Subject - Mathematics (UG Affiliated Colleges) (Developed by Dr. S.S.Bellale)

Subject - Mathematics (UG Affiliated Colleges) (Developed by Dr. S.S.Bellale)

Developed By: Dr. S. S. Bellale, Vice Principal  & Head, Department of Mathematics, Dayanand Science College, Latur
Program Subject Year Semester Paper Unit Unit Name Content YouTube Kinks
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Syllabus, Definition and Basic Concepts

https://www.youtube.com/playlist?
list=PL7TANb4Sj71omv0tRaWWr
MxG1B1XgzjF7

B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Introduction of Real Analysis

https://youtu.be/yjBvP9303gY
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Composition and Field Structure

https://youtu.be/XKKN55uNdgo  
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Field structure

https://youtu.be/jeARqLEJFok  
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Order Structure

https://youtu.be/8AD_JGHPdQo
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Completeness Property

https://youtu.be/9-Q7AnU0CD0  
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Intervals: Open and Closed

https://youtu.be/goY6CpGeFaA  
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Bounded Unbounded Sets

https://youtu.be/8O8e88NiViY
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Supremum and Infimum

https://youtu.be/gQuduTGD2lU
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Examples on Supremum and Infimum

https://youtu.be/1flb9IwnoQo
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Completeness in the Set of Real

https://youtu.be/8fcThn9h3i8
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Archimedean Property of Real Numbers

https://youtu.be/IK5rSuhdj0Y
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Archimedean Property and Dedekind's Property

https://youtu.be/-jfyywJJNq4
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Representation of a Number on Real Line

https://youtu.be/HVWCA2T37vk
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Absolute Value of Real Number

https://youtu.be/oGV3H1fXUeA
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Neighborhood of  Point

https://youtu.be/EElxrbUKvhk
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Open Set and its Examples

https://youtu.be/U4Flke0EBKc  
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Theorems on Open Set

https://youtu.be/nLwwUnSQY1k
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Limit Point of a Set

https://youtu.be/yaku834A8ng
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Bolzano Weierstrass Theorem

https://youtu.be/DdRTFPWChAo
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Examples on Derived Sets

https://youtu.be/FPUCYiVPDSY
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Closure of a Set and Closed Sets

https://youtu.be/oMrS8mwnFEQ
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Some Important  theorems on Closed Sets

https://youtu.be/rk1rMXBx3II
B.Sc.  Mathematics II  III

VI - Real
Analysis I

  I

Sets and
Its Properties

Some Important  theorems on Closed Sets

https://youtu.be/jnQl5QymHXQ
B.Sc.  Mathematics II  IV

IX-Real
Analysis II

  I

Sequence and Series

Examples of Sequences

https://www.youtube.com/playlist?
list=PL7TANb4Sj71pdZzm8
TrN6zl9XZ3hyLWzA
Developed By: Dr. S. S. Bellale, Vice Principal  & Head, Department of Mathematics, Dayanand Science College, Latur
Program Subject Year Semester Paper Unit Unit Name Content YouTube Kinks
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Syllabus, Definition of Metric Spaces

https://youtu.be/WKh1P8ERKJk
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Basic Concepts of and types of metric spaces

https://youtu.be/9jJ4tM_EDnE
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Metric Space on set of Real Numbers

https://youtu.be/aEaO0sUb-nY
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Euclidean Space and its proof

https://youtu.be/ncVsqm8fZlM
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Hilbert's  space and its proof

https://youtu.be/eWY7CCjFQFg
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Rectangular Metric Space

https://youtu.be/8UM16mdc-DQ
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Frechet Metric Spaces

https://youtu.be/02BDAWmk1yE
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Bounded metric Space

https://youtu.be/majcQRbLIdU
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Open and Closed Spheres

https://youtu.be/2ZjaNoadfmY
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Neighborhood of a Point

https://youtu.be/lwXvtXnR8dw
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Open Set and Open Sphere

https://youtu.be/bPDF9GUV-Bs
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Theorems on Open Set

https://youtu.be/s30_9Phkayg
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Adherent Point, Limit Point

https://youtu.be/UNc4VcAFd7c
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Closed Set and Closed Sphere

