Math 152 - Spring 2004

References Cited for Lectures

January 12, 2004 lecture: Intro to Calculus

A detailed predictive model of the mammalian circadian clock
by Daniel B. Forger and Charles S. Peskin
Full paper as a PDF file - December 9, 2003 PNAS 100: 14806-14811

Comments: The detailed mechanisms by which cells within mammals are coordinated to have the same 24 hour clock (the circadian clock) are quite complex. This involves a very large number of interacting enzymes and proteins. The authors develop a mathematical model that describes these complex interactions, using a collection of differential equations. These equations describe the rates at which different reactions occur as a function of the concentrations of the various proteins.

January 21, 2004 lecture: Intro to Derivatives

Human Population: The Next Half Century
by Joel E. Cohen
Full paper as a PDF file - 14 Nov 2003 Science 302:1172-1175

Comments: This paper reviews the history of human population on our planet focusing on the dynamics of the size of the population as well as its growth rates. The author points out how rapidly the human population has been growing, at an increasing rate. Thus the doubling time of the population has changed from 50 years in 1927 to 25 years in 1974. What is gtreatly significant is that the yearly population growth rate has declined over the past 3 decades from 2.1% to 1.2%, associated with a great reduction in the fertility rate (from over 5 to less than 3 children per woman per lifespan. Thge author uses mathematical models to project the changes in population structure (age) through the next 50 years.

February 4, 2004 lecture: Derivatives as Instantaneous rates of change

Ed Karrels Bike Races
Background on his races and A particular race with info on speed, heart rate, altitude and power used

March 31, 2004 lecture: Work and Integrals

SYSTEMS BIOLOGY: Tracing Life's Circuitry
by Elizabeth Pennisi
Full paper as a PDF file - 5 Dec 2003 Science 302: 1646-1649

Comments: This news article described the new area of systems biology as an approach for linking mathematics, engineering and biology to address questions such as how networks of cells function. As I mentioned in class, one of the simplest models for cell cycling is similar in form to the mathematics of oscillations of the springs we discussed. Indeed, the simple harmonic oscillator (a spring without damping) is a bsiac model for much of rhythmic behavior in biology. The idea of systems biology is to link together models for biology at several hierarchical levels (within cells, cells, tissues, whole organisms) and attempt to determine the properties of the whole from the parts (a general gaol in science from a reductionist perspective).

April 5, 2004 lecture: Density Functions and Oceanography

Two UT EEB Faculty manage large numbers of oceanography studies for the National Science Foundation in the Arctic Lee Cooper and Jacqueline Grebmeier and detailed infor about their projects is at Arctic BIO UTK site
The type of data they organize expeditions (on ships) to collect are an expanded version of the type we discuss in this section of the course - distributions of the density of various marine organisms and chemical compounds as a function of depth and location in the ocean. For examples of these types of data, see Biological Atlas of the Arctic Seas and in particular for an example of the type of data similar to what we discuss in class, see Characteristics of Phytoplankton of the Barent's Sea

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