Biocybernetics and Systems Biology Course

by András Aszódi

Calculus demos

The differential quotient

The differential quotient is the slope of the tangent to the graph of the function, it measures how "fast" the function "changes". Formally it is defined as the following limit:

Definition of the differential quotient

The animation shows how the slope of the tangent changes.

Differential quotient

Download CDF

Taylor series

The Taylor series is a polynomial approximation to infinitely many times differentiable functions.

Taylor series

Truncated Taylor series are often used in numerical analysis to approximate functions. The animation below lets you appreciate how the Taylor approximation gets better when more and more terms containing higher-order derivatives are included.

Taylor series

Download CDF

Differential equations

Many mechanistic models rely on differential equations to model cause-effect relationships. Consult the CoCalc differential equation primer (PDF) on how to solve differential equations in SAGE.