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.
INTENDED AUDIENCE: Students, PhD scholars, teachers, industry
PREREQUISITES: Basic School Mathematics
ABOUT THE INSTRUCTOR:
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
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
SUGGESTED READING MATERIALS:
Chiang, A.C. (2005): Fundamental Methods of Mathematical Economics, McGraw Hill, ND.,
CERTIFICATION EXAM :
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