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Lectures On Chemical Reaction Networks

    You'll find below links to scanned copies of  typewritten versions of 4½ out of 9 lectures that I gave at the Mathematics Research Center of the University of Wisconsin-Madison in the autumn of 1979. (Typing was by the wonderful Donna Porcelli.) The occasion was a semester-long in-gathering of people interested in the behavior of complex chemical systems. At the end of that period there was a large meeting, the proceedings of which were published by Academic Press in a book, "Dynamics and Modeling of Reactive Systems," edited by W. Stewart, W. H. Ray and C. Conley. My chapter amounted to a summary of some of the things I talk about during the course of the nine lectures.

    It was an exciting time, which began when Charles Conley called me at the University of Rochester.  He explained the MRC plans for 1979 and asked if I could spend a semester in Wisconsin. He said that they would pay my salary, provided that my salary wasn't too high. I told him my salary. Conley asked if I could come for a year.

    The mix of long-term visitors and permanent Wisconsin people made for a very stimulating mini-sabbatical. Rutherford Aris, Harmon Ray, Warren Stewart, Manfred Morari, and Klavs Jensen were among the active chemical engineers.  Among the mathematicians were Charles Conley, Chris Jones, Neil Fenichel, and Mike Crandall.  At the time, John Nohel was the gracious director of the MRC.  I couldn't have asked for a better group of people to whom I might expose recent thinking about reaction networks.

    The lectures have origins in work initiated by Fritz Horn and Roy Jackson. Much has happened since then, only a small part of it reflected in the lectures, but the early work of Fritz and Roy planted seeds without which little fruit would have come into being. For me, Fritz, Roy, and Rutherford Aris have been  towering examples of chemical engineering scholars and, more importantly, friends.  Fritz died before these lectures were given. He was brilliant. Even now, when I do something I think is nice, I wish Fritz were here to see it.

    People who knew Charles Conley -- and those who know the work he left behind -- agree that he was a dazzling, remarkably innovative mathematician. His great interest in my lectures was an extremely important source of encouragement. (I didn't know at the time that Charlie was interested in just about everything!)

    Here, then, are links to the lectures.

Lecture 1.  Introduction (1500KB)

Lecture 2.  Reaction Networks, Kinetics, and the Induced Differential Equations (1900KB)

Lecture 3.  Two Theorems (2190KB)

Lecture 4.  Some Definitions and Propositions (1963KB)

Lecture 5.  Proof of the Deficiency Zero Theorem (1103KB)

References. Partial Bibliography for Lectures 1-5 (93KB)

Martin Feinberg
Chemical and Biomolecular Engineering & Mathematics
The Ohio State University