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

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.

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

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

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

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

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

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

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

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 27 (Saturday)** - Time of Exams: 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.

- 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