Introductory Mathematical Methods for Biologists
Indian Institute of Technology Bombay and NPTEL via Swayam
Overview
It is an introductory mathematics course for biology students with the aim of training them to do quantitative analysis of biological systems. Students will be trained on how to use the language of mathematics to describe biological processes, how to write down simple mathematical equations for various phenomena occurring in biology.
INTENDED AUDIENCE : Students, PhD scholars, teachers, industryPREREQUISITES : CoreINDUSTRY SUPPORT : NILL
INTENDED AUDIENCE : Students, PhD scholars, teachers, industryPREREQUISITES : CoreINDUSTRY SUPPORT : NILL
Syllabus
COURSE LAYOUT
Week 1:Introduction, Graphs and FunctionsLecture 1 : Introduction
Lecture 2 : Graphs and Functions
Lecture 3 : Equations as Graphs
Lecture 4 : Exponential and Periodic Functions
Lecture 5 : Logarithmic and Other Functions
Week 2:Functions and its Derivatives, Computing Derivatives of Curves
Lecture 6 : Images as 2D/3D Functions
Lecture 7 : Functions and its Derivatives
Lecture 8 : Computing Derivatives of Curves
Lecture 9 : Rules for Calculating Derivatives
Lecture 10 : Understanding Derivatives
Week 3:Plotting Curves , Numerical Calculation of Derivatives, Partial Derivatives
Lecture 11 : Curvature and Second Derivative
Lecture 12 : Plotting Curves
Lecture 13 : Numerical Calculation of Derivatives
Lecture 14 : Function,Derivatives and Series Expansion
Lecture 15 : L'Hopital's Rule and Partial Derivatives
Week 4:Integration and their Graphical Understanding
Lecture 16 : Integration
Lecture 17 : Integration:Rules
Lecture 18 : Graphical Understanding
Lecture 19 : Integration:More Examples
Lecture 20 : Integration: Product of Two Functions
Week 5:Vectors : Position and Movement in 2D, Cell Symmetry : Use of Polar Coordinates
Lecture 21 : Exponential growth and Decay
Lecture 22 : Scalars and Vectors
Lecture 23 : Vectors:Position and Movement in 2D
Lecture 24 : Cell Symmetry:Use of Polar Coordinates
Lecture 25 : Gradient.Forces and Flows :Part I
Week 6: Gradient, Forces and Flows , Understanding Diffusion
Lecture 26 : Gradient.Forces and Flows :Part II
Lecture 27 : Understanding Diffusion
Lecture 28 : Diffusion Constant and Einstein Relation 1905
Lecture 29 : Diffusion Equation
Lecture 30 : Diffusion vs.Active Transport
Week 7:Introduction to Fourier series , Fourier Transform and Statistics
Lecture 31 : Nernst Equation
Lecture 32 : Fourier Series : Part I
Lecture 33 : Fourier Series : Part II
Lecture 34 : Fourier Transform
Lecture 35 : Introduction to Statistics
Week 8:Basics of bio-statistics
Lecture 36 : Mean,Standard deviation and Distribution
Lecture 37 : Frequency Distribution and Probability Distribution
Lecture 38 : Binomial Distribution
Lecture 39 : Normal Distribution
Lecture 40 : Hypothesis Testing and Mathematical Modeling
Taught by
Ranjith Padinhateeri
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