{"id":726,"date":"2021-08-22T12:27:47","date_gmt":"2021-08-22T12:27:47","guid":{"rendered":"https:\/\/santoshdhamone.com\/?page_id=726"},"modified":"2024-01-07T06:18:12","modified_gmt":"2024-01-07T06:18:12","slug":"s-y-b-sc-2","status":"publish","type":"page","link":"https:\/\/santoshdhamone.com\/index.php\/s-y-b-sc-2\/","title":{"rendered":"T. Y. B. Sc."},"content":{"rendered":"\t\t
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T. Y. B. Sc.<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Partial Differential Equations<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Course Code: USMT5A4\/UAMT5A4
\nCredits: 2.5 || Lecture\/week: 3\n\nProbable\/Actual Hrs Available: 45<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tLMS of PDE Course<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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NAME OF UNIT<\/p><\/div><\/div><\/td>

Titles \/ Details<\/p><\/div><\/div><\/td>

Video Lectures<\/p><\/div><\/div><\/td>

Lecture Notes<\/p><\/div><\/div><\/td>

Assignments \/ Practicals<\/p><\/div><\/div><\/td>

Ratings<\/p><\/div><\/div><\/td><\/tr>

First Order Partial Difffferential Equations. <\/strong><\/p>

<\/p><\/div><\/div><\/td>

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

<\/p><\/div><\/div><\/td>

Lecture 1<\/p>


<\/div><\/div> <\/a> <\/div><\/div><\/td>

Unit I<\/p>


<\/div><\/div> <\/a> <\/div><\/div><\/td>

Tutorial 1<\/p>


<\/div><\/div> <\/a> <\/div><\/div><\/td>

Arvind Jadhav Presentation <\/p>


<\/div><\/div> <\/a> <\/div><\/div><\/td><\/tr>

<\/p><\/div><\/div><\/td>

Defifinition, Necessary and suffiffifficient condition for integrability, Charpit’s method, Some stan<\/strong>
dard types, Jacobi’s method, The Cauchy problem.<\/strong><\/p><\/div><\/div><\/td>

Lecture 2<\/p>


<\/div><\/div> <\/a> <\/div><\/div><\/td>

Unit II<\/strong><\/p>


<\/div><\/div> <\/a> <\/div><\/div><\/td>

Tutorial 1 Solution<\/p>


<\/div><\/div> <\/a> <\/div><\/div><\/td>

Tanmay Gavali Presentation<\/p><\/div> <\/a> <\/div><\/div><\/td><\/tr>

<\/p><\/div><\/div><\/td>

<\/p><\/div><\/div><\/td>

Lecture 3
<\/p>


<\/div><\/div> <\/a> <\/div><\/div><\/td>

Unit III<\/span>
<\/p>


<\/div><\/div> <\/a> <\/div><\/div><\/td>

Practical 3
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<\/div><\/div> <\/a> <\/div><\/div><\/td>
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<\/p><\/div><\/div><\/td>

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Lecture 4
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<\/div><\/div> <\/a> <\/div><\/div><\/td>

Lecture 4<\/span>
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MCQ's<\/p>


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<\/p><\/div><\/div><\/td>

Lecture 5
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<\/div><\/div> <\/a> <\/div><\/div><\/td>

Lecture 5<\/span>
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<\/p><\/div><\/div><\/td>

<\/p><\/div><\/div><\/td>

Lecture 6
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<\/div><\/div> <\/a> <\/div><\/div><\/td>

Lecture 6<\/span>
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<\/div><\/div> <\/a> <\/div><\/div><\/td>
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<\/p><\/div><\/div><\/td>

<\/p><\/div><\/div><\/td>

Lecture 7
<\/p>


<\/div><\/div> <\/a> <\/div><\/div><\/td>

Lecture 7<\/span>
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<\/div><\/div> <\/a> <\/div><\/div><\/td>
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<\/p><\/div><\/div><\/td>

Lecture 8
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<\/div><\/div> <\/a> <\/div><\/div><\/td>

Lecture 8<\/span>
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<\/p><\/div><\/div><\/td>

<\/p><\/div><\/div><\/td>

Lecture 9
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<\/div><\/div> <\/a> <\/div><\/div><\/td>

Lecture 9<\/span>
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<\/div><\/div> <\/a> <\/div><\/div><\/td>
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<\/p><\/div><\/div><\/td>

Lecture 10
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<\/div><\/div> <\/a> <\/div><\/div><\/td>

Lecture 10<\/span>
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<\/p><\/div><\/div><\/td>

Lecture 11<\/span>
<\/p>


<\/div><\/div> <\/a> <\/div><\/div><\/td>

Lecture 11<\/span>
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<\/p><\/div><\/div><\/td>

Lecture 12<\/span>
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<\/div><\/div> <\/a> <\/div><\/div><\/td>

Lecture 12<\/span>
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<\/p><\/div><\/div><\/td>

Lecture 13<\/span>
<\/p>


<\/div><\/div> <\/a> <\/div><\/div><\/td>

Lecture 13<\/span><\/p>


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<\/p><\/div><\/div><\/td>

Lecture 14<\/span>
<\/p>


<\/div><\/div> <\/a> <\/div><\/div><\/td>

Lecture 14<\/span>
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Lecture 15<\/span>
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<\/div><\/div> <\/a> <\/div><\/div><\/td>

Lecture 15<\/span>
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    Topology of Metric Spaces<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    Course Code: USMT503<\/p>

    Credits: 2.5 || Lecture\/week: 3
    Probable\/Actual Hrs Available: 45<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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    Unit I : Metric Spaces<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    NAME OF UNIT<\/p><\/div><\/div><\/td>

    Titles \/ Details<\/p><\/div><\/div><\/td>

    Video Lectures<\/p><\/div><\/div><\/td>

    Lecture Notes<\/p><\/div><\/div><\/td>

    Assignments \/ Practicals<\/p><\/div><\/div><\/td>

    Ratings<\/p><\/div><\/div><\/td><\/tr>

    Metric spaces<\/strong><\/p><\/div><\/div><\/td>

    Definition, examples of metric spaces<\/p>

    ,  ,Euclidean space  with its Euclidean<\/p><\/div><\/div><\/td>

    Lecture 1<\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 1<\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Practical 1<\/p>


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    Metric<\/strong> spaces<\/p><\/div><\/div><\/td>

    the spaces l1 and l2 of sequences and the space [a,b]<\/p><\/div><\/div><\/td>

    Lecture 2<\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 2<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Practical 2
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    Metric<\/strong> spaces<\/p><\/div><\/div><\/td>

    the space [a,b], of real valued continuous functions on [a,b]. Discrete metric space.<\/p><\/div><\/div><\/td>

    Lecture 3
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 3<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Practical 3
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    Metric<\/strong> spaces<\/p><\/div><\/div><\/td>

    Distance metric induced by the norm, translation invariance of the metric induced by the norm<\/p><\/div><\/div><\/td>

    Lecture 4
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 4<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Unit Test I<\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    Metric<\/strong> spaces<\/p><\/div><\/div><\/td>

    Metric subspaces, Product of two metric spaces.<\/p><\/div><\/div><\/td>

    Lecture 5
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 5<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    Metric spaces<\/strong><\/p><\/div><\/div><\/td>

    Metric subspaces, Product of two metric spaces.<\/p><\/div><\/div><\/td>

    Lecture 6
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 6<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    Metric spaces<\/strong><\/p><\/div><\/div><\/td>

    sup and sum metric,  (complex numbers)<\/p><\/div><\/div><\/td>

    Lecture 7
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 7<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div>
      • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
      • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
      • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
      • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
      • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
        0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    Metric spaces<\/strong><\/p><\/div><\/div><\/td>

    Open balls and open set in a metric space<\/p><\/div><\/div><\/td>

    Lecture 8
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 8<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    Metric spaces<\/p><\/div><\/div><\/td>

    Open balls and open set in a metric space<\/p><\/div><\/div><\/td>

    Lecture 9
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 9<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    Metric spaces<\/strong><\/p><\/div><\/div><\/td>

    examples of open sets in various metric spaces<\/p><\/div><\/div><\/td>

    Lecture 10
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 10<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    Metric spaces<\/strong><\/p><\/div><\/div><\/td>

    Hausdorff property.  Equivalent metrics.<\/p><\/div><\/div><\/td>

    Lecture 11<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 11<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    Metric<\/strong> spaces<\/p><\/div><\/div><\/td>

    Distance of a point from a set, between sets<\/p><\/div><\/div><\/td>

    Lecture 12<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 12<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    Metric spaces<\/strong><\/p><\/div><\/div><\/td>

    Interior of a set. Properties of open sets. Structure of an open set in IR.<\/p><\/div><\/div><\/td>

    Lecture 13<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 13<\/span><\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    Metric<\/strong> spaces<\/p><\/div><\/div><\/td>

    Hausdorff property.  Equivalent metrics.<\/p><\/div><\/div><\/td>

    Lecture 14<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 14<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    Metric<\/strong> spaces<\/p><\/div><\/div><\/td>

    diameter of a set in a metric space and bounded sets.<\/p><\/div><\/div><\/td>

    Lecture 15<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    Lecture 15<\/span>
    <\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>
    		<\/td>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li>
    • <\/span><\/polygon><\/svg><\/span><\/path><\/svg><\/span><\/path><\/svg><\/span><\/span><\/li><\/ul>
      0\/5<\/div> <\/div> <\/div><\/div><\/td><\/tr>

    <\/p><\/div><\/div>

    Metric spaces<\/p><\/div><\/div><\/td>

    <\/p><\/div><\/div>

    Hausdorff property. <\/p><\/div><\/div><\/td>

    <\/p><\/div><\/div>

    Lecture  16<\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    <\/p><\/div><\/div>

    Lecture 16<\/p>


    <\/div><\/div> <\/a> <\/div><\/div><\/td>

    <\/p><\/div><\/div><\/td>