Recording_Online Lectures_Mathematics - I (UMA010)_EIC1-6

Dear Students, the official recorded lectures of the whole course can be found at the link:

Official Video Lectures Mathematics - I (UMA010)

However, the online videos of Mathematics - I (UMA010) are being recorded in the current session (Odd, 2020 - 21) while taking the online lecture classes of EIC1-6 on zoom platform. In case if you are watching these recordings of lectures then for any comments, suggestions or error you can contact me at

email id: apathania@thapar.edu (Ankush Pathania, Office - G207, School of Mathematics)

Official Old Google Site of the Course Mathematics - I

The Lecture notes of this course are available at the link:

Lecture Notes Mathematics - I (UMA010)

Sequence and Series

EDITED RECORDINGS

Lecture 1 (Overview of the course and definition of the Sequence)

Lecture 2 (Informal definition of the convergence of sequence, Recursive definition of the sequences)

Lecture 3 (Subsequence, Properties of subsequences, Nondecreasing sequence)

Lecture 4 (Bounded above sequence, Upper bound, Least upper bound of sequence and Non decreasing sequence theorem)

Lecture 5 (Properties of limits of sequences, Sandwich theorem and Continuous function theorem)

Lecture 6 (Theorem for using L'Hopital rule and common occurring limits while finding the limits of the sequences)

Lecture 7 (Infinite series, Partial sums of series, Geometric series)

Lecture 8 (Telescoping series and Nth term test for the divergence of the series)

Lecture 9 (Adding or deleting terms in series and some other results of series)

Lecture 10 (Cauchy Integral test, p series test)

Lecture 11 (Direct Comparison test and Limit comparison test, Part 1)

Lecture 12 (Direct Comparison test and Limit comparison test, Part 2)

Lecture 13 (Ratio and Root test)

Lecture 14 (Alternating Series, Alternating series test (AST), Absolute convergence, Absolute convergence test, Conditional convergence)

Lecture 15 (Alternating series continued)

Lecture 16 (Alternating series Estimation theorem (ASET))

Lecture 17 (Power Series, Part 1)

Lecture 18 (Power Series, Part 2)

Lecture 19 (Power series, Part 3)

Lecture 20 (Taylor and Maclaurin Series, Taylor Polynomial, Part 1)

Lecture 21 (Taylor Series by substitution and multiplication)

Lecture 22 (Taylor formula and Remainder Estimation Theorem)

Lecture 23 (Questions of Error Estimates using Taylor formula, Remainder Estimation Theorem and Alternating series estimation theorem)

Lecture 24 (Questions of Error Estimates using Taylor formula, Remainder Estimation Theorem and Alternating series estimation theorem)

Multivariable function and Partial Derivatives

UNEDITED RECORDINGS

Lecture 25 (Limits and Continuity of function of two variables f(x, y))

Lecture 26 (Two path test for the nonexistence of limit of f(x, y), Partial Derivatives)

Lecture 27 (Geometrical interpretation of partial derivatives, some questions related to partial derivatives and Euler's mixed derivative theorem)

Lecture 28 (Chain Rule, Part 1)

Lecture 29 (Chain Rule, Part 2)

Lecture 30 (Directional Derivative, Part 1)

Lecture 31 (Directional Derivative, Part 2)

Lecture 32 (Directional Derivative, Part 3)

Lecture 33 (Extreme values and saddle point of f(x, y))

Lecture 34 (Extreme values and saddle point of f(x, y) continued, Absolute maxima and minima of f(x, y) over closed and bounded region)

Lecture 35 (Absolute maxima and minima of f(x, y) over closed and bounded region continued)

Multiple Integrals and Polar Graphing

UNEDITED RECORDINGS

Lecture 36 (Double Integrals, Fubini's theorem to find the double integral of f(x, y) over a rectangular and non-rectangular region in plane)

Lecture 37 (Finding the limits of integration in Cartesian coordinates, Area in Cartesian coordinates)

Lecture 38 (Area in Cartesian coordinates continued, Reversing the order of integration)

Lecture 39 (Basics of polar coordinates)

Lecture 40 (Polar Graphing, Part 1)

Lecture 41 (Polar Graphing, Part 2)

Lecture 42 (Double Integrals in polar coordinates, Area in Polar coordinates, Finding the limits of integration in Polar coordinates)

Lecture 43 (Double Integrals in Polar coordinates continued, Solving double integrals by Changing Cartesian to polar form)

Complex Analysis

UNEDITED RECORDINGS

Lecture 44 (Complex numbers, Polar and Exponential form)

Lecture 45 (Functions of complex variable, Limit, Continuity and Differentiability of complex variable function)

Lecture 46 (Cauchy - Reimann (CR) Equations)

Lecture 47 (Analytic function, Harmonic function, Harmonic Conjugate)

Lecture 48 (Q related to Harmonic function and Harmonic conjugate, Complex Exponential function)

Lecture 49 (Complex exponential function continued, Complex trigonometric (sine and cosine) functions)