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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)

Lecture 11 - Integration (cont.)

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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