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21 KiB
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MATH-6620: Perturbation Methods
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<meta property="og:title" content="MATH-6620: Perturbation Methods">
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<meta property="og:description" content="This course is devoted to advanced methods rather than theory. Content includes such topics as matched asymptotic expansions, multiple scales, WKB, and homogenization. Applications are made to ODEs, PDEs, difference equations, and integral equations. The methods are illustrated using currently interesting scientific and engineering problems that involve such phenomena as boundary or shock layers, nonlinear wave propagation, bifurcation and stability, and resonance.">
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<h1 id="name">
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Perturbation Methods
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<h2 id="code">
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MATH-6620
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</h2>
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<p>
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This course is devoted to advanced methods rather than theory. Content includes such topics as matched asymptotic expansions, multiple scales, WKB, and homogenization. Applications are made to ODEs, PDEs, difference equations, and integral equations. The methods are illustrated using currently interesting scientific and engineering problems that involve such phenomena as boundary or shock layers, nonlinear wave propagation, bifurcation and stability, and resonance.
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4 credits
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Prereqs:
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<div id="prereq-classes" class="rel-info-courses">
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<a class="course-pill" href="MATH-2400">MATH-2400 Intro Diff Equations</a>
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<div class="pr-and">and</div>
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<a class="course-pill" href="MATH-4600">MATH-4600 Advanced Calculus</a>
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Detailed View
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<th class="spring season-label">Spring</th>
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<th class="summer season-label" colspan="2">Summer</th>
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<th class="fall season-label">Fall</th>
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<th colspan="2"></th>
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<th class="summer2 midsum-label">(Session 1)</th>
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<th class="summer3 midsum-label">(Session 2)</th>
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<th></th>
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</thead>
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<tbody>
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<tr>
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<th class="year">2024</th>
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<td class="term spring offered">
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<div class="view-container detail-view-container">
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<span class="term-course-info">
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<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=202401&subj_in=MATH&crse_in=6620&schd_in=">Perturbation Methods (4c)</a>
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</span>
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<ul class="prof-list">
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<li>Mark H Holmes</li>
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</ul>
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<span class="course-capacity">
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Seats Taken: 15/25
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</span>
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</div>
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</td>
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<td colspan="2" class="term summer not-offered">
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</td>
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<td class="term fall not-offered">
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</td>
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</tr>
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<tr>
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<th class="year">2023</th>
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<td class="term spring not-offered">
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</td>
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<td colspan="2" class="term summer not-offered">
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</td>
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<td class="term fall not-offered">
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</td>
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</tr>
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<tr>
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<th class="year">2022</th>
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<td class="term spring offered">
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<div class="view-container detail-view-container">
