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Course Co-ordinated by IIT Kanpur
Coordinators
 
Dr. Joydeep Dutta
IIT Kanpur

 

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This course intend to develop a thorough understanding of the fundamental aspects of calculus of single variable which is fundamental tool in Sciences, Engineering and Economics.


Modules

Topics

1

Introduction to Numbers,Countability and Uncountability Examples of Irrational numbers,Functions,Limits of Functions-I

2

Limit of Functions-II,Continuous Functions,Intermediate Value Theorem,Maximum Value Theorem,Supremum & Infimum

3

Uniformly Continuous Function,Derivative of a Function,Rules of Differentiation,Derivatives maxima & minima,Rolle TMs Theorem and Lagrange MVT(Mean-Value Theorem)

4

Monotonic Functions and Inverse Functions,Newton TMs Method for solving Equations,Optimization Problems,Integration,Basic Theorems of Integration

5

Indefinite Integrals,Integration by Parts,Integration of Rational Functions,Trapezoidal Rule for evaluating definite integral,Simpson TMs Rule for evaluating definite integral

6

Applications of Definite Integral-I,Applications of Definite Integral-II,Applications of Definite Integral-III,Applications of Definite Integral-IV,Transcendental Functions-I

7

Transcendental Functions-II,Taylor TMs Expansion-I,Taylor TMs Expansion-II,Infinite Sequence-I,Infinite Sequence-II

8

Infinite series and their convergence,Tests for Convergence of a series,Absolute and conditional convergence,Power Series,Historical Development of the Calculus

B.E/B.Tech,B.Sc,

1. Calculus by M Spivak
2.Calculus by Thomos and Finney.

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