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Index
Set Theory
Sequences and Series
Continuity and Differentiability
Integral Calculus
Real Analysis
Differential Calculus
Linear Functional Analysis
Matrix Algebra
Vector Algebra
Complex Analysis
Group Theory
Algebra
Field Theory
Ring Theory
Topology
Ordinary Differential Equations (ODEs)
Partial Differential Equations (PDEs)
Numerical Analysis
Calculus of Variations
Linear Integral Equations
Classical Mechanics
Statistics
Probability and probability Distributions

All videos of Mathematics for IIT JAM, GATE, CSIR NET, UGC NET

Set Theory

Set Operations - 1

26:32 min

Set Theory

26:32 min

Equivalence relation

29:31 min

Set Theory

26:37 min

Dimension of a Vector space

34:51 min

Explanation: Diagonalisable

27:55 min

Set of sets

26:54 min

Row rank and Column rank

29:56 min

Set Operations - 2

28:07 min

Binary Composition

26:25 min

Explanation: Mapping

28:08 min

Explanation: Permutation

30:35 min

Normal Subgroup

32:11 min

Geometric multiplicity

26:01 min

Binary relation

29:10 min

Order of an element

27:34 min

Explanation: Group

27:30 min

Explanation: Groupoid

26:30 min

Explanation: Subgroup

28:31 min

Cyclic Group

30:58 min

Subgroup Operations

28:23 min

Left Cosets

28:59 min

Right Cosets

26:10 min

Explanation: Rings

32:44 min

Vector Spaces

27:12 min

Explanation: Field

28:50 min

Linear Span

29:02 min

Sub - Spaces

29:11 min

Basis of a Vector Space

34:00 min

Complement of subspace

28:48 min

Linear Transformation - 1

28:05 min

Linear Transformation - 2

34:24 min

More on linear mapping

28:58 min

Rank of a Matrix - 1

27:36 min

Rank of a Matrix - 2

29:59 min

Linear Space

32:36 min

System of linear equations

30:04 min

Similar matrices

26:53 min

Eigenvalue of a matrix

28:00 min

Eigenvector

26:47 min

More on eigen value

26:10 min

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Continuity and Differentiability

