Lecture Notes, etc. Updated April 10, 2003

Lecture notes and supplementary notes from courses and seminars:

2002 Spring Mth 619 Seminar. Prime Number Theorem
PDF, 163 KB, 12 pages

Lecture notes on the prime number theorem - incomplete.

2000 Winter Convex hull, Lucas theorem, Aziz's theorem and the Sendov-Ilyeff conjecture
PDF, 551 KB, 15 pages worksheet
MWS, 39 KB, Maple Worksheet

In this worksheet I implement the Jarvis walk for calculating the convex hull of a finite set in the plane. This code is then used to illustrate Lucas' theorem that the set Z(P')  of roots of the derivative  P'(z) of a complex polynomial P(z) lies in the convex hull of the set of roots Z(P) of P(z). Some random polynomials are generated for this purpose. In all cases the convex hull of Z(P') and the convex hull of  Z(P) are much more similar than one might at first expect. I then point out the (trivial) fact that a theorem of Aziz and the conjecture of Sendov and Ilyeff really say something about the Hausdorff distance between Z(P) and Z(P'). Finally I invite you to think about the Sendov-Ilyeff conjecture. All of this is for fun really - and to celebrate Feb 29, 2000, a rare centenary leap day!

1999 Summer Mth 507 Graduate Seminar. Contraction Mappings
PDF, 64 KB, 8 pages

This note discusses abstract metric spaces and the contraction mapping principle. One application given is to prove the existence and uniqueness theorem for initial value problems for systems of ordinary differential equations. Another application is a discussion of iterated function systems.

1998 Summer Mth 507 Graduate Seminar. Remarks on the Fourier Transform
PDF, 102 KB, 9 pages

These notes are from the Summer Graduate Seminar, Mth 507, 1998. The notes are an informal survey of some properties of the Fourier transform and a sketch of the application to operational calculus of non-commuting operators.

1998 Fall Mth 515 Abelain and Tauberian Theorems: Philosophy
PDF, 84 KB, 5 pages, 1 problem

This note gives a philosophical discussion of what is a Tauberian theorem and then provides a number of examples and an exercise. The notes were prepared primarily as an advertisement for Mth 516. The plan was to study the Ikehara-Landau Tauberian theorem and the Prime Number theorem in Mth 516, in addition to other topics dealing with the Fourier-Laplace transform and complex analysis.

1996 Seminar notes: Prime Number Theorem
PDF, 284 KB, 42 pages

These notes are from a seminar on the Riemann hypothesis and related topics offered by Ron Guenther, Mary Flahive and Bent Petersen in 1996. LaTeX-2e was used to prepare the notes.

1993-94 Lecture Notes: Weierstrass Vorbereitungssatz (Preparation Theorem)
PDF 151 KB, 8 pages

These notes are from three lectures from a graduate complex variable (one variable) course offered in 1993-1994. They were prepared using AMS-LaTeX.

1976 Lecture Notes: Riemann Zeta Function
PDF, 131 KB, 13 pages

These notes are from two lectures from a graduate complex variable course offered in 1976. They were prepared (in 1996) using LaTeX 2e.

Copyright © 1976-2002 Bent E. Petersen. The documents and the Maple worksheets described here, may be used, copied and distributed freely, entire and intact, for any educational noncommercial purpose, but may not be distributed in an altered form. If you want to improve on anything, which certainly can be done, then please write your own version(s).

petersen@math.oregonstate.edu

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