Math 312     Sp. 1996

Text: "Fourier Series" by Tolstov, published by Dover,
 and "Boundary Value Problems", 3ed. by David L. Powers.
  1. Mathematical models of physical problems: heat, wave, and
Laplace's equations.


    • Read sections: 11, 20 of Chap. 9; Tolstov, and the 
first section of chapters 2 and 3 in Powers.


    • Work problems: Powers: p. 118; 1, 6: p. 213; 2, 3, 4.

    

  2. Separation of variables, second order boundary value problems.


    • Read sections: 1, 2 of Chap. 9; Tolstov, and pages 
19 - 27 of Powers.


    • Work problems: Powers: p. 27; 1, 3, 7, 8.

    

  3. Linearity, inner products, and coordinates.


    • Read sections: 1 - 7 of Chap. 2; Tolstov.


    • Work problems: 

    

  4. Fourier series representations of functions.


    • Read sections: 1 - 13, and 15 of Chap. 1; Tolstov and
sections 1 -- 6 of Chap. 1; Powers.


    • Work problems: Tolstov: p. 38; 1, 3, 4, 7 - 10, 12;
p. 152; 1, 3, 4: Powers: p. 63; 1, 2; p. 68; 1, 2;
p. 73; 1, 2, 3, 8, 9. 

    

  5. Convergence of Fourier series.


    • Read sections: 1 - 11, Chap. 3; Tolstov, and section 7 
of Chap. 2; Powers.


    • Work problems: Powers: p. 84; 3, 4.

    

  6. Solutions to boundary value problems.


    • Read sections: 1 - 6, Chap. 2; sections 1 and 2, Chap. 3, 
and Chap. 4 of Powers.


    • Work problems: Powers: p. 130; 1, 2, 8; p. 140; 3, 9, 10, 11;
p. 145; 1, 2, 3, 5; p. 213; 6, 8; p. 219; 7; p. 233; 5.

    

  7. Fourier series of functions of more than one variable.


    • Read sections: 1 - 4, Chap. 7, Tolstov.


    • Work problems: Tolstov: p. 195, 3.

    

  8. Solutions to boundary value problems.


    • Read sections: Chap. 5 of Powers.


    • Work problems: Powers: p. 241; 1 - 3; p. 248; 2, 3, 6, 7.
  9. Sturm-Liouville results on eigenfunction expansions. 
    • Read sections: 1 - 7, Chap. 9, Tolstov, and sections
7 and 8, Chap. 2, Powers.


    • Work problems: Powers: p. 150; 1, 2, 4, 7.
  10. Fourier Transform 
    • Read sections: 5 - 11, Chap. 7, Tolstov, and sections
9 - 11, Chap. 1, Powers.


    • Work problems: