T. Y. B. Sc.

Partial Differential Equations

Course Code: USMT5A4/UAMT5A4
Credits: 2.5 || Lecture/week: 3 Probable/Actual Hrs Available: 45

LMS of PDE Course

NAME OF UNIT

Titles / Details

Video Lectures

Lecture Notes

Assignments / Practicals

Ratings

First Order Partial Difffferential Equations. 

Curves and Surfaces, Genesis of fifirst order PDE, Classifification of fifirst order PDE, Classifification
of integrals, The Cauchy problem, Linear Equation of fifirst order, Lagrange’s equation, Pfaffiffiffian
difffferential equations.

Lecture 1

Unit I

Tutorial 1

Arvind Jadhav Presentation 

Defifinition, Necessary and suffiffifficient condition for integrability, Charpit’s method, Some stan
dard types, Jacobi’s method, The Cauchy problem.

Lecture 2

Unit II

Tutorial 1 Solution

Tanmay Gavali Presentation

Lecture 3

Unit III

Practical 3

Lecture 4

Lecture 4

MCQ's


Lecture 5

Lecture 5

Lecture 6

Lecture 6

Lecture 7

Lecture 7

Lecture 8

Lecture 8

Lecture 9

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Lecture 10

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Lecture 11

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Lecture 12

Lecture 12

Lecture 13

Lecture 13

Lecture 14

Lecture 14

Lecture 15

Lecture 15

Topology of Metric Spaces

Course Code: USMT503

Credits: 2.5 || Lecture/week: 3
Probable/Actual Hrs Available: 45

Unit I : Metric Spaces

NAME OF UNIT

Titles / Details

Video Lectures

Lecture Notes

Assignments / Practicals

Ratings

Metric spaces

Definition, examples of metric spaces

,  ,Euclidean space  with its Euclidean

Lecture 1

Lecture 1

Practical 1

Metric spaces

the spaces l1 and l2 of sequences and the space [a,b]

Lecture 2

Lecture 2

Practical 2

Metric spaces

the space [a,b], of real valued continuous functions on [a,b]. Discrete metric space.

Lecture 3

Lecture 3

Practical 3

Metric spaces

Distance metric induced by the norm, translation invariance of the metric induced by the norm

Lecture 4

Lecture 4

Unit Test I

Metric spaces

Metric subspaces, Product of two metric spaces.

Lecture 5

Lecture 5

Metric spaces

Metric subspaces, Product of two metric spaces.

Lecture 6

Lecture 6

Metric spaces

sup and sum metric,  (complex numbers)

Lecture 7

Lecture 7

Metric spaces

Open balls and open set in a metric space

Lecture 8

Lecture 8

Metric spaces

Open balls and open set in a metric space

Lecture 9

Lecture 9

Metric spaces

examples of open sets in various metric spaces

Lecture 10

Lecture 10

Metric spaces

Hausdorff property.  Equivalent metrics.

Lecture 11

Lecture 11

Metric spaces

Distance of a point from a set, between sets

Lecture 12

Lecture 12

Metric spaces

Interior of a set. Properties of open sets. Structure of an open set in IR.

Lecture 13

Lecture 13

Metric spaces

Hausdorff property.  Equivalent metrics.

Lecture 14

Lecture 14

Metric spaces

diameter of a set in a metric space and bounded sets.

Lecture 15

Lecture 15

Metric spaces

Hausdorff property. 

Lecture  16

Lecture 16

Unit II : Sequences & Complete Metric Space

NAME OF UNIT

Titles / Details

Video Lectures

Lecture Notes

Assignments / Practicals

Ratings

Unit II : Sequences & Complete Metric Space

Closed Ball and Solved  Examples


Lecture 1

Lecture 1

Practical 1

Unit II : Sequences & Complete Metric Space

Closed Sets and Solved Example

Lecture 2

Lecture 2

Practical 2

Unit II : Sequences & Complete Metric Space

Properties of Closed Sets

Lecture 3

Lecture 3

Practical 3

Unit II : Sequences & Complete Metric Space

Limit Points and Derived Set. Examples

Lecture 4

Lecture 4

MCQ's

Lecture 5

Lecture 5

Lecture 6

Lecture 6

Lecture 7

Lecture 7

Lecture 8

Lecture 8

Lecture 9

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Lecture 10

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Lecture 11

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Lecture 12

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Lecture 13

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Lecture 14

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Lecture 15

Lecture 15