







Biocalculus






Organization:  Florida State University 
Department:  Department of Mathematics 






College






This course straddles the contentious divide between reform and tradition in calculus. It's goal is to mold biology majors into better scientists by enabling them to use Mathematica wisely, but it's approach embodies a firm conviction that skill in using high technology for complex procedures requires skill in using low technology (e.g., pencil and paper) for simple procedures. So it's outlook is thoroughly modern. But it's style is deliberately oldfashioned.






Lectures and course notebooks posted on the web






Biocalculus introduces the fundamental ideas of calculus from the perspective of a biologist, i.e., it uses biological data to motivate and elucidate concepts that are essential for constructive use of Mathematica in solving biological problems. The approach is heuristic, but systematic. One can develop a great deal of mathematical maturity with remarkably little exposure to mathematical rigor, and these lectures encourage students to develop as much as possible of the first with as little exposure as possible to the second. Topics:  Ordinary functions: an algebraic perspective
 Smoothness and concavity: a graphical perspective
 Quotients, inverses and limits. Modelling photosynthesis
 Ordinary sequences. Fibonacci's rapid rabbits
 Discrete probability distributions. Sums of powers of integers
 Function sequences. Compositions. The exponential and logarithm
 Index functions. Area and signed area
 From index function to ordinary function: ventricular recharge
 Area as limit of a function sequence. D'Arcy Thompson's mini minnows
 Arterial discharge: the area under a polynomial
 From ventricular inflow to volume: integration
 From ventricular volume to inflow: the derivative as growth rate
 Smoothness and concavity: an algebraic perspective
 Making joins smooth: the derivative of a piecewisesmooth function
 Differential notation. The derivative of a sum or multiple
 Sex allocation and the product rule
 How flat must a flatworm be, not to have a heart? The fundamental theorem
 Continuous probability distributions: the fundamental theorem again
 Derivatives of compositions: the chain rule
 Variation in rat pupil area. Implied distributions and integration by substitution
 Properties of exponential and logarithm. The empirical basis of allometry
 Periodic functions: models of rhythms in nature
 Bivariate functions and their extrema: a graphical approach
 More on bivariate functions: partial derivatives and integrals
 The mean and median of a distribution
 The variance. More on improper integrals
 Symmetric distributions
 Differential equations. The conceptual basis of allometry
 Trigonometric function properties
 The method of maximum likelihood












http://www.math.fsu.edu/~mmg/biocalc.html

