# Calculus for Economics, Commerce and Management - Institution: IIT Bombay - Department: Mathematics - Teacher: Prof. Inder Kumar Rana - Level: Undergraduate - Language: English - Subjects: Mathematics - Source: [NPTEL](https://nptel.ac.in/courses/111101109) - Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.) - Syllabus: [at the source](https://nptel.ac.in/courses/111101109) - Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words) 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 1. [Lecture 1 : Introduction to the Course](https://invisiblenetwork.ai/learn/nptel/111101109/52b9448a2d8a) (YouTube) 2. [Lecture 2 : Concept of a Set, Ways of Representing Sets](https://invisiblenetwork.ai/learn/nptel/111101109/0509f8d06830) (YouTube) 3. [Lecture 3 : Venn Diagrams, Operations on Sets](https://invisiblenetwork.ai/learn/nptel/111101109/e6ee7961b4b8) (YouTube) 4. [Lecture 4 : Operations on Sets, Cardinal Number, Real Numbers](https://invisiblenetwork.ai/learn/nptel/111101109/716b6cc9162d) (YouTube) 5. [Lecture 5 : Real Numbers, Sequences](https://invisiblenetwork.ai/learn/nptel/111101109/ee02c2ba1069) (YouTube) 6. [Lecture 6 : Sequences, Convergent Sequences, Bounded Sequences](https://invisiblenetwork.ai/learn/nptel/111101109/7fed99cfb59c) (YouTube) 7. [Lecture 7 : Limit Theorems, Sandwich Theorem, Monotone Sequences, Completeness of Real Numbers](https://invisiblenetwork.ai/learn/nptel/111101109/021d7edb7c91) (YouTube) 8. [Lecture 8 : Relations and Functions](https://invisiblenetwork.ai/learn/nptel/111101109/7fa4ec4d53ba) (YouTube) 9. [Lecture 9 : Functions, Graph of a Functions, Function Formulas](https://invisiblenetwork.ai/learn/nptel/111101109/aa9e442c6489) (YouTube) 10. [Lecture 10 : Function Formulas, Linear Models](https://invisiblenetwork.ai/learn/nptel/111101109/46df0ee0e291) (YouTube) 11. [Lecture 11 : Linear Models, Elasticity, Linear Functions, Nonlinear Models, Quadratic Functions](https://invisiblenetwork.ai/learn/nptel/111101109/7b6f17e5534d) (YouTube) 12. [Lecture 12 : Quadratic Functions, Quadratic Models, Power Function, Exponential Function](https://invisiblenetwork.ai/learn/nptel/111101109/736576d8a352) (YouTube) 13. [Lecture 13 : Exponential Function, Exponential Models, Logarithmic Function](https://invisiblenetwork.ai/learn/nptel/111101109/f111a91a0ef8) (YouTube) 14. [Lecture 14 : Limit of a Function at a Point, Continuous Functions](https://invisiblenetwork.ai/learn/nptel/111101109/ec0faf4dc38e) (YouTube) 15. [Lecture 15 : Limit of a Function at a Point](https://invisiblenetwork.ai/learn/nptel/111101109/5eda3798462e) (YouTube) 16. [Lecture 16 : Limit of a Function at a Point, Left and Right Limits](https://invisiblenetwork.ai/learn/nptel/111101109/6c1e9b0dbe27) (YouTube) 17. [Lecture 17 : Computing Limits, Continuous Functions](https://invisiblenetwork.ai/learn/nptel/111101109/3ab81e934290) (YouTube) 18. [Lecture 18 : Applications of Continuous Functions](https://invisiblenetwork.ai/learn/nptel/111101109/26a43fabb025) (YouTube) 19. [Lecture 19 : Applications of Continuous Functions, Marginal of a Function](https://invisiblenetwork.ai/learn/nptel/111101109/d939ffc41726) (YouTube) 20. [Lecture 20 : Rate of