18.100B Analysis I, Fall 2002
Two options offered, both covering fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Both options show the utility of abstract concepts and teach...
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| Format: | Learning Object |
| Language: | en-US |
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2002
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| Online Access: | http://hdl.handle.net/1721.1/37329 |
| _version_ | 1826203059261276160 |
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| author | Melrose, Richard B. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Melrose, Richard B. |
| author_sort | Melrose, Richard B. |
| collection | MIT |
| description | Two options offered, both covering fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Both options show the utility of abstract concepts and teach understanding and construction of proofs. <I>Option A</I> chooses less abstract definitions and proofs, and gives applications where possible. <I>Option B</I> is more demanding and for students with more mathematical maturity. Places greater emphasis on point-set topology. |
| first_indexed | 2024-09-23T12:31:01Z |
| format | Learning Object |
| id | mit-1721.1/37329 |
| institution | Massachusetts Institute of Technology |
| language | en-US |
| last_indexed | 2025-03-10T10:35:54Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | mit-1721.1/373292025-02-24T15:02:12Z 18.100B Analysis I, Fall 2002 Analysis I Melrose, Richard B. Massachusetts Institute of Technology. Department of Mathematics mathematical analysis convergence of sequences convergence of series continuity differentiability Reimann integral uniformity interchange of limit operations utility of abstract concepts construction of proofs point-set topology n-space sequences of functions series of functions applications real variable metric space sets theorems differentiate differentiable converge uniform 18.100B 18.100 Two options offered, both covering fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Both options show the utility of abstract concepts and teach understanding and construction of proofs. <I>Option A</I> chooses less abstract definitions and proofs, and gives applications where possible. <I>Option B</I> is more demanding and for students with more mathematical maturity. Places greater emphasis on point-set topology. 2002-12 Learning Object 18.100B-Fall2002 local: 18.100B local: IMSCP-MD5-9908abcd0c08bccfaefff61dbbec8d1a http://hdl.handle.net/1721.1/37329 en-US Usage Restrictions: This site (c) Massachusetts Institute of Technology 2003. Content within individual courses is (c) by the individual authors unless otherwise noted. The Massachusetts Institute of Technology is providing this Work (as defined below) under the terms of this Creative Commons public license ("CCPL" or "license"). The Work is protected by copyright and/or other applicable law. Any use of the work other than as authorized under this license is prohibited. By exercising any of the rights to the Work provided here, You (as defined below) accept and agree to be bound by the terms of this license. The Licensor, the Massachusetts Institute of Technology, grants You the rights contained here in consideration of Your acceptance of such terms and conditions. text/html Fall 2002 |
| spellingShingle | mathematical analysis convergence of sequences convergence of series continuity differentiability Reimann integral uniformity interchange of limit operations utility of abstract concepts construction of proofs point-set topology n-space sequences of functions series of functions applications real variable metric space sets theorems differentiate differentiable converge uniform 18.100B 18.100 Melrose, Richard B. 18.100B Analysis I, Fall 2002 |
| title | 18.100B Analysis I, Fall 2002 |
| title_full | 18.100B Analysis I, Fall 2002 |
| title_fullStr | 18.100B Analysis I, Fall 2002 |
| title_full_unstemmed | 18.100B Analysis I, Fall 2002 |
| title_short | 18.100B Analysis I, Fall 2002 |
| title_sort | 18 100b analysis i fall 2002 |
| topic | mathematical analysis convergence of sequences convergence of series continuity differentiability Reimann integral uniformity interchange of limit operations utility of abstract concepts construction of proofs point-set topology n-space sequences of functions series of functions applications real variable metric space sets theorems differentiate differentiable converge uniform 18.100B 18.100 |
| url | http://hdl.handle.net/1721.1/37329 |
| work_keys_str_mv | AT melroserichardb 18100banalysisifall2002 AT melroserichardb analysisi |