Recording_Online Lectures_Mathematics - II (UMA004)_COE19-22

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

Official Video Lectures of Mathematics - II (UMA004)

However, the online videos of Mathematics - II (UMA004) are being recorded in the current session (Even, 2020 - 21) while taking the online lecture classes of COE19-22 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)

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

Lecture Notes Mathematics - II (UMA004)

Unit 1 (Ordinary Differential Equations)

UNEDITED RECORDINGS

There are no recordings of the first eight lectures as classes were taken offline this semester. However students can watch either the official lecture videos (link provided above) or the offline class recordings of session Jan - Jun 2020 on their IMPARTUS account.

First eight lectures covers the topics:

General Overview, Variable Separable method, Equations Reducible to Separable Form

Homogeneous DE, Non Homogeneous DE, Exact DE

Integrating Factor to make DE exact, Finding Integrating factor by Inspection, Leibnitz DE, Bernoulli DE

Second Order Linear Differential equations, Some Theorems and Results

Use of Known Solution to Find Other, HDE with Constant Coefficients, Cauchy Euler HDE, Legendre HDE

Lecture 9 (Methods to find the particular solutions of the NHDE, Method of Undermined coefficients (MOUC), Case 1 Exponential form)

Lecture 10 (Method of Undetermined Coefficients (MOUC) Case 2 Trigonometric form, Case 3 Polynomial form)

Lecture 11 (MOUC Case 4 product of exponential and trigonometric form, Method of Variation of Parameters, MOVP)

Lecture 12 (Solving Nonhomogeneous Legendre and Euler Cauchy DE by MOVP and MOUC)

Lecture 13 (Application of DE to LRC circuit, Solving NHDE when one solution of HDE is given)

Unit 2 (Laplace Transformation/Laplace Transform)

UNEDITED RECORDINGS

Lecture 14 (Laplace transformation and Laplace Transform definition, Formulas of Laplace transform of some functions)

Lecture 15 (Piecewise continuous function, Function of Exponential order and Existence of Laplace Transform)

Lecture 16 (First shifting Property (Property 1), Differentiation of Laplace Transform (Property 2))

Lecture 17 (Integration of Laplace Transform (Property 3), Inverse Laplace Transform)

Lecture 18 (Inverse Laplace Transform continued, Inverse of Property 1, Inverse of Property 2)

Lecture 19 (Inverse of Property 2 continued, Laplace of Derivatives (Property 4))

Lecture 20 (Laplace of Derivatives continued (Application of Laplace to DE), Laplace of Integral (Property 5), Inverse of Laplace of Integral)

Lecture 21 (Inverse of Laplace of Integral (Property 5) continued, Convolution Theorem, Some Prerequisite for Second Shifting property)

Lecture 22 (Second Shifting Property, Qs based on Inverse of Second Shifting Property)

Lecture 23 (Second Shifting Property continued, Dirac Delta function)

Unit 3 (Fourier Series)

UNEDITED RECORDINGS

Lecture 24 (Fourier Series Introduction)

Lecture 25 (Fourier Series continued, Fourier series of Odd and Even function)

Lecture 26 (Fourier Series of Odd and Even function continued, Convergence of Fourier Series)

Lecture 27 (Convergence of Fourier Series continued)

Lecture 28 (Fourier Half Range Sine and Cosine Series)

Lecture 29 (Fourier Half Range Sine and Cosine Series continued, 1 - D Heat Equation)

Lecture 30 (Solution of 1 - D Heat Equation)

Lecture 31 (Solution of 1 - D Heat Equation Continued, How to solve questions of Heat Equation)

DERIVATION OF WAVE EQUATION (LECTURE NOTES ONLY)

Unit 4 (Linear Algebra)

UNEDITED RECORDINGS

Lecture 32 (Row Reduced Echelon Form (RREF) of a Matrix, Rank of a Matrix)

Lecture 33 (Rank of Matrix continued, How to make matrix in RREF, Solving System of Linear Equations (SOLE) by RREF)

Lecture 34 (Solving System of Linear Equations (SOLE) by RREF continued, Inverse of a Matrix)

Lecture 35 (Vector Space, Definition and Examples)

Lecture 36 (Subspace of a Vector space)

Lecture 37 (Span of a Set)

Lecture 38 (Linearly dependent and Independent Set of Vectors, Basis of a Vector Space)

Lecture 39 (Basis of a Vector space continued, Dimension of a Vector Space)

Lecture 40 (Dimensions of Vector Space continued, Eigen Values and Eigen Vectors Introduction)

Lecture 41 (Eigen Values and Eigen Vectors continued, Linear Transformation)