Start Date

25/02/2019

End Date

21/04/2019

Enrollment End Date

25/02/2019

No. of

Enrollments

159 students

No course

syllabus uploaded

**Created by**

IIT Bombay

41

Tutorials

0

Test

0

Assignment

0

Article

0

Weekly Reading list

**Overview**

**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.**

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

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**Faculty**

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.

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

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

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

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

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

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

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

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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