The course is intended for students who desire a rigorous development of the mathematical foundations of the methods used. This course provides the further techniques of ordinary differential equations, which are not covered by AM033 and are of very importance in practice. Systems of first order linear differential equations as well as nonlinear differential equations and stability will be covered. Computational software MATLAB and MAPLE for solving nonlinear problems will be used. The basic partial differential equations of heat conduction, wave propagation, and potential theory will be explored. We will use Fourier Series method for solving boundary value problems. Basic concepts of probability and statistics will be covered. 
    Prerequisite: AM0033 

Professor:          Vladimir Dobrushkin
Office:               37 Manning St, Room 306
Phone:               863-2507 
E-mail:               dobrush@cfm.brown.edu
Office Hours:     Mondays, Wednesdays, and Fridays 9:00 am -- 12:00 noon
Class Times:      Mondays, Wednesdays, and Fridays: 12:00 -- 12:50 
Location:           Barus & Holley  161
Teaching Assistant:  Heng Lian Heng_Lian@brown.edu
TA's office hours:    Thursdays 5pm
Grader:                   Thomas Redd Thomas_Redd@brown.edu
Homework:            Will be assigned on Friday of each week and is due in class  the following Friday; Late homework may not be accepted for grading.  
Exams:     
                          1st     Midterm Exam:  to be announced
                          2nd   Midterm Exam:   to be announced
                          Final Exam:     December 13
Crediting Policy:
For the actual credit (A,B,C,NC) of the course, the final exam counts 40\%, and
each midterm exam 30\%. Partial credit will be given only for accomplishing all correct steps in the solution procedure. 
No books or notes are permitted in the midterm exam. In the final exam, a
digest of up to 10 pages of handwritten notes (not xeroxed) is permitted, but
no book. Pocket computers are not permitted in either exam.

The lecture is mainly based on the text book ``Elementary Differential
Equations and Boundary Value Problems'' by Boyce and Di~Prima (Wiley), but
I may provide different material occasionally (maintaining the core of the
book's material). The last week will be devoted to statistics which is based on
the ``Notes on Statistics'' by C. Raphael (available in class). 

Systems of First Order Linear Ordinary Differential Equations
Nonlinear Ordinary Differential Equations and Stability  
Introduction to Partial Differential Equations
Introduction to Probability and Statistics
Selection of further material to be covered will be determined later.
 
 

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AM0033
AM0034