Канал: Doney Kurian

1 5 Linear deqns Part 2 Bernoulli's eqn

1 5 Linear deqns Part 2 Bernoulli's eqn

1 5 Linear deqns part 1

1 5 Linear deqns part 1

Exact differential equation part 1

Exact differential equation part 1

ODE introduction

ODE introduction

Relative extrema problems

Relative extrema problems

Relative extrema and Saddle point

Relative extrema and Saddle point

Relative extrema in 2 variables part 1

Relative extrema in 2 variables part 1

Laplaces equation to polar form

Laplaces equation to polar form

Bounded set (Real Analysis) : Objective type questions.

Bounded set (Real Analysis) : Objective type questions.

Introduction to Inner product spaces and Schwarz inequality

Introduction to Inner product spaces and Schwarz inequality

Compact linear maps

Compact linear maps

computing limits

computing limits

different limits

different limits

Completion of metric spaces theorem (Part 2)

Completion of metric spaces theorem (Part 2)

Taylor Foguel Theorem

Taylor Foguel Theorem

Completion of a metric space theorem (part 1)

Completion of a metric space theorem (part 1)

L' Hospital's rule (Class 4) : Indeterminate forms 1^∞, 0^∞, ∞^∞

L' Hospital's rule (Class 4) : Indeterminate forms 1^∞, 0^∞, ∞^∞

Some consequences of Hahn Banach extension theorem compressed

Some consequences of Hahn Banach extension theorem compressed

L' Hospital's rule (Class 3) : Indeterminate forms 0.ꝏ and ꝏ - ꝏ.

L' Hospital's rule (Class 3) : Indeterminate forms 0.ꝏ and ꝏ - ꝏ.

Hahn Banach extension theorem

Hahn Banach extension theorem

Contractive function and contractive lemma

Contractive function and contractive lemma

L' Hospital's rule (class 2) : Indeterminate form ∞/∞

L' Hospital's rule (class 2) : Indeterminate form ∞/∞

L'Hospital's Rule (class 1) : Indeterminate form 0 / 0

L'Hospital's Rule (class 1) : Indeterminate form 0 / 0

Norm on the space of bounded linear maps

Norm on the space of bounded linear maps

Bounded linear maps on normed spaces introduction

Bounded linear maps on normed spaces introduction

Characterization of closed sets

Characterization of closed sets

x is a limit point of a subset A of a metric space X iff distance between x and A difference {x} is

x is a limit point of a subset A of a metric space X iff distance between x and A difference {x} is

Subset of a metric space is closed iff it contains all its limit pointe and convergence of a sequenc

Subset of a metric space is closed iff it contains all its limit pointe and convergence of a sequenc

definition of Limit points and Examples

definition of Limit points and Examples

Characteristic of the class of open sets and class of closed sets

Characteristic of the class of open sets and class of closed sets

Definition of open and closed sets and theorem

Definition of open and closed sets and theorem

Open balls and closed balls in metric spaces with examples

Open balls and closed balls in metric spaces with examples

Examples for metric spaces, Diameter of a set in a metric space and distance between a point and a s

Examples for metric spaces, Diameter of a set in a metric space and distance between a point and a s

Examples for metric spaces : Taxicab metric, Max metric and discrete metric.

Examples for metric spaces : Taxicab metric, Max metric and discrete metric.

Norm on product spaces

Norm on product spaces

Cauchy Schwarz and Minkowski's inequalities

Cauchy Schwarz and Minkowski's inequalities

Metric space class 1

Metric space class 1

Norm on quotient space

Norm on quotient space

Derivative of Hyperbolic functions

Derivative of Hyperbolic functions

Fundamental group of crosss product of two spaces

Fundamental group of crosss product of two spaces

Logarithm of a complex number

Logarithm of a complex number

Complex Numbers nth roots of unity

Complex Numbers nth roots of unity

Residue theorem and finding residue of simple poles

Residue theorem and finding residue of simple poles

Multiple integral 1

Multiple integral 1

Theorem 6 18

Theorem 6 18

One point compactification introduction

One point compactification introduction

The property of being a metrizable space is a topological property.

The property of being a metrizable space is a topological property.

Theorem 4 14

Theorem 4 14

Doney Kurian Live Stream

Doney Kurian Live Stream

Necessary and suffficient condition for weak convergenceand if X is finite dimensional, then the wea

Necessary and suffficient condition for weak convergenceand if X is finite dimensional, then the wea

Weak convergence definition and remark

Weak convergence definition and remark

Result for Hahn Banach extension theorem

Result for Hahn Banach extension theorem

Corollary of Hahn BAnach separation theorem

Corollary of Hahn BAnach separation theorem

Hahn - Banach separation theorem

Hahn - Banach separation theorem

Every non zero linear functional on a normed space X is an open map.

Every non zero linear functional on a normed space X is an open map.