Rolle’s theorem and mean value theorem - 1

18:58 min

Rolle’s theorem and mean value theorem - 2

14:02 min

Differentiability: Theorems & Proofs

11:06 min

Continuity and Differentiability: Important formulae

10:40 min

Definition & Examples Of Continuity

15:07 min

Course Introduction - Basic Calculus 1

09:13 min

The Real Line - 1

25:02 min

The Real Line - 2

14:29 min

Absolute Value - 1

21:43 min

Absolute Value - 2

18:20 min

Functions - 1

25:46 min

Functions - 2

21:05 min

Transcendental and Trigonometric Functions - 1

24:59 min

Transcendental and Trigonometric Functions - 2

15:57 min

Limits of Functions - 1

21:06 min

Limits of Functions - 2

14:50 min

Algebra of limits - 1

24:11 min

Algebra of limits - 2

20:40 min

One-sided limits - 1

22:54 min

One-sided limits - 2

17:07 min

Continuity - 1

25:13 min

Infinite limits - 1

27:13 min

Limits at infinity - 2

14:57 min

Continuity - 1

22:49 min

Infinite limits - 2

23:46 min

Continuity - Part 2

21:23 min

Algebra of continuous functions - 1

16:11 min

Algebra of continuous functions - 2

16:47 min

Results on continuity - 1

25:30 min

Results on continuity - 2

19:48 min

Differentiability - 1

25:01 min

Differentiability - 2

23:21 min

Derivative and tangent - 1

23:07 min

Derivative and tangent - 2

13:26 min

Rules of differentiation - 1

28:11 min

Differentiation exercises - 1

24:35 min

Rules of differentiation - 2

18:44 min

Maxima and minima - 1

22:13 min

Differentiation exercises - 2

20:11 min

Maxima and minima - 2

23:30 min

Integral Calculus

Riemann Integral: Upper & Lower Darboux Sum

12:04 min

Improper Integrals: Convergence

15:36 min

Derivative of a Function

31:44 min

Rules of Differentiation

37:48 min

Maxima and Minima

34:58 min

Rolle's Theorem and Lagrange Mean Value Theorem

34:17 min

Newton's Method for solving Equations

35:05 min

Monotonic Functions and Inverse Functions

35:49 min

Optimization Problems

31:51 min

Integration-II : In the spirit of Newton and Leibniz

37:20 min

Integration-I : In the style of Newton and Leibniz

44:49 min

Integration-III : Newton and Leibniz Style

58:40 min

Integration theory of Riemann-I

42:13 min

Fundamental Theorem of Calculus (in Riemann style)

25:33 min

Integration theory of Riemann-II

30:23 min

Integration Rule

33:43 min

Calculating Indefinite Integrals

31:51 min

Improper Integral-I

31:52 min

Improper Integral-II

41:03 min

Application of Definite Integral-I

32:05 min

Application of definite Integral-II

35:08 min

Application of definite Integral-III

29:59 min

Application of definite Integral-III

37:58 min

Numerical Integration-I

32:00 min

Numerical Integration-II

26:58 min

Differential Calculus

Constrained Maxima & Minima

31:41 min

Function Of Several Variable

54:46 min

Gradient of a Scalar Field & Directional Derivative

20:47 min

Derivative as a Linear Transformation

16:10 min

Inverse & Implicit Function Theorem

36:28 min

Engineering Mathematics-I

02:25 min

Rolle's Theorem

28:17 min

Mean Value Theorems

29:34 min

Indeterminate Forms - 1

28:36 min

Indeterminate Forms - 2

31:19 min

Taylor Polynomial

28:17 min

Limit of Function of Two Variables

30:43 min

Evaluation of Limit of Function of Two Variable

26:39 min

Continuity of Function of Two Variable

31:31 min

Partial Derivatives of Function of Two Variable

33:24 min

Partial Derivatives of Higher Order

35:32 min

Differentiability of Functions of Two Variables

35:02 min

Differentiability of Functions of Two Variables (Cont.)

32:45 min

Differentiability of Functions of Two Variables (Cont.)

31:08 min

Derivative & Differentiability

36:20 min

Composite and Homogeneous Functions

33:19 min

Taylor’s Theorem for Functions of Two Variables

27:43 min

Maxima & Minima of Functions of Two Variables

30:51 min

Maxima & Minima of Functions of Two Variables (Cont.)

25:36 min

Maxima & Minima of Functions of Two Variables (Cont.)

