# InfoCoBuild

## Biomathematics

Biomathematics. Instructor: Dr. Ranjith Padinhateeri, Department of Biotechnology, IIT Bombay. This course deals with various mathematical methods used in life sciences. Topics covered in this course include Graphs and functions, Derivative of a function, Techniques of differentiation, Differentiation and its application in Biology, Finding maxima and minima, Plotting functions, Integrals, Techniques of Integration, Scalars and vectors, Differential equations, Nernst equation, Diffusion equation, Mean-square displacement, Einstein relation, Probability and Statistics, Distribution functions, Uniform distribution, Poisson distributions, Fitting a function to experimental data, Fourier series, Fourier transform, Discussion of the use of Fourier transformation in X-ray crystallography, Statistical thermodynamics, Flexible proteins - size and conformations, Polymerization dynamics, Molecular motor motion, Bending and looping of DNA, and Protein organization along DNA. (from nptel.ac.in)

 Introduction

 Calculus Lecture 01 - Introduction Lecture 02 - Graphs and Functions Lecture 03 - Graphs and Functions (cont.) Lecture 04 - Functions and its Derivatives Lecture 05 - Calculation of Derivatives Lecture 06 - Differentiation and its Application in Biology I Lecture 07 - Differentiation and its Application in Biology II Lecture 08 - Differentiation and its Application in Biology III Lecture 09 - Differentiation and its Application in Biology IV Lecture 10 - Integration Lecture 11 - Integration (cont.) Differential Equations Lecture 12 - Differential Equations Lecture 13 - Differential Equations (cont.) Vectors Lecture 14 - Vectors I Lecture 15 - Vectors II Lecture 16 - Vectors III Applications of Calculus and Vector Algebra in Biology Lecture 17 - Nernst Equation Lecture 18 - Diffusion: Diffusion Equation Lecture 19 - Diffusion: Mean-Square Displacement Lecture 20 - Diffusion: Einstein Relation Probability and Statistics in Biology Lecture 21 - Statistics: Mean and Variance Lecture 22 - Statistics: Distribution Function Lecture 23 - Understanding Normal Distribution Lecture 24 - Fitting a Function to Experimental Data Lecture 25 - Size of a Flexible Protein: Simplest Model Lecture 26 - Uniform and Poisson Distributions; Knudson's Analysis Fourier Series and Fourier Transform Lecture 27 - Fourier Series Lecture 28 - Fourier Series (cont.) Lecture 29 - Fourier Transform Mathematical Models in Biology Lecture 30 - Master Equation: Polymerization Dynamics, Molecular Motor Motion Lecture 31 - Evolution: Simplest Model Tutorials Lecture 32 - Tutorials Lecture 33 - Tutorials (cont.) Statistical Thermodynamics of Biological Systems Lecture 34 - Temperature, Energy and Entropy Lecture 35 - Partition Function, Free Energy Lecture 36 - Bending Fluctuations of DNA and Spring-like Proteins Lecture 37 - Force-extension and Looping of DNA Lecture 38 - Thermodynamics of Protein Organization along DNA Lecture 39 - Learning Mathematics with the Help of a Computer

 References Biomathematics Instructor: Dr. Ranjith Padinhateeri, Department of Biotechnology, IIT Bombay. This course deals with various mathematical methods used in life sciences.