 autumn)

Your final Project. Compulsory for every individual: Fr Due Date please read the file, you may submit at latest on Tueusday in Person, (you must see me).

Instructor: Dr. M. Sakalli, any request or questions with a prefixed subject line as "2013DE.YourSubject" to WildSolarianTree at gmail com.

 

Attendance: Your full presence in every class will strictly be observed with random irregular attendance check. You'll be informed in advance if the course will not be hold.

 

Books and resources:

1 - Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems.......

2 - Steven Holzner, Differential Equations For Dummies.......

 

1 - Video Lectures of Prof Arthur Mattuck, 18.03 DE.

2 - Notes of Prof Paul Dawkins's DE 3301.

 

 

Assessment for your final performance.

HW (30): HWs,and prg assignments matlab (and may be maple as well, not sure yet),

please remember, your prging assigments will be rigorously checked and any fradulent submission will reduce your marks of those involved in.

M: 30 Midterm.

F: 40 FinalExam.

I: (a binary value). Your active involvment will be rewarded to top up your marks at least one grade above.

 

A pseudcode of Your Final Differential Performance FNw = (HW, M, F, I).

   FN = HW+M+F;

   FNw = Weigh all marks(FN).

   if FNw >= 50,

     pass,

     if I, FNw++.

   else

     Not successful (you shld try summer course or another dept next year.)

return(FNw)

Tentative Syllabus.

1- Some basics of DEs, - figuring out the general form of DEs, Solutions of DEs. order, degree.

2- First order DEs, f(t,v)=ma=mg - ã v.. Isoclines, direction fields. Linearity, Separable Eqns, Exact Eqns, Integrating Factors, Bernoulli, and modeling with DE's, such as (*) population dynamics, dy/dt= f(x). *Quiz, homogeneous and nonhomogeneous eqns.

3- Existence and Uniquness Thrs. *Prg Assignment with matlab.

4- Logistic Growth Eqns (Boyce). Chaos, bifurcation.

5- Numerical Approx. Write a program of a) Euler('', x0, xf, h), and b) RungeKutta4('function', x0, xf)

6- Linear dependence and independence and the Wronskian. Fundemenatal Set of Solutions, Abel's Thr(Boyce),

7- 2nd order DE's. . oscillations (Boyce Chapters 2-3), Forced vibrations.

8- Higher order DEs; methds a) the undetermined coefficients, b) the variation of parameters. Methods of annihilation to address particular solutions.

9- Power series, convergence/divergence (yakinsamak/iraksmak). Solving DE with power series, near a regular singular point. Euler's, Airy's, Legendre's andBessel's Eqns.

10- LT, convolution, Fourier series. Systems of first order equations, Eigen..

11. Numerical methods with emphesis on truncation error.

 

12. You will be giving two E. systems(matlab) sources.

 

Lecture Notes.

1- Modeling with ODEs, isoclines, direcion fields. You have two questions to be submitted by Monday. 8th Oct, Updated with linearity.

2- Matlab practice and HWs. Due dates first section by Monday and the second section by the next Thursday.

3- Seperable, IF, differences of the linear and non-linear DEs, continuity, existence and uniqueness.....

4- 2. order DEs. study.. and a matlab project sometime next week will be uploaded.

5-Matlab HWs compulsory **** for every individual, you must expect some questions on this regard in exam for example how to avoid for loop, and why. Deadline for both 1st Nov, email to the addr given above. Subject line must include DE22513HW#. You will be asked to run your program and evaluate the results.

Try these codes and try to understand what is happening.

     Prj1. Dir fields. MLfile to be worked out. Matlab Code.

     Prj2. 2nd Order LDE. ML fileto be wrked out. Matlab Code.

 

6 - Study for this Thursday applications of 2nd Order DE.

If you would like to have powerpoint chapters of Boyce, as it is.. please look at here.. very much summarized in the handouts I gave you above.

7- For midterm exam, you will be asked some practices with some slight proofs mentioned in the class. You willbe asked from matlab as well.

First order DEs, f(t,v)=ma=mg - ã v.. Isoclines, direction fields. Linearity, Separable Eqns, Exact Eqns, Integrating Factors.

For midterm exam, you will be asked some practices with some slight proofs mentioned in the class. You willbe asked from matlab as well.

Those who haven't seen me after midterm must..

8- 2nd and 9th Monday Dec Exam, 2nd hr. Your absentia willnot be axcused.

HW. Diff of Lena and Lena tanspose. In matlab. Deadline monday you must submit comparative images. Load Lena, imagesc(diff(Lena, etc..)..or you may try other reference images Boat.bmp.or Boat.mat

Your Project .Matlab. for ODEs, by Erica McEvoy. Deadline 9 dec. Monday.

LectureNotes on Euler Error Analysis GTE and LTE Source Chapt8 of Boyce&DiPrima.

Study RLC, Systems of Equations, phase lines, Chapter 7 of Boyce Prima, or Paul Dawkins. Systems of Equations,.

9- Next: Verlet.m, Systems of Eqns. Exp Shift Rule, More on Pendulum, Laplace, Differential Games****.