MAT 1310 Syllabus

Math 1310 Calculus for the Life Sciences

Text: Modeling the Dynamics of Life: Calculus and Probability for Life Sciences, Adler
Brooks/Cole
ISBN: 053434816

Designed to help life sciences students understand the role mathematics has
played in breakthroughs in epidemiology, genetics, statistics, physiology, and other
biological areas, this text provides students with a thorough grounding in
mathematics, the language, and 'the technology of thought' with which these
developments are created and controlled.

Table of Contents:

Chapter

1.  Introduction to Discrete-Time Dynamical Systems: biology and dynamics; Updating functions: describing growth; Units and dimensions of measurements and functions, linear functions and their graphs; Finding solutions: describing the dynamics; Combining and manipulating functions; Expressing solutions with exponential functions; Power functions and allometry; Oscillations and Trigonometry; Modeling and graphical analysis of updating functions; Equilibria; an example of nonlinear dynamics; Excitable systems: the heart
2. Limits and Derivates: introduction to derivatives; limits; continuity; computing derivatives: Linear and quadratic functions; derivatives of sums, powers, and polynomials; derivatives of products and quotients; the second derivative; curvature and acceleration; derivatives of exponential and logarithmic functions; derivatives of trigonometric functions; the chain rule
3. Applications of Derivatives and Dynamical Systems: stability and derivative; more complex dynamics; maximization; reasoning about functions; limits at infinity; leading behavior and L'Hôpital's Rule; approximating functions with lines and polynomials; Newton's Method; panting and deep breathing
4. Differential Equations, Integrals, and Their Applications: differential Equations; basic differential equations; solving pure-time differential equations