https://youtu.be/tP6BdFbnafw
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Closed Set and theorems

https://youtu.be/Tn17nsQf6rg
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Subspace and theorems

https://youtu.be/pCb4rkpJbW8
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Theorems on Subspace

https://youtu.be/9afyaU3L-dI
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Closure of a Set

https://youtu.be/dKAofJJkKys
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Properties of Closure of a Set

https://youtu.be/Kui27hzvp1o
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Proofs Properties of Closure of a Set

https://youtu.be/R9gc_zbsf6k
B.Sc.  Mathematics III V

XII-
Metric Spaces

  I

Matric
Spaces I

Interior,  Exterior Frontier and Boundary Points

https://youtu.be/Pm7JJl2tsbc
B.Sc.  Mathematics III V

XII-
Metric Spaces

  II

Convergence and Completeness

Play list of Unit

https://www.youtube.com/playlist?
list=PL7TANb4Sj71qh2uWfatm
401WSm1D1dDqD
B.Sc.  Mathematics III V

XII-
Metric Spaces

  II

Convergence and Completeness

Convergence and Cauchy Sequence

https://youtu.be/X2tJohpC7x8
B.Sc.  Mathematics III V

XII-
Metric Spaces

  II

Convergence and Completeness

Cauchy Sequence

https://youtu.be/gMM3IjX-C4Q
B.Sc.  Mathematics III V

XII-
Metric Spaces

  II

Convergence and Completeness

Complete Metric Space

https://youtu.be/9sDiisOKuQE
B.Sc.  Mathematics III V

XII-
Metric Spaces

  II

Convergence and Completeness

Examples on Complete Metric Space

https://youtu.be/MOHFASs4afA
B.Sc.  Mathematics III V

XII-
Metric Spaces

  II

Convergence and Completeness

Examples on Complete Metric Space

https://youtu.be/09ojp8s1hYw
B.Sc.  Mathematics III V

XII-
Metric Spaces

  II

Convergence and Completeness

Subspace of Complete Metric Space

https://youtu.be/UNrrJFzC-8Y
B.Sc.  Mathematics III V

XII-
Metric Spaces

  II

Convergence and Completeness

Cantor's Intersection Theorem

https://youtu.be/Tuld69hTNJI
B.Sc.  Mathematics III V

XII-
Metric Spaces

  II

Convergence and Completeness

Dense set, First and Second Category Sets

https://youtu.be/JmIPLqXrZnw
B.Sc.  Mathematics III V

XII-
Metric Spaces

  II

Convergence and Completeness

Baire's Category Theorem

https://youtu.be/al9_fHY1WD4
B.Sc.  Mathematics III V

XII-
Metric Spaces

  II

Convergence and Completeness

Continuity and Uniform Continuity

https://youtu.be/-mnjRDGxxbs
B.Sc.  Mathematics III V

XII-
Metric Spaces

  II

Convergence and Completeness

Theorems on Continuity

https://youtu.be/4LZvBRmIdfM
B.Sc.  Mathematics III V

XII-
Metric Spaces

  III

Compactness

Theorems and Examples on Compactness

https://www.youtube.com/playlist?
list=PL7TANb4Sj71rv0hS44
GGeBLlSdCKShbPr

Developed By: Dr. S. S. Bellale, Vice Principal  & Head, Department of Mathematics, Dayanand Science College, Latur
Program Subject Year Semester Paper Unit Unit Name Content YouTube Kinks
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Forces Acting on a Particle

https://www.youtube.com/playlist?
list=PL7TANb4Sj71pLT9rJ
JN1XlDpqv9Lythw2
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Definitions, law of parallelogram, resultant vector

https://youtu.be/sdJ2i4ys-7I
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Magnitude and Direction of Resultant

https://youtu.be/4JHSDXt6Xqg
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Theorem on Magnitude and Direction of Resultant

https://youtu.be/84GGK_Ax5jA
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Examples on Resultant of Two Forces

https://youtu.be/4oMGkNKFuFs
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Magnitude and Direction of Resultant

https://youtu.be/u0CLRrMbcHc
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Problems on Resultant of two forces

https://youtu.be/CxOU1aEtny8
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Components  of Resolved forces

