Class Homepage: Math 441 E13

Differential Equations

Instructor:

Vadim Zharnitsky

  • Meetings: MWF 1-1:50am (106B8 ENGR HALL)
  • Office: 273 Altgeld Hall
  • Phone number: (217)244-5032
  • Office hours: WF 2-3 pm or by appointment
  • E-mail: vzh@illinois.edu
  • Website: https://math.uiuc.edu/~vz/441.html
  • Grader: Hsiao, Ting-Yang

    • Communication

    The best way to reach me is by email vzh@illinois.edu. I regularly read my mail and will reply to you usually within a couple of hours. If you do not hear from me within 24 hours, please contact me again. All major course announcements will be made by email through Moodle.

    Learning Management System:

    All course materials will be made available on Moodle, and all assignments will be handled via Moodle. To log in to Moodle, please click here and log in using your university net-id and password, and two-factor authentication. Then go to MY COURSES and you should see this course there (you need to be registered for the course to see it).

    Discussion forum

    We will use campuswire for the discussion forum. More information will be provided during the first week of classes.

    Textbook:

    Boyce, DiPrima, "Elementary differential equations and boundary value problems", 10th edition. If you have 9th edition, you can still use it but you need to ensure that the numbering of the problems is correct. You can borrow for a short time 10th edition in Mathematics library.

    Mathematics department syllabus

    math 441 syllabus

    Grading: 

    Homework     10%
Exam #1      25%   Monday, February 27, (Entire class period)
Exam #2      25%   Monday, April 10,   (Entire class period)
Final Exam   40%   Tuesday, May 9, 8-11 am.

Grade cutoffs:


    


    
  A     
  B     
  C     
  D     
  F     

    


    
 90-100   
 80-90    
 70-80    
 60-70    
 < 60     

    


    



    Homework:  
    
Homework assignments will become available on Monday  will be due next Monday by 9am. 
The first assignemnt is due on January 23.  Late homework will be accepted
with 10% penalty if submitted within 24 hours after the deadline, 20% penalty if submitted within 24-48 hours after the deadline, etc.

All solutions should be submitted as a single pdf file on Moodle. Please do not upload jpg files. Arrange the problems in the right order  and
with the right orientation (so they do not have to be rotated). You may use the CamScanner app for more
convenient scanning. One feature that is very useful is the "Batch" feature that gives you the option of forming
a single pdf file  after you take the pictures in sequence. It is compatible across devices, free, and very convenient
to use as well.


You are allowed and even encoraged to collaborate with your classmates on the homework, but you have to write down your own 
solutions.  



    Exams: 
    
There will be 2 exams and one three hour final exam during
the semester.  Each of the exams will contain one or more problems, with
some data modified, from the homework submitted before the exam. There will
be also questions on the theory that was presented in the lectures.


    Make-up policy
    
Make-up exams will not be given, unless  your absence is approved by the emergency dean
(in case of an illness, personal or family emergency).


    Schedule: (updated as class progresses) 
    

    

    

    
 Lectures     
 Dates   
 Text    
 Topics    
 Homework Problems    
 HW due    

    


    
 1    
 W 1/18    
 1.1-1.3    
 Introduction    
 Sect 1.1: # 15-20,
               Sect 1.3: # 1-6, 14,  15, 16.
            
      Sect 2.1: # 13, 15, 16.       		
   HW 1  1/23  

    


    
 2   
  F 1/20   
  2.1  
  First order linear eqs.   

    



    
 3   
  M 1/23   
  2.2  
  Separable  eqs.  
  Sect. 2.2: 7, 8, 15.   Sect 2.6: # 6, 7, 10, 16, 25. 
       Sect. 2.4: # 4, 11, 27.       		
 HW 2   1/30  

    



    
 4   
 W 1/25    
 2.6   
 Integrating factors and exact eqs.   

    


    
  5   
  F 1/27  
  2.4  
  Difference between linear and nonlinear eqs.   

    



    
  6   
  M 1/30   
  2.3  
  Modeling with 1st order equations 
 Sect. 2.3:  2, 8, 16. Sect. 2.5: 2, 9, 12, 26.  
 HW 3  2/6  

    





    
 7   
 W 2/1   
 2.3   
  Modeling with 1st order equations 

    


    
  8  
  F 2/3  
  2.5  
  Autonomous equations and population dynamics  

    





    
 9  
 M 2/6   
 2.8  
  The Picard existence and uniqueness theorem 
 Review Sequences/Series convergence for Class on 2/8. 
     Sect. 2.8: 2,  13, 14, 15, 17.  
    		
