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All Exams  >   UPSC  >   Mathematics Optional Notes for UPSC  >   All Videos

All videos of Mathematics Optional Notes for UPSC for UPSC CSE Exam

Linear Algebra

What is a Vector Space?

06:58 min

Vector Spaces over R and C

08:01 min

Introduction to Linerar Space

15:46 min

Linear Dependence and Independence

08:16 min

Linear Independence

12:56 min

Subspaces- Linear Algebra

13:04 min

Subspace Proof Example

05:42 min

Linear Independence and Bases

08:40 min

Linear Algebra - Dimensions

11:14 min

Basis and Dimensions

10:06 min

Linear Transformation and Matrices

10:59 min

Inverse matrices, column space and null space

12:09 min

Rank and Nullity of a Matrix ( Row Echeleon )

22:10 min

Linear Transformation on Vector Spaces

09:11 min

Matrix Transormations

11:32 min

Linear Transformations

09:19 min

Introduction to Matrices

11:23 min

Adding and Subtracting Matrices

06:12 min

Scalar Multiplication of Matrices and Matrix Operations

06:37 min

Multiplying Matrices

17:40 min

Row Echelon Form of the Matrix

11:11 min

Reduced Row Echelon Form of Matrix

08:44 min

Gauss Jordan Elimination & Reduced Row Echelon Form

10:51 min

Similarity of Matrices

19:39 min

Rank of Matrix

17:17 min

Finding Rank of a Matrix

03:25 min

Inverse of 3X3 Matrix

15:21 min

Inverse of a Matrix

04:27 min

Inverse Matrices and their Properties

12:00 min

Inverse of Matrix: Example

06:22 min

System of Linear Equations- 1

04:04 min

System of Linear Equations- 2

04:16 min

Solution Sets for System of Equations

11:25 min

Eigenvalues and Eigenvectors

17:16 min

Finding of Eigenvalues and Eigenvectors

17:10 min

Introduction to Characteristic Polynomial, Eigenvalues and Eigenvectors

17:53 min

Characteristic Polynomial

12:01 min

Finding Characteristic Polynomial of a Matrix

03:54 min

The Cayley Hamilton Theorem

21:38 min

Cayley Hamilton Theorem

31:23 min

Overview of Symmetric Matrix

07:00 min

Overview of Skew Symmetric Matrix

06:51 min

Symmetric Matrix

25:51 min

Symmetric and Skew Symmetric Matrix

11:31 min

What is Hermitian Matrix

06:00 min

What is Skew Hermitian Matrix

02:28 min

Theorem on Hermitian and Skew Hermitian Matrix

09:00 min

Hermitian Matrix

46:55 min

Hermitian, Normal and Unitary Matrix

05:52 min

Orthogonal Matrix

04:44 min

Proving a Matrix is Orthogonal

03:19 min

Problem on Unitary Matrix

07:10 min

Problem on Orthogonal Matrix

05:22 min

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Calculus

Fun Video: Overview of Limits and Derivatives

10:02 min

Examples of Limits of Polynomials (with Explanation)

05:42 min

Limits: Examples Part 1

10:03 min

Introduction to Limits: Part 1

11:32 min

Limits By Using Standard Formula

38:07 min

Limits of Non-Algebraic Functions

41:32 min

Advanced Exponential Limits - 1

38:31 min

Advanced Exponential Limits - 2

34:07 min

Newton-Leibniz Formula for Limits

29:17 min

Limits and Continuity Definitions

12:06 min

Limits and Continuity Graphical Interpretation of Continuity

11:20 min

Limits and Continuity Difference between Not Defined, infinity, 0 and approaching 0

08:21 min

Limits and Continuity Indeterminate Forms

03:45 min

Limits and Continuity Important Formulas

05:19 min

Limits and Continuity Examples of Direct Substitution, Factorization, Rationalization

19:18 min

Limits and Continuity Examples of sinx/x, tanx/x, (e^x-1)/x, (a^x-1)/x problems

13:33 min

Limits and Continuity Examples of log(1+x)/x, infinity/infinity problems

09:43 min

Limits and Continuity Series Expansion

14:05 min

Limits and Continuity L'Hospital Rule and other topics

07:45 min

Video: Continuity of a Function

08:28 min

Continuity & Differentiability

27:32 min

Proof of theorem stating Differentiability implies Continuity

11:40 min

Problems on Continuity & Differentiability - 1

49:29 min

Problems on Continuity & Differentiability - 2

54:30 min

Short Tricks for Continuity & Differentiability

54:29 min

Continuity & Differentiability- 2

28:38 min

Continuity & Differentiability- 3

20:51 min

Mean Value Theorem

06:37 min

Maxima and Minima

04:30 min

Examples : Absolute maxima and minima

13:15 min

Finding maxima and Minima Using Second Derivative Test (with Example)

