Recording_Online Lectures_Mathematics - I (UMA010)_G1-5+G8

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 G1-5+G8 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

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

Lecture Notes Mathematics - I (UMA010)

Sequence and Series

UNEDITED RECORDINGS

Lecture 1 (Overview of the course)

Lecture 2 (Sequence, Convergence of sequence)

Lecture 3 ( Recursive definition of the sequences, Nondecreasing sequence, Bounded above sequence, Upper bound and Least upper bound of sequence)

Lecture 4 (Non decreasing sequence theorem)

Lecture 5 (Some properties of limits of sequence, Sandwich theorem, 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 (Geometric series continued, Telescoping series)

Lecture 9 (nth term test for the divergence of the series, Effect of adding or deleting terms on the convergence/divergence of series)

Lecture 10 (Some other results of series, Cauchy Integral test)

Lecture 11 (Cauchy Integral test continued, P series test)

Lecture 12 (Direct comparison test, Limit comparison test, Part 1)

Lecture 13 (Direct comparison test, Limit comparison test, Part 2)

Lecture 14 (Ratio test, Root test)

Lecture 15 (Alternating Series, Alternating series test (AST), Absolute convergence, Absolute convergence test)

Lecture 16 (Alternating series continued)

Lecture 17 (Alternating series and Estimation theorem, Some other questions of alternating series)

Lecture 18 (Power Series, Part 1)

Lecture 19 (Power Series, Part 2)

Lecture 20 (Power Series, Part 3)

Lecture 21 (Taylor and Maclaurin Series, Taylor Polynomial,)

Lecture 22 (Taylor Series by substitution and multiplication, Taylor formula)

Lecture 23 (Remainder Estimation Theorem, 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 continued)

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 (Partial derivatives continued, Euler's mixed derivative theorem and Chain Rule)

Lecture 28 (Chain Rule continued, Geometrical interpretation of partial derivatives)

Lecture 29 (Directional Derivatives (DD), Geometrical Interpretation of DD, Properties of DD)

Lecture 30 (Properties of DD continued, Physical Interpretation of DD)

Lecture 31 (Some other questions of DD, Extreme values and saddle point of f(x, y))

Lecture 32 (Extreme values and saddle point of f(x, y) continued, Absolute maxima and minima of f(x, y) over closed and bounded region)

Lecture 33 (Absolute maxima and minima of f(x, y) over closed and bounded region continued)

Multiple Integrals and Polar Graphing

UNEDITED RECORDINGS

Lecture 34 (Double Integrals, Fubini's theorem to find the double integral of f(x, y) over a rectangular and non-rectangular region in plane, Finding the limits of integration in Cartesian coordinates)

Lecture 35 (Finding the limits of integration in Cartesian coordinates continued, Area in Cartesian coordinates, Reversing the order of integration)

Lecture 36 (Basics of polar coordinates)

Lecture 37 (Polar Graphing)

Lecture 38 (Polar Graphing continued, Double Integrals in polar coordinates, Area in Polar coordinates, Finding the limits of integration in Polar coordinates)

Lecture 39 (Area in Polar coordinates, Finding the limits of integration in Polar coordinates continued)

Lecture 40 (Solving double integrals by Changing Cartesian to polar form)

Complex Analysis

UNEDITED RECORDINGS

Lecture 41 (Complex numbers, Polar and Exponential form, Functions of complex variable, Limit of complex variable function)

Lecture 42 (Continuity and Differentiability of complex variable function, Cauchy - Reimann (CR) Equations)

Lecture 43 (Analytic function, Harmonic function, Harmonic Conjugate, Q related to Harmonic function and Harmonic conjugate)

Lecture 44 (Complex Exponential function, Complex trigonometric (sine and cosine) functions)