Jim Herod's Home Page

James V. Herod, Professor Emeritus

School of Mathematics

Georgia Institute of Technology

Atlanta GA

USmail: P O Box 1038, Grove Hill, AL 36451

email: jherod@tds.net

Phone: (251) 275 2244


First note that I have retired. I no longer maintain an office at Georgia Tech. Look at my address above! I do answer email. This is the best way to contact me when I am at home. When I travel, my email is different.


What follows is a collection of things that please me. I list them in no particular order, give a brief description of what they are about, and provide a contact point to access more details.


1. A New Interest:   It is true that I have published a work of fiction titled Gathering Moss. Publication date was January, 2008. Some of the action in the book takes place on the campus of Georgia Tech, some at the University of Alabama, and some at the University of Montana. There are both science and mathematics in the book. The technical parts are written to be accessible to the general reading public. Is it a surprise that a person who has spent a life in mathematics would write a book of fiction? I say no. One can look at the process of engaging a person in the pleasure of science, mathematics, or fiction as a continuation of the old Southern tradition of story-telling. After all, a good lecture tells a story; and a good story-teller creates the narrative to fit the intended audience.


2. No More Same Old Calculus: Before I retired, Professor George Cain and I made a common observation: most students entering Georgia Tech have already had the calculus. Because they think they already know the calculus, they often fail to note that the college course expects a deeper understanding of the concepts. Or, the students are bored because their high school calculus was such a good course. Cain and I wanted to make the materials fresh and exciting. Our decision was to present the notions of calculus in a multidimensional setting at the outset. This would take more time than typical in a second year calculus course because we would constantly go back to re-look at the one dimensional setting from this multidimensional perspective. Where could we find a text? Can you guess?


3. Asynchronous Studies in Undergraduate Partial Differential Equations: Georgia Tech now offers graduate programs in engineering where the materials stream over the web for students scattered all over the country. I participated in this program for several summers after I retired. The last time was during summer, 2006. There were streaming lectures, class notes, detailed calculations, and a bulletin board for class discussions. Some of these materials are accessible from my web site.


4. Notes for a course in Partial Differential Equations: In the Winter of 2003, I was commissioned to write a set of notes for studies in classical linear partial differential equations and to publish these notes on the web site for Maple Waterloo Software, Inc. These notes are available at this site with minor modifications from what appears at the Maple site. The modifications occur as small changes are made to the text or to the models, and as additions are created to amplify these ideas.


5. An Introduction to the Mathematics of Biology: Unsuspecting students often are surprised that mathematics could be so important in Biology. Even professionals are likely to think that the mathematics of biology is statistics. Yes, statistics is important in biology. There is also modeling. A good mathematical model for a biological phenomenon can illustrate what is observed in life, can predict outcomes, and can give directions for biological research. During the years before Professor Edward Yeargers and I retired, we joined with Professor Ron Shonkwiler in teaching an undergraduate course in mathematical biology. A text came out of our joint efforts. You will find that I keep all the Maple syntax current, as well as provide a list of errors we have found after printing.


6. Studies in the First Two Years of Undergraduate Mathematics: As students are introduced to the concepts of undergraduate mathematics, they often wish to see applications of the ideas. The models presented in this section have evolved through teaching, as well as through discussions with faculty at Georgia Tech and other universities. These studies are made available with the hope that students will find the models give insight, and that other faculty will use them in methods which seem appropriate.


7. An Introduction to the Linear Algebra of Infinite Dimensional Spaces: Graduate students in Mathematics and in several engineering disciplines include in their studies the notions of Hilbert Spaces. It was a course that I taught often at Georgia Tech and, consequently, developed a set of notes. The notes are pretty compact. They serve as an introduction to studies in more general infinite dimensional spaces.


8. An Introduction to the Use of Maple for Applications: I am asked fairly often about how to accomplish different type tasks with Maple. I created some materials that can be used to get an introduction to the use of Maple for classroom instruction and for analyzing applications from a variety of sources.


9. First Order Differential Equations with Periodic Forcing Functions: In this Maple worksheet, we consider solutions Y for the differential equation Y '(t) = A Y(t) + F(t). In case A is a number and F is a real valued function, students in an introductory calculus course often can make a solution for the equation. If A is a matrix, students in an introductory ordinary differential equations course likely can formulate a solution if F is vector valued. The interest here is a view for how to handle this problem for A in a class of differential operators. We review all three situations in this expository discussion. Our principal interest is in periodic solutions in case F is periodic. The pleasure is in putting the three settings into one context.


10. MAA Short Course, March 2002: At a joint regional meeting of the American Mathematical Society and the Mathematics Association of America, Professor Ron Shonkwiler, Professor Edward Yeargers, and I presented a short course on An Introduction to the Mathematics of Biology. Notes for the course are posted on this web site.


11. Maple Conference, Summer 2006: The Maple document located at this site was the basis of a presentation at the Maple Conference in July, 2006. The paper was co-authored with Don Jones .  Using the diffusion equation with periodic endpoint boundary conditions, the paper illustrates how to compute both the periodic solution and the particular solution for a partial differential equation with specified initial conditions. With three dimensional graphics and with animations, the coalescence of the particular solution to the periodic solution can be observed. A similar analysis is made for the wave equation with periodic endpoint boundary conditions. Also, techniques are shown for using Maple to compute numerical solutions for these equations.


12. Connections: Often I get email inquiries from both sides of the Atlantic asking from where my family comes. Usually, the author of the message wants to know if we are related. I am fortunate to have several cousins interested in making these connections. I am the second son of Joseph Wheeler Herod.