08:15 min

Introduction to Orthogonal Matrix

03:08 min

Real Numbers

24:46 min

Functions of Real Variables

13:34 min

Introduction to Limits

20:20 min

Limits and L'Hospital's Rule

18:27 min

Limits and Limit Laws in Calculus

12:49 min

Continuity and Differentiability

32:48 min

Understanding Mean Value Theorem

19:40 min

Taylor's Theorem

07:01 min

Taylor's Remainder Theorem

14:08 min

Indeterminate Forms

07:31 min

Horizontal and Vertical Asymptotes

31:36 min

Curve Sketching: First and Second Derivative

41:29 min

Functions of Several Variables

20:14 min

Introduction to Partial Derivatives

10:56 min

Partial Derivatives

60:33 min

Langrage's Multipliers

33:46 min

What is Jacobian

27:14 min

How to Find Jacobian Matrix

09:58 min

Finding Definite Integral using Reimann Sums

13:18 min

Reimann's Sum

08:56 min

Indefinite Integral

29:00 min

Improper Integrals

13:56 min

Double and Triple Integrals

15:29 min

Double Integrals-1

10:29 min

Double Integrals-2

09:51 min

Double Integrals-3

08:04 min

Triple Integrals-1

10:38 min

Triple Integrals-2

07:26 min

Triple Integrals-3

11:48 min

Analytic Geometry

Different Forms of Line

19:33 min

Two-Point Form of Line

19:16 min

Straight Line in Perpendicular Form

29:04 min

Different Forms of Straight Line

20:44 min

Problems on various Forms of Straight Line

18:55 min

Reduction of Different Forms of Straight Line

18:33 min

Parallel & Perpendicular Lines

16:06 min

Distance of Point From Straight Line

17:48 min

Family of Lines

16:17 min

Problems on Family of Lines

18:59 min

Concurrency of Three Lines

13:58 min

Mirror Image of Point

24:49 min

Equation of Reflected Ray

14:50 min

Problems on Reflection of Ray

13:26 min

Coordinate System in a Plane- 1

46:55 min

Coordinate System in a Plane- 2

35:54 min

Coordinate System in a Plane- 3

41:27 min

Coordinate System in a Plane- 4

45:02 min

Surface Area of Revolution By Integration

30:36 min

Introduction to Polar Coordinates

22:29 min

Point Plotting in 3D Coordinate System

07:27 min

Second Degree Equation with 3 Variables

06:09 min

Quadratic Equation with 3 Variables

10:53 min

Understanding Equation of Sphere

03:40 min

Equation of Sphere

09:29 min

General Equation of Cone

07:58 min

Hyperboloid of One and Two Sheets

05:49 min

The Ellipsoid

05:55 min

Hyperboloid of One Sheets

06:31 min

Hyperboloid of Two Sheets

08:37 min

The Hyperbolic Paraboloid

07:46 min

The Elliptical Paraboloid

06:02 min

Equation of Sphere

09:41 min

The Elliptical Cone

07:20 min

Ordinary Differential Equations

Introduction to Differential Equations (includes Order and Degree of a Differential Equation)

09:38 min

Differential Equations Representing a Family of Curves

07:11 min

Homogeneous Differential Equations and their Solution

07:04 min

Solving Differential Equations by Variables Separable Method

09:06 min

General solution and Particular Solution of a Differential Equation

04:54 min

Linear Differential Equations and their Solution using Integrating Factor

05:37 min

Formation of a Differential Equation whose General Solution is Given

04:48 min

Formulation and Interpretation of Differential Equations

09:04 min

First Order Differential Equation

07:49 min

First Order Linear Differential Equation

22:28 min

Method of Integrating Factors

05:07 min

Integrating Factor

09:14 min

Orthogonal Trajectory in Differential Equations

11:25 min

Clairaut's Equation

08:16 min

How to Solve Clairaut's Equation

09:43 min

Linear Second Order Homogeneous Differential Equations with Constant Coef

10:16 min

Solved Example: Linear Second Order Differential Equation

07:23 min

Initial Value Problem

07:13 min

Introduction to Complimentary Function and Particular Integral

14:54 min

Solved Example: Complimentary Function and Particular Integral

16:40 min

Second Order Linear Differential Equation

25:17 min

Second-order linear equations with variable coefficients

56:23 min

Cauchy Euler Equation

14:05 min

Variation of Parameters

11:36 min

Variation of Parameters (Non Homogenous)

