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Updated regularly; only authoritative version is current version!
Homework assignments pertinent to each lecture will be posted 
shortly after the lecture is completeted.
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Last update: Sun Dec 14 21:33:32 MST 2003
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           Math. 312 - Homework Assignments and Exams Schedule
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Based on R. Haberman's text.
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			     Syllabus
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   I. The method of separation of variables: Heat flow.
  II. Fourier Series and vibrations: 
              strings, membranes, electromagnetic waves.
 III. Problems with symmetry: Sturm-Liouville theory and the
              special functions of mathematical physics.
  IV. Green's functions: sources for the Heat, Laplace and Wave equations.
   V. Introduction to characteristics: conservation laws and shock waves.
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 1( 8/26) 1.1-3 one-dimensional heat conduction
 2( 8/28) 1.4, 2.1-2.3.4 Separation of variables
   Set 1 (due 9/4) 1.2.5, 1.3.2, 1.4.1(a,c,f), 1.4.3, 1.4.10, 2.3.2(b,d),
                   2.3.4(a) 
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 3( 9/ 2) 2.3.5-2.4   Examples - heat conduction
 4( 9/ 4) 2.5.1     Laplace's equation in a rectangle
   Set 2 (due 9/11) 2.3.8, 2.4.1(a,b,c), 2.4.2, 2.5.1(a,e)
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 5( 9/ 9) 2.5.2   Laplace's equation in a disk
 6( 9/11) 3.1-3 Fourier Series and variants.
   Set 3 (due 9/18) 2.5.3a, 2.5.6a, 2.5.8a, 
                    3.3.2(a,d), 3.3.3a, 3.3.10, 3.3.13
The last day to drop a course in order to receive a refund or credit
Friday, September 12
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 7( 9/16) 3.4   Properties of Fourier Series; 
 8( 9/18) 3.4   Example: diffusion equation with a source
   Set 4 (due 9/25) 3.4.6, 3.4.9, 3.4.12, 3.5.7
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 9( 9/23) 3.5 Integration of Fourier series; Review
10( 9/25) Overview.
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          Exam Part I  (Ch. 1,2,3) due in class, 2:00
11( 9/30) 4.4 Vibrating String with fixed ends.
12(10/ 2) 5.1-3   Sturm-Liouville theory and eigenvalue problems
          5.8 General boundary conditions 
   Set 5 (due 10/9) 4.4.(1,3), 5.3.(5,6)(a,b,c), 5.3.7
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13(10/ 7) 5.4-5   Self-adjoint Operators
          5.6-8   Rayleigh quotient and approximation of eigenvalues
14(10/ 9) 5.10 Approximation properties
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15(10/14) 7.1-4   Separating the time; heat conduction vs. wave propagation:
                  the Helmholtz equation
   Set 6 (due 10/23) 5.(3.3, 5.1g, 5A.5, 6.1c, 7.1, 8.3, 8.10, 10.2(b))
**(10/16-17)  Fall Break
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16(10/21) 7.5-6   Green's formula and Rayleigh Quotient
17(10/23) 7.7   Bessel functions and cylindrical symmetry
   Set 7 (due 11/ 4) 7.5.(6, 7, 8a), 7.7.(3a, 8, 10, 12(a,c))
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18(10/28) 7.8,9  More on Bessel functions: series and recurrence relations
19(10/30)          ""
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20(11/ 4)          ""       
21(11/ 6) 7.10   Legendre polynomials and spherical symmetry
          Exam Part II (Ch. 4-5-7 including Bessel fncs) - due 11/13
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22(11/11) 7.10   Legendre polynomials, spherical harmonics 
23(11/13)        """"
    Set 8 (due 11/20) 7.10.3c, 7.10.9c, (+problem given in class)
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24(11/18) 8.1-4   Problems with sources: heat equation
25(11/20) 8.6   Poisson's equation
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26(11/25) 9.5, 8.6     Electrostatics: Poisson's equation and images
   Set 9 (due 12/4) 8.3(1c, 7), 8.4.1b, 8.6(3a, 5, 6, 9ab) 
**(11/27-28) Thanksgiving Break
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27(12/ 2) 8.5 Forced vibrations; resonance
          9.1-3   Green's functions
28(12/ 4) 9.3   Delta functions; sources 
   Set 10 (due 12/11) 9.3(1, 5abc, 13ab, 15ab, 21, 25ab)
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29(12/ 9) 12.1-2 Characteristics
30(12/11) 12.6   Shock Waves 
 Exam Part III (Ch. 7.10, 8.1-6, 9.1-3) (due in my office by 14:30, T 12/16)
  < (1) 7.10.10c, (2) 8.3.1b, (3) 8.3.6,        (4) 8.4.2, 
    (5) 8.5.3,   (6) 8.5.6,  (7) 9.3.11ab-12b, (8) 9.3.23-24  >
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