Biomathematics. Instructor: Dr. Ranjith Padinhateeri, Department of Biotechnology, IIT Bombay.
September 25, 2023
English
English [CC]
Description
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)
Course Curriculum
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- Lecture 01 – Introduction Unlimited
- Lecture 02 – Graphs and Functions Unlimited
- Lecture 03 – Graphs and Functions (cont.) Unlimited
- Lecture 04 – Functions and its Derivatives Unlimited
- Lecture 05 – Calculation of Derivatives Unlimited
- Lecture 06 – Differentiation and its Application in Biology I Unlimited
- Lecture 07 – Differentiation and its Application in Biology II Unlimited
- Lecture 08 – Differentiation and its Application in Biology III Unlimited
- Lecture 09 – Differentiation and its Application in Biology IV Unlimited
- Lecture 10 – Integration Unlimited
- Lecture 11 – Integration (cont.) Unlimited
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- Lecture 12 – Differential Equations Unlimited
- Lecture 13 – Differential Equations (cont.) Unlimited
- Lecture 14 – Vectors I Unlimited
- Lecture 15 – Vectors II Unlimited
- Lecture 16 – Vectors III Unlimited
- Lecture 21 – Statistics: Mean and Variance Unlimited
- Lecture 22 – Statistics: Distribution Function Unlimited
- Lecture 23 – Understanding Normal Distribution Unlimited
- Lecture 24 – Fitting a Function to Experimental Data Unlimited
- Lecture 25 – Size of a Flexible Protein: Simplest Model Unlimited
- Lecture 26 – Uniform and Poisson Distributions; Knudson’s Analysis Unlimited
- Lecture 30 – Master Equation: Polymerization Dynamics, Molecular Motor Motion Unlimited
- Lecture 31 – Evolution: Simplest Model Unlimited
- Lecture 34 – Temperature, Energy and Entropy Unlimited
- Lecture 35 – Partition Function, Free Energy Unlimited
- Lecture 36 – Bending Fluctuations of DNA and Spring-like Proteins Unlimited
- Lecture 37 – Force-extension and Looping of DNA Unlimited
- Lecture 38 – Thermodynamics of Protein Organization along DNA Unlimited
- Lecture 39 – Learning Mathematics with the Help of a Computer Unlimited
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