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Calculus of One Real Variable - Introduction - Prof.Joydeep Dutta

Introduction to Numbers

Countability and Uncountability

Examples of Irrational numbers

Functions

Limits of Functions-I

Limit of Functions- II

Continuous Functions

Intermediate Value Theorem

Maximum Value Theorem

Supremum and Infimum

Rules of Differentiation

Monotonic Functions and Inverse Functions

Maxima and Minima

Rolle's Theorem and Lagrange Mean Value Theorem (MVT)

Derivative of a Function

Newton's Method for solving Equations

Optimization Problems

Integration-III : Newton and Leibnitz Style

Integration-I : In the style of Newton and Leibnitz

Integration-II : In the spirit of Newton and Leibnitz

Integration theory of Riemann-I

Integration theory of Riemann-II

Integration Rule

Fundamental Theorem of Calculus (in Riemann style)

The Kurzweil-Henstock Integral (K-H Integral)

Improper Integral-II

Improper Integral-I

Calculating Indefinite Integrals

Application of Definite Integral-I

Application of definite Integral-II

Application of definite Integral-III

Application of definite Integral-III (Contd.)

Numerical Integration-I

Numerical Integration-II

Sequences

Sequence (continued)

Infinite Series

Taylors Theorem, other issues and end of the course-I

infinite series (continued)

Taylors Theorem, other issues and end of the course-II

Description:

INTENDED SUPPORT: First year engineering, science and economics students with mathematics as the main course. PRE-REQUISITES: Basic Mathematics till 12th standard COURSE OUTLINE: This course intends to develop a thorough understanding of the fundamental aspects of calculus of a single variable which is a fundamental tool in Sciences, Engineering and Economics.

Calculus of One Real Variable

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#Mathematics #Calculus #Differentiation #Integration #Fundamental Theorem of Calculus #Intermediate Value Theorem

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