OFFICE: Math 450 OFFICE HOURS: Tuesday 1:30-2:30 pm + by appointment PHONE: (765) 494-1975 EMAIL: eremenko@math.purdue.edu GENERAL INFORMATION AND POLICIES
Homework 1 (due January 17, before the class starts)
Read Chapter 1 and Appendices 1,2. Do: p.7: 1,3,5,6,7;
p. 11: 3, 4, p. 17: 1, 3, 5.
Math Library (3-d floor, Math building) has the textbook on reserve.
Homework 2 (due January 24) pp. 26-28: derive 4, 7, 16, p. 37: 1a-d, 2, 3, 4, p. 42: 5, 6, 7.
Homework 3 p. 47: 1,3,5; p. 56: 1,3,4,5; Read p. 62-67; p. 67: 3,4,9.
Homework 4 p. 71: 1,4,6,7, p. 79: 2,3,4,9, p. 85: 2,4,6,7.
Homework 5 p. 85: 1,3,5, p. 93, 1, 2, 3,4, 5, 7, 8, 10;
Homework 6 (due Tuesday, Febr 21). p. 107: 1ab, 2, 5, 6, 7ab, p. 113: 2, 4, 5, 7.
Homework 7. P.119: 1,2,3,5,6abc, p. 126: 1, 2, 3, 4.
An interesting monument to Friedrich Wilhelm Bessel in Bremen.
Homework 8. p. 132: 1, 2. p. 137: 1, 11, p. 143: 2, 8. p. 149: 1,3,6. p. 156: 1, 3.
Legendre and Fourier. This is the only known portrait of Adrien-Marie Legendre. But there are many pictures of Fourier. Enjoy the break!
Homework 9 (due March 27) p. 173: 1,2,8, p. 183: 1, 4, 5, 8.
Nodal lines (zero lines of eigenfunctions), also known as "Chladni plates" a movie of the experiment with sand of the kind that I described. But they use a metal plate instead of a paper membrane.
Homework 10
p. 189: 1, 2, 3;
p. 212: 1abcd, 3, 4, 224: 2, 4, 12.
AND
the following problems A, B and C:
A. Suppose that f is in L^2(R). Restate the following
conditions on f in terms of its Fourier transform:
a) f is even,
b) f is odd,
c) f is real,
B. Relate the Fourier transform of f to the Fourier transform of
f(at-b) and exp(itc)f(t), where a, b and c are real numbers.
C. If we iterate the Fourier transform twice,
what will be the result?
Homework 11 p. 234: 1, 2, 7, p. 240: 1, 4, 5, p. 247: 1, 2, 5, 10.
Homework 12 p. 313: 3, 4, 5. p. 320: 2, 3, 6,
This was the last homework, but one problem from the new material (Sections 9.3, 9.4) will be on the final exam.
