# Calculus Of One Real Variable

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.

**COURSE LAYOUT**

Week 1: Lecture 1: Introduction to Numbers

Lecture 2: Countability and Uncountability

Lecture 3: Examples of Irrational numbers

Lecture 4: Functions

Lecture 5: Limits of Functions-I

Week 2: Lecture 6: Limit of Functions-II

Lecture 7: Continuous Functions

Lecture 8: Intermediate Value Theorem

Lecture 9: Maximum Value Theorem

Lecture 10: Supremum & Infimum

Week 3: Lecture 11: Derivative of a Function

Lecture 12: Rules of Differentiation

Lecture 13: Derivatives maxima & minima

Lecture 14: Rolle’s Theorem and Lagrange MVT(Mean-Value Theorem)

Lecture 15: Monotonic Functions and Inverse Function

Week 4: Lecture 16: Newton’s Method for solving Equations

Lecture 17: Optimization Problems

Lecture 18: Integration-I : In the style of Newton and Leibnitz

Lecture 19: Integration-II : In the spirit of Newton and Leibnitz

Lecture 20: Integration-III : Newton and Leibnitz Style

Week 5: Lecture 21: Indefinite Integrals

Lecture 22: Integration by Parts

Lecture 23: Integration of Rational Functions

Lecture 24: Trapezoidal Rule for evaluating definite integral

Lecture 25: Simpson’s Rule for evaluating definite integral

Week 6: Lecture 26: Applications of Definite Integral-I

Lecture 27: Applications of Definite Integral-II

Lecture 28: Applications of Definite Integral-III

Lecture 29: Applications of Definite Integral-IV

Lecture 30: Transcendental Functions-I

Week 7: Lecture 31: Transcendental Functions-II

Lecture 32: Taylor’s Expansion-I

Lecture 33: Taylor’s Expansion-II

Lecture 34: Infinite Sequence-I

Lecture 35: Infinite Sequence-II

Week 8: Lecture 36: Infinite series and their convergence

Lecture 37: Tests for Convergence of a series

Lecture 38: Absolute and conditional convergence

Lecture 39: Power Series

Lecture 40: Historical Development of the Calculus.

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