38:36 min

Linear Functional Analysis

Balls and Spheres

52:03 min

Metric Spaces - 1

04:37 min

Compactness Criterion & its Proof

09:17 min

Normed Linear Space: Concepts & Example

12:03 min

Metric Spaces: Definition and Examples

52:56 min

Metric Spaces: Examples and Elementary Concepts

52:09 min

Closure Points, Limit Points and isolated Points

52:20 min

Open Sets

51:29 min

Closed sets

51:14 min

Sequences in Metric Spaces

51:44 min

Explanation: Completeness

49:20 min

Baire Category Theorem

53:38 min

Limit and Continuity of a Function defined on a Metric space

53:27 min

Continuous Functions on a Metric Space

54:19 min

Explanation: Connectedness

40:05 min

Uniform Continuity

51:01 min

Connected Sets

54:53 min

Explanation: Compactness

51:22 min

Compactness - Continued

51:59 min

Continuous Functions on Compact Sets

53:20 min

Characterizations of Compact Sets

56:29 min

Matrix Algebra

Matric Algebra - 2

05:55 min

Matrix Algebra - 3

11:47 min

Matrix Algebra - 4

08:12 min

Matrix Algebra - 8

11:56 min

Matrix Algebra - 6

04:36 min

Matrix Algebra - 7

12:11 min

Matrix Algebra - 8

12:17 min

Inner Product Continued

26:29 min

Results on Orthogonality

27:38 min

Vector Spaces

29:03 min

Vector Subspaces and Linear Span

31:02 min

Basic Results on Linear Independence

32:00 min

Linear Combination, Linear Independence and Dependence

39:28 min

Results on Linear Independence Continued

27:45 min

Basis of a Finite Dimensional Vector Space

42:00 min

Fundamental Spaces associated with a Matrix

35:02 min

Rank - Nullity Theorem

24:43 min

Definition and Examples of Linear Transformations

30:11 min

Results on Linear Transformations

26:48 min

Fundamental Theorem of Linear Algebra

36:01 min

Isomorphism of Vector Spaces

21:43 min

Rank-Nullity Theorem and Applications

30:32 min

Ordered Basis of a Finite Dimensional Vector Space

32:03 min

Ordered Basis Continued

15:37 min

Matrix of a Linear transformation

26:58 min

Inner Product Space

29:30 min

Matrix of a Linear transformation Continued

25:03 min

Matrix of Linear Transformations Continued

28:52 min

Cauchy Schwarz Inequality

28:56 min

Projection on a Vector

31:44 min

Projection on a Vector

31:44 min

Results on Orthogonality

35:06 min

Vector Algebra

Permutations and the Inverse of a Matrix

30:57 min

Vector intro for linear algebra

05:49 min

Matrix Product Recalled

27:06 min

Matrix: Examples, Transpose and Addition

23:49 min

System of n Linear Equations in n Unknowns

27:37 min

Introduction to System of Linear Equations

25:46 min

Linear Dependence & Independence

17:10 min

Introduction: Linear Algebra

09:02 min

Basis and Dimension

17:45 min

Linear transformations

13:52 min

Notations, Motivation and Definition

29:13 min

Matrix Multiplication

37:30 min

Matrix Product Continued

18:06 min

Inverse of a Matrix

29:59 min

Some Initial Results on Linear Systems

19:16 min

Row Echelon Form (REF)

28:07 min

LU Decomposition - Simplest Form

31:47 min

Elementary Matrices

15:06 min

Row Reduced Echelon Form (RREF)

