MATH 127: Biocalculus with applications in modeling

Calculus for the life sciences, Biocalculus for short, is a first course in calculus geared towards researchers biology and biomedicine who have little or no previous exposure the subject. It covers all fundamental topics of single-variable calculus, but with a focus on concepts and application in the natural sciences, as opposed to proofs of theorems or arcane symbol manipulation.

The course includes a brief review of review of pre-calculus topics like algebra, analytic geometry , and trigonometric functions. Students who think they would benefit from a refresher are encouraged to take a foundations and precalculus course.

The course then quickly leaps into the mathematics of infinity and beyond: infinitesimal quantities, differentials, infinite sequences, and whether it is possible to divide by zero.

Practical applications of Calculus in research will be emphasized, especially mathematical modeling of biological systems: Ordinary Differential Equation (ODE) models, optimization, population dynamics (e.g. epidemiological) and equilibria, phase plots analysis, among others.

Prerequisites A pre-calculus course (half-semester or equivalent) is recommended, but not required. Knowledge of trigonometry, basic algebra, and basic graphing is required (but a brief review is part of the course).

Learning Objectives:

• Understand the concept of functions, their limits, and continuity
• Become familiar with differentiation and integration techniques of single-variable functions
• Introduce applications of calculus to scientific research