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<span class="term-course-info">
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<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=202201&subj_in=MATH&crse_in=6620&schd_in=">Perturbation Methods (4c)</a>
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</span>
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<ul class="prof-list">
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||
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|
<li>Ashwani Kumar Kapila</li>
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||
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</ul>
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||
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<span class="course-capacity">
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Seats Taken: 6/20
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</span>
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||
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</div>
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</td>
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<td colspan="2" class="term summer not-offered">
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</td>
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<td class="term fall not-offered">
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</td>
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</tr>
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<tr>
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<th class="year">2021</th>
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<td class="term spring not-offered">
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</td>
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<td colspan="2" class="term summer not-offered">
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</td>
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<td class="term fall not-offered">
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</td>
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</tr>
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<tr>
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<th class="year">2020</th>
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||
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<td class="term spring offered">
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||
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<div class="view-container detail-view-container">
|
||
|
|
<span class="term-course-info">
|
||
|
|
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=202001&subj_in=MATH&crse_in=6620&schd_in=">Perturbation Methods (4c)</a>
|
||
|
|
</span>
|
||
|
|
<ul class="prof-list">
|
||
|
|
<li>Ashwani Kumar Kapila</li>
|
||
|
|
</ul>
|
||
|
|
<span class="course-capacity">
|
||
|
|
Seats Taken: 19/40
|
||
|
|
</span>
|
||
|
|
</div>
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
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||
|
|
</td>
|
||
|
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<td class="term fall not-offered">
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||
|
|
</td>
|
||
|
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</tr>
|
||
|
|
<tr>
|
||
|
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<th class="year">2019</th>
|
||
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<td class="term spring not-offered">
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||
|
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</td>
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||
|
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<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
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</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2018</th>
|
||
|
|
<td class="term spring offered">
|
||
|
|
<div class="view-container detail-view-container">
|
||
|
|
<span class="term-course-info">
|
||
|
|
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=201801&subj_in=MATH&crse_in=6620&schd_in=">Perturbation Methods (4c)</a>
|
||
|
|
</span>
|
||
|
|
<ul class="prof-list">
|
||
|
|
<li>Ashwani Kumar Kapila</li>
|
||
|
|
</ul>
|
||
|
|
<span class="course-capacity">
|
||
|
|
Seats Taken: 10/30
|
||
|
|
</span>
|
||
|
|
</div>
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
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<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2017</th>
|
||
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<td class="term spring not-offered">
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||
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</td>
|
||
|
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<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
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||
|
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</td>
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||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2016</th>
|
||
|
|
<td class="term spring offered">
|
||
|
|
<div class="view-container detail-view-container">
|
||
|
|
<span class="term-course-info">
|
||
|
|
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=201601&subj_in=MATH&crse_in=6620&schd_in=">Perturbation Methods (4c)</a>
|
||
|
|
</span>
|
||
|
|
<ul class="prof-list">
|
||
|
|
<li>Ashwani Kumar Kapila</li>
|
||
|
|
</ul>
|
||
|
|
<span class="course-capacity">
|
||
|
|
Seats Taken: 22/30
|
||
|
|
</span>
|
||
|
|
</div>
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2015</th>
|
||
|