15:20 min

Rank of a matrix

39:14 min

RREF and Inverse

35:40 min

Row Reduced Echelon Form (RREF) Continued

26:42 min

Solution Set of a System of Linear Equations

31:49 min

Explanation: Determinant

28:36 min

Inverse and the Cramer's Rule

31:42 min

Complex Analysis

Complex Analysis: Contour integration

20:17 min

Complex Analysis: Schwarz Lemma

04:20 min

Open Mapping Theorem: Statement and Proof

15:46 min

Complex Analysis: Taylor Series For Complex Variable

21:33 min

Application of Residue Theorem

23:08 min

Conformal Mapping in Complex Variables

14:19 min

Mobius Transformations

02:45 min

Hyperbolic Functions: Definitions, Identities, Derivatives, and Inverses

07:34 min

Application of Conformal Mapping to Potential Theory

44:07 min

Conformal mapping from disk to disk and angular region to disk

39:46 min

Conformal mapping from half plane to disk and half plane to half plane-I

44:53 min

Analytic Function

42:00 min

Conformal Mapping-I

64:37 min

Conformal Mapping-II

38:18 min

Cauchy-Riemann Equations

50:14 min

Harmonic Functions, Harmonic Conjugates and Milne's Method

35:07 min

Applications to the Problems of Potential Flow-I

26:31 min

Applications to the Problems of Potential Flow-II

55:12 min

Cauchy's Theorem - I

55:50 min

Cauchy's Theorem-II

30:32 min

Complex Integration

42:41 min

Cauchy's Integral Formula for the Derivatives of Analytic Function

58:30 min

Morera's Theorem, Liouville's Theorem and Fundamental Theorem of Algebra

52:31 min

Winding Number and Maximum Modulus Principle

37:20 min

Sequences and Series

32:49 min

Uniform Convergence of Series

30:10 min

Power Series

31:55 min

Taylor Series

31:28 min

Zeros and Singularities of an Analytic Function

42:16 min

Residue at a Singularity

35:24 min

Meromorphic Functions

42:53 min

Residue Theorem

49:09 min

Evaluation of real integrals using residues-I

39:20 min

Evaluation of real integrals using residues-II

56:08 min

Evaluation of real integrals using residues-III

27:32 min

Evaluation of real integrals using residues-IV

36:38 min

Evaluation of real integrals using residues-V

36:04 min

Bilinear Transformations

60:00 min

Cross Ratio

37:32 min

Laurent Series

43:51 min

Group Theory

Group Theory: Permutation Group

34:00 min

Group Theory: Cyclic Group

21:47 min

Group Theory: Subgroup

30:22 min

Group Theory: Normal Subgroup

25:50 min

Group Theory: Quotient Group

11:08 min

Sylow First Theorem: Proof and Example

12:23 min

Sylow Second Theorem: Proof and Example

08:37 min

Group Theory: Homomorphism

25:48 min

Cayley's Theorem

23:30 min

Class Equations: Group Theory

14:46 min

Set Theory

26:37 min

Set Operations

26:32 min

Set Operations (contd.)

28:07 min

Set of sets

26:54 min

Binary relation

29:10 min

Explanation: Mapping

28:08 min

Equivalence relation

29:31 min

Binary Composition

26:25 min

Explanation: Permutation

30:35 min

Explanation: Groupoid

26:30 min

Explanation: Group

27:30 min

Order of an element

27:34 min

Explanation: Subgroup

28:31 min

Cyclic Group

30:58 min

Subgroup Operations

28:23 min

Right Cosets

26:10 min

Left Cosets

28:59 min

Normal Subgroup

32:11 min

Field Theory

Field Theory: Finite Fields

51:15 min

Field Theory: Extension Fields

11:57 min

Field Theory: Galois Theory

14:45 min

Hilbert Basis Theorem

40:25 min

Irreducible, prime elements

30:24 min

Principal Ideal Domains

28:05 min

Irreducible, prime elements, GCD

26:29 min

Unique Factorization Domains 1

34:55 min

Unique Factorization Domains 2

34:18 min

Gauss Lemma

34:04 min

Eisenstein Criterion and Problems

46:22 min

Z[X] is a UFD

36:27 min

Problems 2

35:44 min

Problems 3

39:53 min

Field extensions 1

36:57 min

Field extensions 2

34:33 min

Degree of a field extension 1

31:18 min

Algebraic elements form a field

27:42 min

Degree of a field extension 2

38:40 min

Splitting fields

37:05 min

Field homomorphisms

28:33 min

Finite fields 1

28:51 min

Finite fields 2

42:19 min

Finite fields 3

28:06 min

Ring Theory

Ring Theory: Prime Ideal

13:01 min

Ring Theory: Maximal Ideal

15:25 min

Ring Theory: Principal Ideal Domain

05:56 min

Ring Theory: Euclidean Domain

17:11 min

Introduction, main definitions

31:37 min

Examples of rings

32:44 min

More Examples of Rings

32:52 min

Polynomial rings 1

31:25 min

Polynomial rings 2

20:25 min

Explanation: Homomorphisms

31:10 min

Problems 1

32:03 min

Problems 2

31:55 min

Problems 3

33:33 min

Problems 4

31:38 min

Problems 5

32:25 min

Problems 6

38:16 min

Kernels, ideals

26:44 min

Quotient rings

36:53 min

Examples of correspondence theorem

31:09 min

First isomorphism and correspondence theorems

32:17 min

Prime ideals

30:31 min

Maximal ideals, integral domains

33:27 min

Existence of maximal ideals

30:52 min

Field of fractions, Noetherian rings 1

34:16 min

Noetherian rings 2

32:43 min

Ordinary Differential Equations (ODEs)