Change, Differentiation](https://invisiblenetwork.ai/learn/nptel/111101109/10bb466fdc3e) (YouTube) 21. [Lecture 21 : Rules of Differentiation](https://invisiblenetwork.ai/learn/nptel/111101109/6806e59fa671) (YouTube) 22. [Lecture 22 : Derivatives of Some Functions, Marginal, Elasticity](https://invisiblenetwork.ai/learn/nptel/111101109/9759ff60985c) (YouTube) 23. [Lecture 23 : Elasticity, Increasing and Decreasing Functions, Optimization, Mean Value Theorem](https://invisiblenetwork.ai/learn/nptel/111101109/888c7f2d4d34) (YouTube) 24. [Lecture 24 : Mean Value Theorem, Marginal Analysis, Local Maxima and Minima](https://invisiblenetwork.ai/learn/nptel/111101109/0290c7d279d6) (YouTube) 25. [Lecture 25 : Local Maxima and Minima](https://invisiblenetwork.ai/learn/nptel/111101109/50745a87e788) (YouTube) 26. [Lecture 26 : Local Maxima and Minima, Continuity Test, First Derivative Test, Successive Differentiation](https://invisiblenetwork.ai/learn/nptel/111101109/b4384342b546) (YouTube) 27. [Lecture 27 : Successive Differentiation, Second Derivative Test](https://invisiblenetwork.ai/learn/nptel/111101109/f45c4e636a92) (YouTube) 28. [Lecture 28 : Average and Marginal Product, Marginal of Revenue and Cost, Absolute Maximum and Minimum](https://invisiblenetwork.ai/learn/nptel/111101109/2971ac4cc2a5) (YouTube) 29. [Lecture 29 : Absolute Maximum and Minimum](https://invisiblenetwork.ai/learn/nptel/111101109/0da1d0ffeae6) (YouTube) 30. [Lecture 30 : Monopoly Market, Revenue and Elasticity](https://invisiblenetwork.ai/learn/nptel/111101109/0fe5c4d962b3) (YouTube) 31. [Lecture 31 : Property of Marginals, Monopoly Market, Publisher v/s Author Problem](https://invisiblenetwork.ai/learn/nptel/111101109/49b5ee7797cc) (YouTube) 32. [Lecture 32 : Convex and Concave Functions](https://invisiblenetwork.ai/learn/nptel/111101109/ffc42dfcbbb5) (YouTube) 33. [Lecture 33 : Derivative Tests for Convexity, Concavity and Points of Inflection, Higher Order Derivative Conditions](https://invisiblenetwork.ai/learn/nptel/111101109/9d31a431dcaf) (YouTube) 34. [Lecture 34 : Convex and Concave Functions, Asymptotes](https://invisiblenetwork.ai/learn/nptel/111101109/121cfa6494f8) (YouTube) 35. [Lecture 35 : Asymptotes, Curve Sketching](https://invisiblenetwork.ai/learn/nptel/111101109/b97851cbb195) (YouTube) 36. [Lecture 36 : Functions of Two Variables, Visualizing Graph, Level Curves, Contour Lines](https://invisiblenetwork.ai/learn/nptel/111101109/e0993ee9817b) (YouTube) 37. [Lecture 37 : Partial Derivatives and Application to Marginal Analysis](https://invisiblenetwork.ai/learn/nptel/111101109/f4db7be06c65) (YouTube) 38. [Lecture 38 : Marginals in Cobb-Douglas model, partial derivatives and elasticity, chain rules](https://invisiblenetwork.ai/learn/nptel/111101109/374461d2a03e) (YouTube) 39. [Lecture 39 : Chain Rules, Higher Order Partial Derivatives, Local Maxima and Minima, Critical Points](https://invisiblenetwork.ai/learn/nptel/111101109/f6fdf6f039ed) (YouTube) 40. [Lecture 40 : Saddle Points, Derivative Tests, Absolute Maxima and Minima](https://invisiblenetwork.ai/learn/nptel/111101109/15e682523132) (YouTube) 41. [Lecture 41 : Some Examples, Constrained Maxima and Minima](https://invisiblenetwork.ai/learn/nptel/111101109/cc66a231fb25) (YouTube)