Third result for Hahn Banach separation theorem

Third result for Hahn Banach separation theorem

partially ordered set, totally ordered set and Zorns lemma

partially ordered set, totally ordered set and Zorns lemma

If X is a normed space and Y a subspace of X which is not a hyperspace in X, then Y^c is connected.

If X is a normed space and Y a subspace of X which is not a hyperspace in X, then Y^c is connected.

A complex linear functional from a given real linear functional

A complex linear functional from a given real linear functional

Examples for discontinuous linear map

Examples for discontinuous linear map

System of equations with infinite no of solutions

System of equations with infinite no of solutions

Rank of matrix and solution of the given system

Rank of matrix and solution of the given system

For a linear map F, R(F) is finite dimensional implies that F is continuous iff R(F) is closed

For a linear map F, R(F) is finite dimensional implies that F is continuous iff R(F) is closed

Every bijective linear map on a finite dimensional normed space is a homeomorphism

Every bijective linear map on a finite dimensional normed space is a homeomorphism

linear homeomorphism on normed spaces.

linear homeomorphism on normed spaces.

Some conditions for a linear map from normed space X to normed space Y to be continuous (part 2)

Some conditions for a linear map from normed space X to normed space Y to be continuous (part 2)

Some conditions for a linear map from normed space X to normed space Y to be continuous

Some conditions for a linear map from normed space X to normed space Y to be continuous

Condition for Two norms in a linear space X are comparable.

Condition for Two norms in a linear space X are comparable.

Strictly convex normed space definition and examples,

Strictly convex normed space definition and examples,

Let X be a normed space and Y be a subspace of X Then interior of Y is non empty iff Y=X

Let X be a normed space and Y be a subspace of X Then interior of Y is non empty iff Y=X

In a normed space X, sum of two sets is open if one of them is open

In a normed space X, sum of two sets is open if one of them is open

In a normed space X, open ball and closed ball are convex sets

In a normed space X, open ball and closed ball are convex sets

Basis and Dimension introduction

Basis and Dimension introduction

A normed space X is finite dimensional implies that every closed and bounded subset of X is compact

A normed space X is finite dimensional implies that every closed and bounded subset of X is compact

Solution of the system of equations using matrices cases of infinite solutions and unique solution

Solution of the system of equations using matrices cases of infinite solutions and unique solution

Infinite dimensional subspace of a normed space may not be closed in X

Infinite dimensional subspace of a normed space may not be closed in X

Convergence and boundedness of a sequence in a finite dimensional normed space

Convergence and boundedness of a sequence in a finite dimensional normed space

Finite dimensional normed space is complete.

Finite dimensional normed space is complete.

solving the system of linear equations using the matrix with elementary row operations 1

solving the system of linear equations using the matrix with elementary row operations 1

F Riesz lemma

F Riesz lemma

FA 20. Necessary and sufficient condition for the convergence of a sequence in the quotient space

FA 20. Necessary and sufficient condition for the convergence of a sequence in the quotient space

FA 19. Quotient norm 4th property

FA 19. Quotient norm 4th property

FA 18. quotient norm triangle inequality

FA 18. quotient norm triangle inequality

FA 17. norm in quotient normed space proof 1 and 2

FA 17. norm in quotient normed space proof 1 and 2

FA 16. If X is a normed space and Y is a subspace of X, then Y and its closure are normed spaces

FA 16. If X is a normed space and Y is a subspace of X, then Y and its closure are normed spaces

FA 15 Function space example for normed space

FA 15 Function space example for normed space

FA 14. l^p subset c0

FA 14. l^p subset c0

FA 13. Some properties in l^p

FA 13. Some properties in l^p

FA 12. Jensen's Inequality and l^p subset l^r for p less than r

FA 12. Jensen's Inequality and l^p subset l^r for p less than r

FA 11. Sequence Space, Eg for Normed space

FA 11. Sequence Space, Eg for Normed space

FA 10. More about normed spaces

FA 10. More about normed spaces

FA 9. Unit balls in R^2 with norm 1, norm 2, norm infinity

FA 9. Unit balls in R^2 with norm 1, norm 2, norm infinity

FA 8. Examples of Nrmed Spaces K^n with norm p

FA 8. Examples of Nrmed Spaces K^n with norm p

FA 7. Normed Space Class 3 Properties of norm

FA 7. Normed Space Class 3 Properties of norm

FA 6. Normed space class 2 Norm Properties

FA 6. Normed space class 2 Norm Properties

FA 5. Normed Space Class 1 Norm

FA 5. Normed Space Class 1 Norm

FA 4. Vector Space 4

FA 4. Vector Space 4

FA 3. Vector Space Part 3

FA 3. Vector Space Part 3

FA 2. Vector Space Part 2

FA 2. Vector Space Part 2

FA 1. Vector Space Part 1

FA 1. Vector Space Part 1