Teaching Differential Equations without Computer Graphics Solutions is a Crime

In the early 1980s computer graphics revolutionized the teaching of ordinary differential equations (ODEs). Yet the movement to teach and learn the qualitative methods that interactive graphics affords seems to have lost momentum. There still exist college courses, even at big universities, being taught without the immense power that computer graphics has brought to differential equations. The vast majority of ODEs that arise in mathematical models are nonlinear, and linearization only approximates solutions sufficiently near an equilibrium. Introductory courses need to include nonlinear DEs. Graphs of phase plane trajectories and time series solutions allow one to see and analyze the crucial behaviors, whether or not analytic solutions exist. Furthermore, interactivity is key to experimenting with parameters in order to modify behaviors. Now, a quarter of a century later, we have far more technology--but many features of the original software have been lost in the rush to the future. We have both educational and software concerns. This is not only an academic issue--scientists at multiple nonacademic agencies (e.g., FDA, NIH, USCGS) immediately took up our software tools in the late 1980s, and increasingly more of our students come from fields that did not traditionally require mathematics background. We should not be depriving today\u27s students of the skills to analyze behaviors of solutions to ODEs

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Differential equations a dynamical systems approach: ordinary differential equations

This is a corrected third printing of the first part of the text Differential Equations: A Dynamical Systems Approach written by John Hubbard and Beverly West. The authors' main emphasis in this book is on ordinary differential equations. The book is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. Traditional courses on differential equations focus on techniques leading to solutions. Yet most differential equations do not admit solutions which can be written in elementary terms. The authors have taken the view that a differential equations defines functions; the object of the theory is to understand the behavior of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods. The companion software, MacMath, is designed to bring these notions to life

MacMath 92: a dynamical systems software package for the Macintosh

MacMath is a scientific toolkit for the Macintosh computer consisting of twelve graphics programs. It supports mathematical computation and experimentation in dynamical systems, both for differential equations and for iteration. The MacMath package was designed to accompany the textbooks Differential Equations: A Dynamical Systems Approach Part I & II. The text and software was developed for a junior-senior level course in applicable mathematics at Cornell University, in order to take advantage of excellent and easily accessible graphics. MacMath addresses differential equations and iteration such as: analyzer, diffeq, phase plane, diffeq 3D views, numerical methods, periodic differential equations, cascade, 2D iteration, eigenfinder, jacobidraw, fourier, planets. These versatile programs greatly enhance the understanding of the mathematics in these topics. Qualitative analysis of the picture leads to quantitative results and even to new mathematics. This new edition includes the latest version of the Mac Math diskette, 9.2

Differential Equations & Linear Algebra

https://digitalcommons.library.umaine.edu/fac_monographs/1085/thumbnail.jp

Interactions of Avocado (Persea americana) Cytochrome P-450 with Monoterpenoids

The microsomal fraction of avocado (Persea americana) mesocarp is a rich source of cytochrome P-450 active in the demethylation of xenobiotics. Cytochrome P-450 from this tissue has been purified and well characterized at the molecular level (DP O'Keefe, KJ Leto [1989] Plant Physiol 89: 1141-1149; KR Bozak, H Yu, R Sirevag, RE Christoffersen [1990] Proc Natl Acad Sci USA 87: 3904-3908). Despite this extensive characterization, the role of the enzyme in vivo was not established. Optical and electron paramagnetic resonance binding studies described here suggest that the monoterpenoids, nerol and geraniol, are substrates of avocado cytochrome P-450 (spectral dissociation constant of 7.2 and 35 micromolar, respectively). Avocado microsomes have been shown to catalyze the hydroxylation of these monoterpenoids, and both nerol and geraniol have been shown to inhibit the activity of avocado cytochrome P-450 toward the artificial substrate 7-ethoxycoumarin, with nerol a competitive inhibitor of this activity