Calculus 1 Scientific Modeling and Differential Calculus

Many mathematical models in the natural and social sciences take the form of systems of differential equations. This introduction to the calculus is organized around the construction and analysis of these models focusing on the mathematical questions they raise. Models are drawn from biology economics and physics. The important elementary functions of analysis arise as solutions of these models in special cases. 

The mathematical theme of the course is local linearity. Topics include the definition of the derivative rules for computing derivatives Euler's Method Newton's Method Taylor polynomials error analysis optimization and an introduction to the differential calculus of functions of two variables.