First Order Ordinary Differential Equations

08:26 min

Variable Separable Differential Equations

04:15 min

Linear Differential Equation

06:25 min

Exact Differential Equation

07:27 min

Homogeneous Differential Equation

06:20 min

Reducible to Exact Differential Equation

11:14 min

Introduction to Ordinary Differential Equations (ODE)

24:30 min

Methods for First Order ODE's - Homogeneous Equations

33:52 min

Methods for First order ODE's - Exact Equations

31:56 min

Methods for First order ODE's - Reducible to Exact Equations

30:47 min

Methods for First Order ODE's Continued

21:21 min

Non-Exact Equations - Finding Integrating Factors

32:56 min

Methods for First order ODE's - Reducible to Exact Equations Continued

34:43 min

Linear First Order ODE and Bernoulli's Equation

44:30 min

Introduction to Second order ODE's

33:43 min

Properties of solutions of second order homogeneous ODE's

40:15 min

Abel's formula to find the other solution

28:39 min

Abel's formula - Demonstration

26:21 min

Second Order ODE's with constant coefficients

66:47 min

Method of undetermined coefficients

34:59 min

Euler: Cauchy equation

38:53 min

Non homogeneous ODEs Variation of Parameters

33:56 min

Demonstration of Method of undetermined coefficients

39:38 min

Power Series Solutions to Second Order ODE's

36:13 min

Power Series and its properties

29:54 min

Power Series Solutions Continued

37:03 min

Partial Differential Equations (PDEs)

