M531 - Discrete Models of Physical Systems,  Fall 2003
MWF 3; http://www.math.colostate.edu/~juliana/M531.html
Instructor: Dr. I. Oprea: http://www.math.colostate.edu/~juliana,
Office Hours:  W 4:10-5:00PM, TWF 10:00 – 11:00 AM  and by appt., Phone: 491-6751 Office
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.


  • 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.


    Course objectives

    Additional info:
    A.  below is a link to a more detailed (free) linear algebra text book, in the event that  you didn't have any linear algebra course in the past or if you want some extra problems to do: Jim Hefferon, Linear Algebra: http://joshua.smcvt.edu/linalg.html or if the link doesn't work, you can find the book and the solutions here.
    B. A FORTRAN code to compute eigenvalues of Sturm Liouville Problems

    HW assignments (don't forget to press the Reload button before checking what's new on this page!)
    HW #1,
    HW #2: see hand out;
    HW #3: problems 2,8, page 35, 5-pag. 59;
    HW #4: 2,9,10 - pag.59; 19, 20 from the yellow page hand out in class
    HW #5: 2,3,4,8 from handout material, Problem A, here
    HW #6: 1,3,6,8,9,11,15,17 from handout material; if you've missed the class, you can find an extra copy on my office's door.
    HW #7: Least Squares Problems; Strogatz, Ch. 5; 5.2.1, 5.2.3-5.2.11;
    HW #8: Pinsky:       0.1.4 #1,     0.1.5 #4;   0.2.4: #1
    HW #9: 0.3: #6; 1.1.1, 1.2.16
    HW # 10: 1.6.2-1.6.5 (pag. 96),  2.2.1,2.2.3 (pag.120) due December 1; Friday 21 November lecture is about 2.4.3-2.4.6
    Last HW, due Wed.10, problem #4, Section 2.5 (pag. 168)

    You can take a look at the homework assignments from M531 Fall 2002 here