IIT Bombay Course , Prof. Ranjith Padinhateeri

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IIT Bombay Course , Prof. Ranjith Padinhateeri

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

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

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Biomathematics by Dr. Ranjith Padinhateeri, Department of Biotechnology, IIT Bombay.For more details on NPTEL visit httpnptel.iitm.ac.in

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The above video lectures are presented by IITBombay, India, under the program NPTEL, there are more than 350+ NPTEL courses Online available.
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- 1.Introduction
- 2.Graphs and Functions
- 3.Graph & Function II
- 4.Function and its derivatives
- 5.Function and its derivatives
- 6.Differentiation and its application in biology
- 7.Differentiation and its application
- 8.Differentiation and its application(Contd...) I
- 9.Differentiation and its application(Contd...) II
- 10.Integration
- 11.Differential Equations
- 12.Differential Equations - part 2
- 13.Vectors
- 14.Vectors - 2
- 15.Vectors - 3
- 16.Application of calculus and vector in biology
- 17.Diffusion
- 18.Diffusion II
- 19.Diffusion III
- 20.Statistics
- 21.Probability Distribution
- 22.Understanding Normal Distribution
- 23.Fitting a Function to Experimental Data
- 24.Size of a Folded Protein Simplest Model
- 25.Uniform Distribution
- 26.Fourier Series
- 27.Fourier Series II
- 28.Fourier Transform
- 29.Master Equation Polymerization Dynamics, Molecular Motor Motion
- 30.Simple Mathematical Models to Understand Evolution
- 31.Tutorial and Discussion
- 32.Tutorial and Discussion II
- 33.Statistical Thermodynamics of Biological Systems Part - I
- 34.Statistical Thermodynamics of Biological Systems Part - II
- 35.Statistical Thermodynamics of Biological Systems Part - III
- 36.Statistical Thermodynamics of Biological Systems Part - IV
- 37.Thermodynamics of Protein Organization along DNA

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