Harley Flanders

Harley M. Flanders (September 13, 1925 – July 26, 2013) was an American mathematician, known for several textbooks and contributions to his fields: algebra and algebraic number theory, linear algebra, electrical networks, scientific computing.

Life Flanders was a sophomore calculus student of Lester R. Ford at the Illinois Institute of Technology and asked for more challenging reading. Ford recommended A Course in Mathematical Analysis by Édouard Goursat, translated by Earle Hedrick, which included challenging exercises. Flanders recalled in 2001 that the final exercise required a proof of a formula for the derivatives of a composite function, generalizing the chain rule, in a form now called the Faa di Bruno formula.

Flanders received his bachelors (1946), masters (1947) and PhD (1949) at the University of Chicago on the dissertation Unification of class field theory advised by Otto Schilling and André Weil. He held the Bateman Fellowship at Caltech. He joined the faculty at University of California at Berkeley. In 1955 Flanders heard Charles Loewner speak there on continuous groups. Notes were taken and the lectures appeared in a limited form with the expectation that Loewner would produce a book on the topic. With his death in 1968 the notes drew the attention of Murray H. Protter and Flanders. They edited Loewner's talks and in 1971 The MIT Press published Charles Loewner: Theory of Continuous Groups. The book was re-issued in 2008.

Teaching posts Flanders held included the faculty at Purdue University (1960-1970), Tel Aviv University (1970–77), visiting professor at Georgia Tech (1977–78), visiting scholar at Florida Atlantic University (1978–85), University of Michigan, Ann Arbor (1985–97, 2000–), University of North Florida (1997–2000), and distinguished mathematician in residence at Jacksonville University (1997–2000).

Flanders was Editor-in-Chief, American Mathematical Monthly, 1969–1973. He also wrote calculus software MicroCalc, ver 1–7 (1975–). Recalling his early exposure to the formula of Faa di Bruno, Flanders wrote, "I think Faa's formula is quite inefficient for the practical computation of numerical (not symbolic) derivatives."

In 1954, Flanders considered the converse of the Poincaré lemma.

In 1963, Flanders published Differential Forms with Applications to the Physical Sciences which connected applied mathematics and differential forms. A reviewer affirmed that the book forms such a bridge with differential geometry. Republished in 1989 by Dover Books, the book includes a succinct mathematical electromagnetism, where the electric and magnetic components of the field pertain to complementary 2-forms, obtained from exterior derivation of the electromagnetic four-potential.

Awards MAA Lester R. Ford Award 1969 NCRIPTAL/EDUCOM Distinguished Software Award 1987 NCRIPTAL/EDUCOM Distinguished Software Award 1989 Lifetime Senior Member, IEEE 1998

Mathematics education In 1970, Flanders published the first of several useful textbooks for topics commonly taught at college level: with Justin Jesse Price and Robert R. Korfhage a text on Calculus was distributed by Academic Press. With J. J. Price, Flanders also wrote Elementary Functions and Analytic Geometry (1973) and Introductory College Mathematics: with Linear Algebra and Finite Mathematics (1974). With both J.J. Price and R.R. Korfhage, Flanders wrote First Course in Calculus with Analytic Geometry (1974) and Second Course in Calculus (1974).

To support the recruitment of students with capacity to follow these courses, some works on precalculus mathematics were written with J.J. Price: Algebra (1975), Trigonometry (1975), Algebra and Trigonometry (1981), Precalculus Mathematics (1981), and College Algebra (1982).

Flanders continued with Single-Variable Calculus (1981) and another Calculus in 1985

In 1984, Flanders published his textbook on Pascal language: Scientific Pascal (1984) for which a second edition was published in 1996 by Birkhäuser. That year he also published Calculus: A lab course with MicroCalc (Springer-Verlag).

Selected papers

with P. M. Lin:

with Harald K. Wimmer:

with Harald K. Wimmer:

with Herbert Fischer: