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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 04 - Functions and its Derivatives


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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