Jan 2019: Calculus for Economics, Commerce & Management

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I.K. Rana
IIT Bombay
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Course Language
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Course Category
Learning Path
Post graduate
Course Length
20 Hours
Weekly time commitments
10 Hours
Course Completion
Yes, after passing all tests.
Exam Date
To be announced










Weekly Reading list


DEADLINE Feb 25, 2019 - 5:00 PM

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 https://onlinecourses.nptel.ac.in (Go to this url and search for this course)for credit transfer, final examination, certification, discussion forum and assignments.




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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

To access the content, please enroll in the course.


I.K. Rana

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
Lec 1 : Introduction to the Course
Lec 2 : Concept of a Set,ways of representing sets
Lec 3 : Venn diagrams, operations on sets
Lec 4 : Operations on sets, cardinal number, real numbers
Lec 5 : Real numbers, Sequences
Week 2  Basic set theory and concept of functions
Lec 6 : Sequences, convergent sequences, bounded sequences
Lec 7 :  Limit theorems, sandwich theorem, monotone sequences, completeness of real numbers
Lec 8 :  Relations and functions
Lec 9 :  Functions, graph of a functions, function formulas
Lec 10 : Function formulas, linear models
Week 3 Limits and Continuity of a function of one variable and its applications
Lec 11 : Linear models, elasticity, linear functions, nonlinear models, quadratic functions
Lec 12 : Quadratic functions, quadratic models, power function, exponential function
Lec 13 : Exponential function, exponential models, logarithmic function
Lec 14 : Limit of a function at a point, continuous functions
Lec 15 : Limit of a function at a point
Week 4 Derivative and tools to compute
Lec 16 : Limit of a function at a point, left and right limits
Lec 17 : Computing limits, continuous functions
Lec 18 : Applications of continuous functions
Lec 19 : Applications of continuous functions, marginal of a function
Lec 20 : Rate of change, differentiation
Week 5 Application of derivatives in increasing/decreasing
Lec 21: Rules of differentiation
Lec 22 : Derivatives of some functions, marginal, elasticity
Lec 23: Elasticity, increasing and decreasing functions, optimization, mean value theorem
Lec 24: Mean value theorem, marginal analysis, local maxima and minima
Lec 25 : Local maxima and minima
Week 6 :Application of derivatives in optimization
Lec 26: Local maxima and minima, continuity test, first derivative test, successive differentiation
Lec 27: Successive differentiation, second derivative test
Lec 28: Average and marginal product, marginal of revenue and cost, absolute maximum and  minimum
Lec 29: Absolute maximum and minimum
Lec 30 : Monopoly market, revenue and elasticity
Week 7 :Functions of several variables
Lec 31: Property of marginals, monopoly market, publisher v/s author problem
Lec 32 : Convex and concave functions
Lec 33 : Derivative tests for convexity, concavity and points of inflection, higher order derivative conditions
Lec 34 : Convex and concave functions, asymptotes
Lec 35 : Asymptotes, curve sketching
Week 8:Applications
Lec 36 :Functions of two variables, visualizing graph, level curves, contour lines
Lec 37 : Partial derivatives and application to marginal analysis
Lec 38 : Marginals in Cobb-Douglas model, partial derivatives and elasticity, chain rules
Lec 39 : Chain rules, higher order partial derivatives, local maxima and minima, critical points
Lec 40 : Saddle points, derivative tests, absolute maxima and minima
Lec 41 : Some examples, constrained maxima and minima



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