First Order Partial Differential Equation: Solution of Lagrange Form

16:29 min

Cauchy Problem for First Order PDEs

30:50 min

Classification of Second Order PDEs

13:47 min

Method of Separation of Variables for Heat Equation- 1

11:09 min

Method of Separation of Variables for Heat Equation- 2

10:51 min

First order equations in two variables-1

36:04 min

First order equations in two variables-2

29:59 min

First order equations in two variables-3

35:04 min

First order equations in two variables-4

34:54 min

First order equations in two variables-5

37:43 min

First order equations in more than two variables-6

35:44 min

First order equations in more than two variables-7

42:43 min

First order equations in more than two variables-8

43:33 min

Classification - 1

34:13 min

Classification - 2

40:31 min

Classification - 3

34:02 min

Laplace and Poisson equations-1

32:12 min

Laplace and Poisson equations-2

31:31 min

Laplace and Poisson equations-3

24:09 min

Laplace and Poisson equations-4

29:59 min

Laplace and Poisson equations-5

32:55 min

Laplace and Poisson equations-6

29:27 min

Laplace and Poisson equations-7

38:31 min

Laplace and Poisson equations-8

32:57 min

Laplace and Poisson equations-9

28:09 min

Laplace and Poisson equations-10

37:49 min

One dimensional heat equation-1

32:07 min

One dimensional heat equation-2

27:03 min

Numerical Analysis

Gauss Elimination Method

17:18 min

Gauss-Seidel Method

15:48 min

Numerical Solutions of ODEs using Picard Method

11:03 min

Numerical solutions of ODEs using modified Euler method

13:24 min

Numerical Solutions of ODEs using Runge-Kutta Method

14:20 min

Introduction to Numerical Analysis

50:23 min

Interpolating Polynomials

49:37 min

Polynomial Approximation

48:35 min

Error in the Interpolating polynomial

49:45 min

Properties of Divided Difference

50:01 min

Cubic Spline Interpolation

47:47 min

Cubic Hermite Interpolation

50:16 min

Piecewise Polynomial Approximation

47:58 min

Numerical Integration: Basic Rules

49:41 min

Tutorial - 1

51:55 min

Composite Numerical Integration

46:42 min

Gauss 2-point Rule: Error

45:21 min

Gauss 2-point Rule: Construction

54:50 min

Numerical Differentiation

49:10 min

Convergence of Gaussian Integration

48:49 min

Tutorial - 2

52:53 min

Gauss Elimination

46:38 min

L U decomposition

46:26 min

Gauss Elimination with partial pivoting

44:59 min

Cholesky decomposition

47:18 min

Calculus of Variations

Calculus of Variations

21:10 min

Derivation of the Euler-Lagrange Equation

07:51 min

Calculus of variations: Basic concepts-I

32:58 min

Calculus of variations: Basic concepts-II

33:19 min

Calculus of variations: Introduction

29:27 min

Calculus of variations: Basic concepts and Euler's equation

41:17 min

Euler's equation: Some particular cases

37:45 min

Euler's Equation Examples

40:53 min

Brachistochrone problem and Euler's equation-I

32:19 min

Euler's equation : A particular case and Geodesics

39:14 min

Variational problems in parametric form

42:19 min

Functions of several independent variables

33:22 min

Variational derivative and invariance of Euler's equation

38:49 min

Variational problems of general type

32:47 min

Isoperimetric problem-II

38:26 min

Invariance of Euler's equation and isoperimetric problem-I

37:01 min

Variational problem involving a conditional extremum-I

29:13 min

Variational problems with moving boundaries-I

37:10 min

Variational problem involving a conditional extremum-II

35:43 min

Variational problems with moving boundaries-II

24:06 min

Linear Integral Equations

Linear Integral Equation of the First and Second Kind of Fredholm Type

12:18 min

Linear Integral Equation of the First and Second Kind of Volterra Type

11:11 min

Integral equations, calculus of variations and its applications

02:23 min

Conversion of IVP into integral equations

24:46 min

Definition and classification of linear integral equations

27:54 min

Conversion of integral equations into differential equations

34:51 min

Conversion of BVP into an integral equations

30:02 min

Integro-differential equations

24:21 min

Fredholm integral equation with separable kernel: Theory

34:35 min

Solution of integral equations by successive substitutions

28:34 min

Fredholm integral equation with separable kernel: Examples

34:27 min

Solution of integral equations by successive approximations

33:47 min

Solution of integral equations by successive approximations: Resolvent kernel

27:05 min

Singular integral equations-I

29:17 min

Singular integral equations-II

22:03 min

Cauchy type integral equations-II

25:41 min

Cauchy type integral equations-I

45:48 min

Cauchy type integral equations-V

33:26 min

Cauchy type integral equations-IV

30:49 min

Cauchy type integral equations-III

34:47 min

Solution of integral equations using Fourier transform

19:35 min

Solution of integral equations using Hilbert transform -I

32:24 min

Solution of integral equations using Hilbert transform-II

29:03 min

Classical Mechanics

Generalised Coordinates in Classical Mechanics

47:42 min

Lagrange's Equation of Motion in Classical Mechanics

28:59 min

Hamilton’s Principle - Classical Mechanics

43:56 min

Principle of Least Action - Classical Mechanics

10:15 min

Theory of Small Oscillations - Classical Mechanics

03:45 min

Generalized Coordinates, Configuration Space

59:55 min

Introduction, Constraints

44:45 min

D'Alembert's Principle

31:59 min

Principle of Virtual Work

40:10 min

Lagrange's Equations

37:55 min

Hamilton's Principle

43:56 min

Hamilton's Equations

59:37 min

Variational Calculus, Lagrange's Equations

75:40 min

Conservation Laws, Routh's procedure

41:36 min

Canonical Transformations

61:34 min

An Example: Bead on Spinning Ring

41:40 min

Symplectic Condition

47:24 min

Canonical Invariants, Harmonic Oscillator

33:03 min

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