 HW 4  2/13    

    


    
  10  
  W 2/8  
  2.8  
  The Picard existence and uniqueness theorem 

    



    
  11 
  F 2/10   
  2.8  
  The Picard existence and uniqueness theorem 

    




    
 12  
 M 2/13   
 3.1  
 n-th order linear ODEs, Examples. 
 Sect. 3.1: 16, 17, 23. Sect. 3.2: 5, 16, 20, 21.  
 HW 5  2/20    

    


    
  13  
  W 2/15  
  3.1 
  n-th order linear ODEs, Existence-Uniqueness.  

    



    
  14 
  F 2/17   
  3.2, 4.2  
 n-th order linear ODEs, Wronskian, Linear Independence. 

    








    
  15 
  M 2/20   
  3.2, 4.1  
 n-th order linear ODEs  
   Optional (do NOT submit this HWK) problems to prepare for Exam 1: Sect 2.1: 1-20, 34-37. Sect. 2.2: 1-28. 
                                                   
Sect. 2.4: 1-16. Sect. 2.6: 1-12. Sect. 2.8: 1-3, 13-14, 15-19.  Sect. 3.1: 1-18, 25. 
     Sect. 3.2: 1-6, 7-12, 16-20, 24-27, 38-40. 
Sect. 4.1: 1-6, 7-10, 11-16, 17, 21, 24, 25.  



      Checklist for Exam 1    
    		
 HWK for 
     Exam 1      
    		




    


    
  16  
  W 2/22 
  3.2, 2.9 
  n-th order linear ODEs, special cases  

    



    
  17 
  F 2/24   
  3.5,4.3  
 n-th order linear ODEs   

    






    
 Exam 1  
 M 2/27  
 ---  
 Exam  
 Sect. 3.3: 20, 22. Sect 3.4:  14, 16. Sect. 4.2: 13, 15.
 HW 6  3/6    

    


    
  18  
  W 3/1 
  3.3-3.4, 4.1-4.2 
  n-th order linear ODEs. Homogeneous eqs. with constant coefficients. 

    



    
  19 
  F 3/3   
  3.3-3.4, 4.1-4.2  
 n-th order linear ODEs. Homogeneous eqs. with constant coefficients. 

    




    
 20  
 M 3/6   
 3.5, 3.6, 4.3, 4.4  
 Undetermined coeff.  Variation of parameters for nth order linear ODEs. 
  Sect. 3.4: 27. Sect. 3.5: 8, 10, 35, 36. Sect. 3.6 : 2, 13.  
 HW 7  3/20    

    


    
  21  
  W 3/8  
  3.5, 3.6, 4.3, 4.4  
  Undetermined coeff.  Variation of parameters for nth order linear ODEs. 

    



    
  22 
  F 3/10   
  3.7, 3.8  
  Applications. Mechanical vibrations. 

    




    
 23  
 M 3/20   
 3.7, 3.8  
 Mechanical vibraions
  Sect. 3.7: 3, 7. Sect. 3.8: 9, 15. Sect. 5.1: 7, 8, 16.    
 HW 8  3/27    

    


    
  24  
  W 3/22  
  5.1   
  Review of power series 

    



    
  25 
  F 3/24   
  5.2, 5.3  
  Series solutions near an ordinary point 

    





    
 26  
 M 3/27   
 5.2, 5.3  
 Series solutions near an ordinary point 
   Sect. 5.2: 2, 20. Sect. 5.3: 8. 5Sect. 5.4: 6, 25.     
 HW 9  4/03    

    


    
  27  
  W 3/29  
  5.4  
  Regular singularities. Euler equations. 

    



    
  28 
  F 3/31   
  7.1, 7.2.  
 Linear systems. Modeling. Review of Matrices.