M531 - Discrete Models of Physical Systems, Fall 2002
MWF 3; http://www.math.colostate.edu/~juliana/M531.html
Instructor: Dr. I. Oprea: http://www.math.colostate.edu/~juliana, Office Hours: MW 11-12 AM and by appointment
Foundations of Analysis of Mathematical Models

The course develops the mathematical background for the analytical analysis of physical models involving linear algebra and ordinary and partial differential equations. This course provides the foundation for further study in applied mathematics and the numerical and analytical analysis of physical models.  The course is aimed primarily at engineering graduate students.

Textbooks:

• Sheldon Axler,  Linear Algebra Done Right, 2nd Ed,  Springer  Verlag (1997)
• Mark Pinsky,  Partial Differential Equations and Boundary-Value Problems with Applications, 3-rd Ed, 2003, Waveland Press Inc, ISBN: 1-57766-275-X

• Topics to be covered
1.   Linear Algebra and Matrix Theory: Mathematical modeling, vector spaces, linear transformations and  matrices, determinants, eigenvalues and eigenvectors, least squares  applications;
2.   Ordinary Differential Equations: Systems of  equations, exponential and fundamental  matrices, nonhomogeneous equations, computing solutions
3.   Partial Differential Equations: Classification of equations, Fourier series,  Sturm-Lioville problems, boundary value problems    in rectangular  and cylindrical  coordinates, Fourier transforms.

HW assignments
HW#1: Problem #5, pag. 19. HW#2: Problems 1-3, 8 pag. 35. HW#3: Problem One: here, Problems # 5,9,11, 12, pag. 59, and a last one here. HW#4: Problems 1, 5, 6 pag. 94; sol. to Problem 1 here. HW#5: Part 1, Part Two.  HW#6: here.HW#7: two problems of choice + 3 ODEs handed out in class. HW#8: Problems 1-10. HW#9:  0.1.1 : # 2,3,5; 0.1.2 : # 2,4;0.1.4 : # 1;0.1.5 : # 1-4; 0.2.2 : # 1;0.2.3 : # 1;0.2.4 : # 1;

HW#10: Pag. 33 : 4-6; Pag. 44:  4, 15 a)-d); 16:a,b;17:a,b,
HW#11: Pag. 96: 1-6, 7, Problem: solve equation (1.6.1) with periodic boundary conditions; problem 5.4.2.
HW#12: pag. 108 (from Exercises2.1): pb: 1,2,11,12, pag. 120, pb.3 (from Exercises 2.2)

XCREDIT (Copyright M. Viele, B. Twitchell): plot of the surface; Matlab code,  another plot.
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. The take home final: (link here) pdf  or ps or jpeg (pag1 and pag2)
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