09:58 min

Laplace Transforms

19:27 min

Inverse Laplace Transform Example using Partial Fractions

08:53 min

Inverse Laplace Transform

12:44 min

Laplace Transform of Elementary Functions

41:48 min

Initial Value Problem: Second Order Differential Equation

26:17 min

Dynamics & Statics

Simple Harmonic Motion

26:23 min

Compound Pendulum

08:11 min

Equivalent Length of a Simple Pendulum

11:31 min

Energy of Oscillation in Angular SHM

05:05 min

Cases of Spring Combinations in SHM

07:21 min

SHM of Free Bodies in Absence of External Forces

06:42 min

Motion in a Plane

42:39 min

Projectile Motion

73:15 min

Short Tricks: Projectile Motion

02:13 min

Velocity of a Particle During Projectile

03:05 min

Position and Trajectory of Projectile

05:10 min

Projectile in Moving Reference Frame

07:04 min

Projectile on Inclined Plane

11:36 min

Work and Energy

11:23 min

Principle of Work & Energy

15:08 min

Work-Energy Theorem

04:33 min

Potential Energy

12:37 min

The Law of Conservation of Energy

10:10 min

Kepler's Laws of Planetary Motion

01:47 min

Kepler's Law & Proofs

36:41 min

Kepler's Laws of Planetary Motion-Second Law

09:12 min

Kepler's Laws of Planetary Motion-Third Law

04:49 min

Stable, Unstable, and Neutral Equilibrium

01:05 min

Introduction to Rectilinear Motion

07:29 min

Rectilinear Motion Problems

16:14 min

Constrained Motion-1

09:11 min

Constrained Motion-2

02:01 min

Static and Kinetic Friction

24:49 min

Static Friction

04:14 min

Principle of Virtual Work

12:08 min

Stable and Unstable Equilibrium Points

07:22 min

Equilibrium of Rigid Bodies 3D force Systems

10:14 min

Algebra

Group Definition

11:15 min

Understanding Subgroups

15:51 min

Cyclic Group

12:27 min

Cosets and their Properties

15:21 min

Lagrange's Theorem

14:05 min

Normal and Quotient Subgroups

11:24 min

Normal Subgroups

09:14 min

Factor Groups

16:59 min

Group Homomorphism

10:04 min

The Kernel of a Group Homomorphism

04:53 min

Homomorphism and Isomorphism Theorems

12:47 min

Natural Proof of First Isomorphism Theorem

13:08 min

Permutation Group

15:31 min

Properties of Permutation

16:00 min

Cayley's Theorem

04:40 min

Definiton of Ring

06:51 min

Ring Examples

07:18 min

Units in a Ring

07:14 min

Intution Behind Subrings

10:22 min

Subring Proof Examples

12:21 min

Ideals in Ring Theory

11:57 min

Ideals and Factor Rings

19:58 min

Examples of Ideals and Factor Rings

13:34 min

Ring Homomorphism

10:01 min

Inegral Domain

07:34 min

Principle Ideal Domain

28:05 min

Euclidean Domains

26:15 min

Unique Factorization Domain-1

34:55 min

Unique Factorization Domain-2

34:18 min

Field Definition

08:06 min

Quotient Fields

27:27 min

Real Analysis

Ordered Fields and the Real Number System

10:51 min

Least Upper Bound Property

10:36 min

Definition of the Limit of a Sequence

13:59 min

Limits of the Sequence

11:20 min

Introduction to Cauchy Sequence

15:53 min

Sequence is Cauchy if and only if it Converges

24:23 min

Completeness of the Real Number

15:29 min

The Real Number Line (completeness, cardinality, and measure)

07:42 min

Convergence and Divergence - Introduction to Series

16:18 min

Series Convergence Tests

15:36 min

Absolute Convergence, Conditional Convergence, and Divergence

13:07 min

Determining Absolute or Conditional Convergence

16:04 min

Checking for Absolute Convergence

19:15 min

Rearrange a Series

14:20 min

Rearrangements of absolutely convergent series

11:19 min

Continuity

21:41 min

Continuity and Examples

09:59 min

What is Uniform Continuity

06:23 min

Uniform Continuity: Basics

07:14 min

Uniform Continuity: Example

09:39 min

Continous Function On Compact Sets

13:17 min

Introduction to the Riemann Integral

38:16 min

Real Analysis - Riemann Integrability

19:18 min

Improper Integrals- 1

18:34 min

Improper Integrals- 2

10:00 min

Fundamental theorems of integral calculus

20:46 min

The Fundamental Theorem of Calculus

09:38 min

Uniform convergence of sequences and series of functions

50:47 min

Pointwise and Uniform Convergence Visualized

07:51 min

Proof: Differentiability Theorem on Uniform convergence of Sequence of Functions

24:20 min

Partial Derivatives of Functions of Two And Three Variables

09:29 min

Local Maxima and Minima of Function

14:18 min

Complex Analysis

Conformal Mapping in Complex Variables

14:19 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

Cauchy-Riemann Equations

50:14 min

Harmonic Functions, Harmonic Conjugates and Milne's Method

35:07 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

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

Laurent Series

43:51 min

Complex Analysis: Contour integration

20:17 min