Calculus of One Real Variable

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 - 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.