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<td class="term spring not-offered">
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2014</th>
|
||
|
|
<td class="term spring offered">
|
||
|
|
<div class="view-container detail-view-container">
|
||
|
|
<span class="term-course-info">
|
||
|
|
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=201401&subj_in=MATH&crse_in=6620&schd_in=">Perturbation Methods (4c)</a>
|
||
|
|
</span>
|
||
|
|
<ul class="prof-list">
|
||
|
|
<li>Ashwani Kumar Kapila</li>
|
||
|
|
</ul>
|
||
|
|
<span class="course-capacity">
|
||
|
|
Seats Taken: 15/30
|
||
|
|
</span>
|
||
|
|
</div>
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2013</th>
|
||
|
|
<td class="term spring not-offered">
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2012</th>
|
||
|
|
<td class="term spring offered">
|
||
|
|
<div class="view-container detail-view-container">
|
||
|
|
<span class="term-course-info">
|
||
|
|
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=201201&subj_in=MATH&crse_in=6620&schd_in=">Perturbation Methods (4c)</a>
|
||
|
|
</span>
|
||
|
|
<ul class="prof-list">
|
||
|
|
<li>Mark H Holmes</li>
|
||
|
|
</ul>
|
||
|
|
<span class="course-capacity">
|
||
|
|
Seats Taken: 30/30
|
||
|
|
</span>
|
||
|
|
</div>
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2011</th>
|
||
|
|
<td class="term spring not-offered">
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2010</th>
|
||
|
|
<td class="term spring offered">
|
||
|
|
<div class="view-container detail-view-container">
|
||
|
|
<span class="term-course-info">
|
||
|
|
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=201001&subj_in=MATH&crse_in=6620&schd_in=">Perturbation Methods (4c)</a>
|
||
|
|
</span>
|
||
|
|
<ul class="prof-list">
|
||
|
|
<li>Peter R Kramer</li>
|
||
|
|
</ul>
|
||
|
|
<span class="course-capacity">
|
||
|
|
Seats Taken: 20/30
|
||
|
|
</span>
|
||
|
|
</div>
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2009</th>
|
||
|
|
<td class="term spring not-offered">
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2008</th>
|
||
|
|
<td class="term spring offered">
|
||
|
|
<div class="view-container detail-view-container">
|
||
|
|
<span class="term-course-info">
|
||
|
|
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=200801&subj_in=MATH&crse_in=6620&schd_in=">Perturbation Methods (4c)</a>
|
||
|
|
</span>
|
||
|
|
<ul class="prof-list">
|
||
|
|
<li>Michael R. Foster</li>
|
||
|
|
</ul>
|
||
|
|
<span class="course-capacity">
|
||
|
|
Seats Taken: 15/30
|
||
|
|
</span>
|
||
|
|
</div>
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2007</th>
|
||
|
|
<td class="term spring not-offered">
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2006</th>
|
||
|
|
<td class="term spring offered">
|
||
|
|
<div class="view-container detail-view-container">
|
||
|
|
<span class="term-course-info">
|
||
|
|
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=200601&subj_in=MATH&crse_in=6620&schd_in=">Perturbation Methods (4c)</a>
|
||
|
|
</span>
|
||
|
|
<ul class="prof-list">
|
||
|
|
<li>Christopher Wahle</li>
|
||
|
|
</ul>
|
||
|
|
<span class="course-capacity">
|
||
|
|
Seats Taken: 18/30
|
||
|
|
</span>
|
||
|
|
</div>
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2005</th>
|
||
|
|
<td class="term spring not-offered">
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2004</th>
|
||
|
|
<td class="term spring offered">
|
||
|
|
<div class="view-container detail-view-container">
|
||
|
|
<span class="term-course-info">
|
||
|
|
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=200401&subj_in=MATH&crse_in=6620&schd_in=">Perturbation Methods (4c)</a>
|
||
|
|
</span>
|
||
|
|
<ul class="prof-list">
|
||
|
|
<li>Christopher Wahle</li>
|
||
|
|
</ul>
|
||
|
|
<span class="course-capacity">
|
||
|
|
Seats Taken: 11/30
|
||
|
|
</span>
|
||
|
|
</div>
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2003</th>
|
||
|
|
<td class="term spring not-offered">
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2002</th>
|
||
|
|
<td class="term spring offered">
|
||
|
|
<div class="view-container detail-view-container">
|
||
|
|
<span class="term-course-info">
|
||
|
|
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=200201&subj_in=MATH&crse_in=6620&schd_in=">Perturbation Methods (4c)</a>
|
||
|
|
</span>
|
||
|
|
<ul class="prof-list">
|
||
|
|
<li>Ashwani Kumar Kapila</li>
|
||
|
|
</ul>
|
||
|
|
<span class="course-capacity">
|
||
|
|
Seats Taken: 7/30
|
||
|
|
</span>
|
||
|
|
</div>
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2001</th>
|
||
|
|
<td class="term spring not-offered">
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">2000</th>
|
||
|
|
<td class="term spring offered">
|
||
|
|
<div class="view-container detail-view-container">
|
||
|
|
<span class="term-course-info">
|
||
|
|
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=200001&subj_in=MATH&crse_in=6620&schd_in=">Perturbation Methods (4c)</a>
|
||
|
|
</span>
|
||
|
|
<ul class="prof-list">
|
||
|
|
<li>Ashwani Kumar Kapila</li>
|
||
|
|
</ul>
|
||
|
|
<span class="course-capacity">
|
||
|
|
Seats Taken: 8/30
|
||
|
|
</span>
|
||
|
|
</div>
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">1999</th>
|
||
|
|
<td class="term spring not-offered">
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
<tr>
|
||
|
|
<th class="year">1998</th>
|
||
|
|
<td class="term spring unscheduled">
|
||
|
|
</td>
|
||
|
|
<td colspan="2" class="term summer not-offered">
|
||
|
|
</td>
|
||
|
|
<td class="term fall not-offered">
|
||
|
|
</td>
|
||
|
|
</tr>
|
||
|
|
</tbody>
|
||
|
|
</table>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
</body>
|
||
|
|
</html>
|