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MATH-6840: Numerical Solution of Partial Differential Equations
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<meta property="og:description" content="Numerical methods and analysis for linear and nonlinear PDEs with applications from heat conduction, wave propagation, solid and fluid mechanics, and other areas. Basic concepts of stability and convergence (such as Lax equivalence theorem, CFL condition, GKS stability theory, energy methods). Methods for parabolic problems (finite differences, method of lines, ADI, operator splitting), methods for hyperbolic problems (vector systems and characteristics, dissipation and dispersion, shock capturing and tracking schemes), methods for elliptic problems (finite difference and finite volume methods).">
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<h1 id="name">
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Numerical Solution of Partial Differential Equations
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</h1>
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<h2 id="code">
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MATH-6840
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</h2>
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<p>
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Numerical methods and analysis for linear and nonlinear PDEs with applications from heat conduction, wave propagation, solid and fluid mechanics, and other areas. Basic concepts of stability and convergence (such as Lax equivalence theorem, CFL condition, GKS stability theory, energy methods). Methods for parabolic problems (finite differences, method of lines, ADI, operator splitting), methods for hyperbolic problems (vector systems and characteristics, dissipation and dispersion, shock capturing and tracking schemes), methods for elliptic problems (finite difference and finite volume methods).
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4 credits
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Prereqs:
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one of:
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<a class="course-pill" href="MATH-4800">MATH-4800 Numerical Computing</a>
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<a class="course-pill" href="CSCI-4800">CSCI-4800 Numerical Computing</a>
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<th></th>
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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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</tr>
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<tr>
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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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</tr>
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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=6840&schd_in=">Numerical Solutions Of P (4c)</a>
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</span>
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<ul class="prof-list">
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<li>Jeffrey William Banks</li>
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</ul>
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<span class="course-capacity">
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Seats Taken: 0/25
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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 unscheduled">
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</td>
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<td class="term fall unscheduled">
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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 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=202301&subj_in=MATH&crse_in=6840&schd_in=">Numerical Solutions Of P (4c)</a>
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</span>
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<ul class="prof-list">
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<li>William Douglas Henshaw</li>
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</ul>
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<span class="course-capacity">
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Seats Taken: 10/30
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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">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=6840&schd_in=">Numerical Solutions Of P (4c)</a>
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</span>
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<ul class="prof-list">
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<li>Jeffrey William Banks</li>
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</ul>
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<span class="course-capacity">
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Seats Taken: 14/30
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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">2021</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=202101&subj_in=MATH&crse_in=6840&schd_in=">Numerical Solutions Of P (4c)</a>
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</span>
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<ul class="prof-list">
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<li>Jeffrey William Banks</li>
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</ul>
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<span class="course-capacity">
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Seats Taken: 9/40
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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">2020</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=202001&subj_in=MATH&crse_in=6840&schd_in=">Numerical Solutions Of P (4c)</a>
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</span>
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<ul class="prof-list">
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<li>William Douglas Henshaw</li>
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</ul>
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<span class="course-capacity">
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Seats Taken: 17/40
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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">2019</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=201901&subj_in=MATH&crse_in=6840&schd_in=">Numerical Solutions Of P (4c)</a>
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</span>
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<ul class="prof-list">
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<li>William Douglas Henshaw</li>
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</ul>
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<span class="course-capacity">
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Seats Taken: 21/40
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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">2018</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">
|
|
<a href="https://sis.rpi.edu/rss/bwckctlg.p_disp_listcrse?term_in=201801&subj_in=MATH&crse_in=6840&schd_in=">Numerical Solutions Of P (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Jeffrey William Banks</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 25/40
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</span>
|
|
</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>
|
|
<th class="year">2017</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>
|
|
<th class="year">2016</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>
|
|
<th class="year">2015</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>
|
|
<td class="term fall 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=201509&subj_in=MATH&crse_in=6840&schd_in=">Numerical Solutions Of P (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Jeffrey William Banks</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 27/30
|
|
</span>
|
|
</div>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<th class="year">2014</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>
|
|
</tr>
|
|
<tr>
|
|
<th class="year">2013</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">
|
|
</td>
|
|
<td class="term fall 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=201309&subj_in=MATH&crse_in=6840&schd_in=">Numerical Solutions Of P (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Donald W Schwendeman</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 25/30
|
|
</span>
|
|
</div>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<th class="year">2012</th>
|
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<td class="term spring not-offered">
|
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</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">2011</th>
|
|
<td class="term spring not-offered">
|
|
</td>
|
|
<td colspan="2" class="term summer not-offered">
|
|
</td>
|
|
<td class="term fall 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=201109&subj_in=MATH&crse_in=6840&schd_in=">Numerical Solutions Of P (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Moayyed A Hussain</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 5/30
|
|
</span>
|
|
</div>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<th class="year">2010</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">2009</th>
|
|
<td class="term spring not-offered">
|
|
</td>
|
|
<td colspan="2" class="term summer not-offered">
|
|
</td>
|
|
<td class="term fall 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=200909&subj_in=MATH&crse_in=6840&schd_in=">Numerical Solutions Of P (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Donald W Schwendeman</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 21/38
|
|
</span>
|
|
</div>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<th class="year">2008</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">2007</th>
|
|
<td class="term spring not-offered">
|
|
</td>
|
|
<td colspan="2" class="term summer not-offered">
|
|
</td>
|
|
<td class="term fall 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=200709&subj_in=MATH&crse_in=6840&schd_in=">Numerical Solutions Of P (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Donald W Schwendeman</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 8/30
|
|
</span>
|
|
</div>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<th class="year">2006</th>
|
|
<td class="term spring not-offered">
|
|
</td>
|
|
<td colspan="2" class="term summer not-offered">
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|
</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 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=200509&subj_in=MATH&crse_in=6840&schd_in=">Numerical Solutions Of Part. (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Donald W Schwendeman</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 11/30
|
|
</span>
|
|
</div>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<th class="year">2004</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">2003</th>
|
|
<td class="term spring not-offered">
|
|
</td>
|
|
<td colspan="2" class="term summer not-offered">
|
|
</td>
|
|
<td class="term fall 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=200309&subj_in=MATH&crse_in=6840&schd_in=">Numerical Solutions Of P (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Donald W Schwendeman</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 18/40
|
|
</span>
|
|
</div>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<th class="year">2002</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">2001</th>
|
|
<td class="term spring not-offered">
|
|
</td>
|
|
<td colspan="2" class="term summer not-offered">
|
|
</td>
|
|
<td class="term fall 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=200109&subj_in=MATH&crse_in=6840&schd_in=">Numerical Solutions Of P (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Donald W Schwendeman</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 6/30
|
|
</span>
|
|
</div>
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<th class="year">2000</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">1999</th>
|
|
<td class="term spring not-offered">
|
|
</td>
|
|
<td colspan="2" class="term summer not-offered">
|
|
</td>
|
|
<td class="term fall 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=199909&subj_in=MATH&crse_in=6840&schd_in=">Num Solutions Of Pdes (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Joseph E Flaherty</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 18/30
|
|
</span>
|
|
</div>
|
|
</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>
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