NPTEL : NOC:Basic Calculus 1 and 2 (Mathematics)

Co-ordinators : Prof. Parasar Mohanty


Lecture 1 - Real numbers and Archimedean property

Lecture 2 - Supremum and Decimal representation of Reals

Lecture 3 - Functions

Lecture 4 - Functions continued and Limits

Lecture 5 - Limits (Continued...)

Lecture 6 - Limits (Continued...) and Continuity

Lecture 7 - Continuity and Intermediate Value Property

Lecture 8 - Differentiation

Lecture 9 - Chain Rule

Lecture 10 - Nth derivative of a function

Lecture 11 - Local extrema and Rolle's theorem

Lecture 12 - Mean value theorem and Monotone functions

Lecture 13 - Local extremum tests

Lecture 14 - Concavity and points of inflection

Lecture 15 - Asymptotes and plotting graph of functions

Lecture 16 - Optimization and L'Hospital Rule

Lecture 17 - L'Hospital Rule continued and Cauchy Mean value theorem

Lecture 18 - Approximation of Roots

Lecture 19 - Antiderivative and Riemann Integration

Lecture 20 - Riemann's criterion for Integrability

Lecture 21 - Integration and its properties

Lecture 22 - Area and Mean value theorem for integrals

Lecture 23 - Fundamental theorem of Calculus

Lecture 24 - Integration by parts and Trapezoidal rule

Lecture 25 - Simpson's rule and Substitution in integrals

Lecture 26 - Area between curves

Lecture 27 - Arc Length and Parametric curves

Lecture 28 - Polar Co-ordinates

Lecture 29 - Area of curves in polar coordinates

Lecture 30 - Volume of solids

Lecture 31 - Improper Integrals

Lecture 32 - Sequences

Lecture 33 - Algebra of sequences and Sandwich theorem

Lecture 34 - Subsequences

Lecture 35 - Series

Lecture 36 - Comparison tests for Series

Lecture 37 - Ratio and Root test for series

Lecture 38 - Integral test and Leibniz test for series

Lecture 39 - Revision - I

Lecture 40 - Revision - II