https://youtu.be/lpQ_hS7Y_po
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Algebraic Sum of Resolved Parts

https://youtu.be/UKppWcvWttM
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Magnitude and   Direction of Resultant of n Forces

https://youtu.be/y7SlEw-vlw0
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Examples Resolved parts

https://youtu.be/_ArpIi4pA-s
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Examples on Resolved Parts

https://youtu.be/3MNKr208Ofg
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Examples on Resolved Parts

https://youtu.be/3Jirj-nQU5c
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Examples on Resolved Parts

https://youtu.be/86I76IqigGk 
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Resultant  of Parallel Forces

https://youtu.be/tXGfOJAQJXo
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Resultant  of Parallel Forces

https://youtu.be/1Mpca3vVQpI
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Algebraic Sum of Resolved Part

https://youtu.be/V_0Gvv2Tndk
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  I

Forces Acting
on a Particle

Examples on Resultant of Parallel Forces

https://youtu.be/w2EfOWNsZFQ
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  II

Equilibrium of
Forces Acting
on a Particle

Equilibrium of Forces

https://www.youtube.com/playlist?
list=PL7TANb4Sj71oloNC
-jrURnjWp1Z6nix6i
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  II

Equilibrium of
Forces Acting
on a Particle

Triangle Law of Forces

https://youtu.be/4xY-jqMQmsQ
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  II

Equilibrium of
Forces Acting
on a Particle

Converse of Triangle Law of Forces

https://youtu.be/Xax0MALbpdo
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  II

Equilibrium of
Forces Acting
on a Particle

Polygon of a Forces

https://youtu.be/cNmgdyPFfNw
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  II

Equilibrium of
Forces Acting
on a Particle

Lami's Theorem

https://youtu.be/_vljRRO6NlE
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  II

Equilibrium of
Forces Acting
on a Particle

Condition of Equilibrium

https://youtu.be/H52YKzDJC78
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  II

Equilibrium of
Forces Acting
on a Particle

Examples on Equilibrium of Forces

https://youtu.be/pms7fUCzjmY
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  II

Equilibrium of
Forces Acting
on a Particle

Examples on Equilibrium of forces

https://youtu.be/slpGWUl8GxE
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  III

Forces Acting
on a Rigid
Body

Forces Acting on a Rigid Body

https://www.youtube.com/playlist?
list=PL7TANb4Sj71qEOvvps0Ph-
gaFdQJ-xSgW

B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  III

Forces Acting 
on a Rigid 
Body

Forces Acting on a Rigid Body

https://youtu.be/qsun3q6hk7s
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  III

Forces Acting 
on a Rigid 
Body

The Sum of Vector Moments

https://youtu.be/wfa6PHzcAhY
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  III

Forces Acting 
on a Rigid 
Body

Examples on Forces Acting on Rigid Body

https://youtu.be/foZMYZ0MsYQ
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  III

Forces Acting 
on a Rigid 
Body

Examples on Vector Moment

https://youtu.be/_PizVQo8qFM
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  III

Forces Acting 
on a Rigid 
Body

Vector Moments of Parallel Forces

https://youtu.be/4WN2UySXajY
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  III

Forces Acting 
on a Rigid 
Body

Couples

https://youtu.be/iq3XO_0Zlvs
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  III

Forces Acting 
on a Rigid 
Body

Moment of the Couple

https://youtu.be/fuJq3rT_-_g
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  III

Forces Acting 
on a Rigid 
Body

Two Couples acting on a Rigid body

https://youtu.be/rKf6h96e2YQ
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  III

Forces Acting 
on a Rigid 
Body

Vector Moment of the Resultant Couples

https://youtu.be/hQ-hg5bxNwA
B.Sc.  Mathematics III V

XIV(B)-
Mechanics-I

  III

Forces Acting 
on a Rigid 
Body

Vector Moment of the Resultant Couples

https://youtu.be/PVyxAA3MZCc
B.Sc.  Mathematics III VI

P-XVII (B)
Mechanics-II

  I

Dynamics of a Particle

Dynamics of a Particle

https://www.youtube.com/playlist?
list=PL7TANb4Sj71qZkICGBlb
zrEcq9pXkxZH4


 

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