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Course11110110941 lectures

Calculus for Economics, Commerce and Management

Prof. Inder Kumar Rana · IIT Bombay

Start with lecture 1 At NPTEL

About

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

Lectures

Week 1

  1. Lecture 1 : Introduction to the Course YouTube
  2. Lecture 2 : Concept of a Set, Ways of Representing Sets YouTube
  3. Lecture 3 : Venn Diagrams, Operations on Sets YouTube
  4. Lecture 4 : Operations on Sets, Cardinal Number, Real Numbers YouTube
  5. Lecture 5 : Real Numbers, Sequences YouTube

Week 2

  1. Lecture 6 : Sequences, Convergent Sequences, Bounded Sequences YouTube
  2. Lecture 7 : Limit Theorems, Sandwich Theorem, Monotone Sequences, Completeness of Real Numbers YouTube
  3. Lecture 8 : Relations and Functions YouTube
  4. Lecture 9 : Functions, Graph of a Functions, Function Formulas YouTube
  5. Lecture 10 : Function Formulas, Linear Models YouTube

Week 3

  1. Lecture 11 : Linear Models, Elasticity, Linear Functions, Nonlinear Models, Quadratic Functions YouTube
  2. Lecture 12 : Quadratic Functions, Quadratic Models, Power Function, Exponential Function YouTube
  3. Lecture 13 : Exponential Function, Exponential Models, Logarithmic Function YouTube
  4. Lecture 14 : Limit of a Function at a Point, Continuous Functions YouTube
  5. Lecture 15 : Limit of a Function at a Point YouTube

Week 4

  1. Lecture 16 : Limit of a Function at a Point, Left and Right Limits YouTube
  2. Lecture 17 : Computing Limits, Continuous Functions YouTube
  3. Lecture 18 : Applications of Continuous Functions YouTube
  4. Lecture 19 : Applications of Continuous Functions, Marginal of a Function YouTube
  5. Lecture 20 : Rate of Change, Differentiation YouTube

Week 5

  1. Lecture 21 : Rules of Differentiation YouTube
  2. Lecture 22 : Derivatives of Some Functions, Marginal, Elasticity YouTube
  3. Lecture 23 : Elasticity, Increasing and Decreasing Functions, Optimization, Mean Value Theorem YouTube
  4. Lecture 24 : Mean Value Theorem, Marginal Analysis, Local Maxima and Minima YouTube
  5. Lecture 25 : Local Maxima and Minima YouTube

Week 6

  1. Lecture 26 : Local Maxima and Minima, Continuity Test, First Derivative Test, Successive Differentiation YouTube
  2. Lecture 27 : Successive Differentiation, Second Derivative Test YouTube
  3. Lecture 28 : Average and Marginal Product, Marginal of Revenue and Cost, Absolute Maximum and Minimum YouTube
  4. Lecture 29 : Absolute Maximum and Minimum YouTube
  5. Lecture 30 : Monopoly Market, Revenue and Elasticity YouTube

Week 7

  1. Lecture 31 : Property of Marginals, Monopoly Market, Publisher v/s Author Problem YouTube
  2. Lecture 32 : Convex and Concave Functions YouTube
  3. Lecture 33 : Derivative Tests for Convexity, Concavity and Points of Inflection, Higher Order Derivative Conditions YouTube
  4. Lecture 34 : Convex and Concave Functions, Asymptotes YouTube
  5. Lecture 35 : Asymptotes, Curve Sketching YouTube

Week 8

  1. Lecture 36 : Functions of Two Variables, Visualizing Graph, Level Curves, Contour Lines YouTube
  2. Lecture 37 : Partial Derivatives and Application to Marginal Analysis YouTube
  3. Lecture 38 : Marginals in Cobb-Douglas model, partial derivatives and elasticity, chain rules YouTube
  4. Lecture 39 : Chain Rules, Higher Order Partial Derivatives, Local Maxima and Minima, Critical Points YouTube
  5. Lecture 40 : Saddle Points, Derivative Tests, Absolute Maxima and Minima YouTube
  6. Lecture 41 : Some Examples, Constrained Maxima and Minima YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Mathematics
Teacher
Prof. Inder Kumar Rana
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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