Courses » Calculus for Economics,Commerce and Management

Calculus for Economics,Commerce and Management


This course is based on the course"mathematics for Economics, Commerce and Management", which was run at IIT Bombay for 8 years. Mathematical tools give a precise way of formulating and analyzing a problem and to make logical conclusions. Knowledge of mathematical concepts and tools have have become necessary for students aspiring for higher studies and career in any branch of Economics, Commerce and Management. Math for ECM aims to strengthen the mathematical foundations of students of Economics, Commerce, and Management. Professionals working in these field, wishing to upgrade their knowledge, will also benefit. The stress of the course will be on building the concepts and their applications. The main topic will be Calculus and its applications.

Students, PhD scholars, teachers, industry



PREREQUISITES: Basic School Mathematics


Prof. Inder K. Rana presently is an Emeritus Fellow at Department of mathematics, IIT Bombay. He has an experience of 36 years of teaching mathematics courses to undergraduate (B. Tech) and master’s M.Sc. students at IIT Bombay. He has authored 4 books,namely,“Introduction to measure and Integration” American Mathematical Society, Graduate Studies in Mathematics Volume 45, 2000,“From Numbers to Analysis” World Scientific Press, 1998 ,Calculus @IITB: Concepts and Examples, math4all, India, 2007 “From Geometry to Algebra: A course in Linear Algebra” math4all, India, 2007.He has won three awards,“C. L. Chandna Mathematics Award” for the year 2000 in recognition of distinguished and outstanding contributions to mathematics research and teaching. The award is given by ‘SaraswatiVishvas Canada”,“Excellence in Teaching” award for the year 2004 Awarded by IIT Bombay, based on the evaluations by students."Aryabhata Award" 2012 All India Ramanujan Math Club, India, for teaching and work towards math education in India.


Week 1 Revision of basic concepts from Mathematical finance

Lecture 1 : Introduction to the Course
Lecture 2 : Concept of a Set,ways of representing sets
Lecture 3 : Venn diagrams, operations on sets
Lecture 4 : Operations on sets, cardinal number, real numbers
Lecture 5 : Real numbers, Sequences

Week 2  Basic set theory and concept of functions

Lecture 6 :   Sequences, convergent sequences, bounded sequences
Lecture 7 :   Limit theorems, sandwich theorem, monotone sequences, completeness of real numbers
Lecture 8 :   Relations and functions
Lecture 9 :   Functions, graph of a functions, function formulas
Lecture 10 : Function formulas, linear models

Week 3 Limits and Continuity of a function of one variable and its applications

Lecture 11 : Linear models, elasticity, linear functions, nonlinear models, quadratic functions
Lecture 12 : Quadratic functions, quadratic models, power function, exponential function
Lecture 13 : Exponential function, exponential models, logarithmic function
Lecture 14 : Limit of a function at a point, continuous functions
Lecture 15 : Limit of a function at a point

Week 4 Derivative and tools to compute

Lecture 16 : Limit of a function at a point, left and right limits
Lecture 17 : Computing limits, continuous functions
Lecture 18 : Applications of continuous functions
Lecture 19 : Applications of continuous functions, marginal of a function
Lecture 20 : Rate of change, differentiation

Week 5 Application of derivatives in increasing/decreasing

Lecture 21 : Rules of differentiation
Lecture 22 : Derivatives of some functions, marginal, elasticity
Lecture 23 : Elasticity, increasing and decreasing functions, optimization, mean value theorem
Lecture 24 : Mean value theorem, marginal analysis, local maxima and minima
Lecture 25 : Local maxima and minima

Week 6 Application of derivatives in optimization

Lecture 26 : Local maxima and minima, continuity test, first derivative test, successive differentiation
Lecture 27 : Successive differentiation, second derivative test
Lecture 28 : Average and marginal product, marginal of revenue and cost, absolute maximum and                            minimum
Lecture 29 : Absolute maximum and minimum
Lecture 30 : Monopoly market, revenue and elasticity

Week 7 Functions of several variables

Lecture 31 : Property of marginals, monopoly market, publisher v/s author problem
Lecture 32 : Convex and concave functions
Lecture 33 : Derivative tests for convexity, concavity and points of inflection, higher order derivative                          conditions
Lecture 34 : Convex and concave functions, asymptotes
Lecture 35 : Asymptotes, curve sketching

Week 8 Applications

Lecture 36 : Functions of two variables, visualizing graph, level curves, contour lines
Lecture 37 : Partial derivatives and application to marginal analysis
Lecture 38 : Marginals in Cobb-Douglas model, partial derivatives and elasticity, chain rules
Lecture 39 : Chain rules, higher order partial derivatives, local maxima and minima, critical points
Lecture 40 : Saddle points, derivative tests, absolute maxima and minima
Lecture 41 : Some examples, constrained maxima and minima


Chiang, A.C. (2005): Fundamental Methods of Mathematical Economics, McGraw Hill, ND.,
  • The exam is optional for a fee.
  • Date and Time of Exams: April 28 (Saturday) and April 29 (Sunday) : Afternoon session: 2pm to 5pm
  • Exam for this course will be available in one session on both 28 and 29 April.
  • 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.


  • Final score will be calculated as : 25% assignment score + 75% final exam score
  • 25% assignment score is calculated as 25% of average of  Best 6 out of 8 assignments
  • E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. 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