CALCULUS OF ONE REAL VARIABLE

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

ABOUT INSTRUCTOR :Prof. Joydeep Dutta is currently a Professor of Economics at the Department of Humanities and Social Sciences, IIT Kanpur. He was previously a Professor at the Department of Mathematics and Statistics at IIT Kanpur. His reseach interest primarily lies in optimization though he loves Mathematics as a whole.

COURSE PLAN :Week 01 :

Week 02 :

Week 03 :

Week 04 :

Week 05 :

Week 06 :

Week 07 :

Week 08 :

PROF. JOYDEEP DUTTADepartment of Humanities and Social SciencesIIT Kanpur

Introduction to Numbers, Countability and Uncountability, Examples of Irrational numbers, Function,

Limits of Functions-I.

Limit of Functions-II, Continuous Functions, Intermediate Value Theorem, Maximum Value Theorem,

Supremum & In�mum

Derivative of a Function, Rules of Di�erentiation, Derivatives maxima & minima, Rolle’s Theorem and

Lagrange MVT(Mean-Value Theorem), Monotonic Functions and Inverse Function.

Newton’s Method for solving Equations, Optimization ProblemsIntegration-I : In the style of Newton

and Leibnitz, Integration-II : In the spirit of Newton and Leibnitz, Integration-III : Newton and Leibnitz

Style

Inde�nite Integrals, Integration by Parts, Integration of Rational Functions, Trapezoidal Rule for

evaluating de�nite integral, Simpson’s Rule for evaluating de�nite integral.

Applications of De�nite Integral-I, Applications of De�nite Integral-II, Applications of De�nite

Integral-III, Applications of De�nite Integral-IV, Transcendental Functions-I.

Transcendental Functions-II, Taylor’s Expansion-I, Taylor’s Expansion-II, In�nite Sequence-I, In�nite

Sequence-II

In�nite series and their convergence, Tests for Convergence of a series, Absolute and conditional

convergence, Power Series, Historical Development of the Calculus.

TYPE OF COURSECOURSE DURATIONEXAM DATE

Rerun | Core | UG8 weeks (29 Jul’19 - 20 Sep’19) 29 Sep 2019

:::

INTENDED SUPPORTPRE-REQUISITES

B.E/B.Tech, B.ScBasic Mathematics till 12th standard

::

278