Biomathematics

Overview

Contents:
Functions : Introduce the idea of functions using examples from Biology. Eg. Velocity of molecular motors as a function of ATP concentration
Derivative of a function,Techniques of differentiation : Eg. Concentration gradient; Pressure, entropy etc as derivatives of free energy

Finding maxima, minima, Plotting functions : Minimum of free energy; Plotting Gaussian, exponential function etc using examples from biology, Energy landscape
Integrals, Techniques of Integration : Integration as calculation of area under the curve.
Scalars and vectors. Spherical polar coordinates and cylindrical coordinates : 3-dimensional configuration of proteins, Structure of nucleosomes, 3D structure of chromatin

Ordinary differential equations, Partial differential equations, Solving differential equations : Rate equations (eg. Actin polymerization), Diffusion etc
Fourier series, Fourier transformation : Discussion of the use of Fourier transformation in X-ray crystallography and in optics, Examples from neurobiology
Introduction to probability : Discussion of stochastic processes in biology (Eg. bacterial motion), Application in statistical thermodynamics

Probability distributions, Average, variance, standard deviation etc : Eg. length distribution of microtubules with dynamics instability. Finding average length and standard deviation of the filament lengths; DNA loop formation probability.
Binomial distribution , Gaussian distribution , Poisson distribution : Eg. End-to-end distance distribution of proteins/DNA/RNA; Run and tumble motion of bacteria etc
Master equations : Eg. Modeling gene expression, polymerization of actin/microtubules