# Introductory Mathematical Methods for Biologists

By Prof. Ranjit Padinhateeri   |   IIT Bombay
Learners enrolled: 567
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, industry
PREREQUISITES        : Core
INDUSTRY SUPPORT  : NILL
Summary
 Course Status : Completed Course Type : Core Duration : 8 weeks Category : Biological Sciences & Bioengineering Credit Points : 2 Level : Undergraduate/Postgraduate Start Date : 21 Feb 2022 End Date : 15 Apr 2022 Enrollment Ends : 21 Feb 2022 Exam Date : 24 Apr 2022 IST

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

### Course layout

Week 1  : Introduction, Graphs and Functions

Lecture 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

### Books and references

Mathematics for Biological Scientists, M. Aitken, B. Broadhursts, S. Haldky, Garland Science (2009)

### Instructor bio

IIT Bombay
Prof.Ranjith Padinhateeri completed his MSc and PhD in Physics from IIT Madras. During PhD he studied statistical mechanics of DNA. After PhD he did post-doctoral research in University of Illinois Chicago, USA, Northwestern University. Evanston, USA, and Institute Curie, Paris, France. He does his research in the broad area of biological physics. Prof.Ranjith Padinhateeri does theoretical studies to understand various biological phenomena using a variety of tools from physics, including equilibrium and non-equilibrium statistical mechanics, polymer physics, and soft-matter theory. He tackle research problems using a combination of computational and analytical methods. His Specific areas of interest include Nucleosome dynamics, Chromatin assembly, DNA mechanics and self-assembly of proteins

### Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 24 April 2022 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Bombay.It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team