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MATH-6640: Complex Variables and Integral Transforms with Applications
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<meta property="og:title" content="MATH-6640: Complex Variables and Integral Transforms with Applications">
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<meta property="og:description" content="Review of basic complex variables theory; power series, analytic functions, singularities, and integration in the complex plane. Integral transforms (Laplace, Fourier, etc.) in the complex plane, with application to solution of PDEs and integral equations. Asymptotic expansions of integrals (Laplace method, methods of steepest descent and stationary phase), with emphasis on extraction of useful information from inversion integrals of transforms. Problems to be drawn from linear models in science and engineering.">
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<h1 id="name">
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Complex Variables and Integral Transforms with Applications
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MATH-6640
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</h2>
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<p>
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Review of basic complex variables theory; power series, analytic functions, singularities, and integration in the complex plane. Integral transforms (Laplace, Fourier, etc.) in the complex plane, with application to solution of PDEs and integral equations. Asymptotic expansions of integrals (Laplace method, methods of steepest descent and stationary phase), with emphasis on extraction of useful information from inversion integrals of transforms. Problems to be drawn from linear models in science and engineering.
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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 Introduction to Differential Equations</a>
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<div class="pr-and">and</div>
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<a class="course-pill" href="MATH-4300">MATH-4300 Introduction to Complex Variables: Theory and Applications</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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<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">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=6640&schd_in=">Complx Vari Integral Transform (4c)</a>
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</span>
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<ul class="prof-list">
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<li>Ashwani Kumar Kapila</li>
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</ul>
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<span class="course-capacity">
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Seats Taken: 5/25
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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">2022</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">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=6640&schd_in=">Complx Vari Integral Transform (4c)</a>
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</span>
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<ul class="prof-list">
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<li>Ashwani Kumar Kapila</li>
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</ul>
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<span class="course-capacity">
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Seats Taken: 16/30
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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">2020</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">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=6640&schd_in=">Complx Vari Integral Transform (4c)</a>
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</span>
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<ul class="prof-list">
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<li>Ashwani Kumar Kapila</li>
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</ul>
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<span class="course-capacity">
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Seats Taken: 11/25
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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">2018</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">2017</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=201701&subj_in=MATH&crse_in=6640&schd_in=">Complx Vari Integral Transform (4c)</a>
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</span>
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<ul class="prof-list">
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<li>Isom Herron</li>
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</ul>
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<span class="course-capacity">
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Seats Taken: 9/30
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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">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>
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<th class="year">2015</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=201501&subj_in=MATH&crse_in=6640&schd_in=">Complx Vari Integral Transform (4c)</a>
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</span>
|
|
<ul class="prof-list">
|
|
<li>Ashwani Kumar Kapila</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 16/30
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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>
|
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<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>
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</tr>
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<tr>
|
|
<th class="year">2013</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=201301&subj_in=MATH&crse_in=6640&schd_in=">Complx Vari Integral Transform (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Gregor Kovacic</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 26/30
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|
</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>
|
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<tr>
|
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<th class="year">2012</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>
|
|
<tr>
|
|
<th class="year">2011</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=201101&subj_in=MATH&crse_in=6640&schd_in=">Complx Vari Integral Transform (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Ashwani Kumar Kapila</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 20/30
|
|
</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>
|
|
</tr>
|
|
<tr>
|
|
<th class="year">2010</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>
|
|
<tr>
|
|
<th class="year">2009</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=200901&subj_in=MATH&crse_in=6640&schd_in=">Complx Vari Integral Transform (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Isom Herron</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 12/40
|
|
</span>
|
|
</div>
|
|
</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 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 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=200701&subj_in=MATH&crse_in=6640&schd_in=">Complx Vari Integral Transform (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Isom Herron</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">2006</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">2005</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=200501&subj_in=MATH&crse_in=6640&schd_in=">Complx Vari Integral Transform (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Ashwani Kumar Kapila</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 14/30
|
|
</span>
|
|
</div>
|
|
</td>
|
|
<td colspan="2" class="term summer not-offered">
|
|
</td>
|
|
<td class="term fall not-offered">
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<th class="year">2004</th>
|
|
<td class="term spring not-offered">
|
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</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">2003</th>
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|
<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=200301&subj_in=MATH&crse_in=6640&schd_in=">Complx Vari Integral Transform (4c)</a>
|
|
</span>
|
|
<ul class="prof-list">
|
|
<li>Isom Herron</li>
|
|
</ul>
|
|
<span class="course-capacity">
|
|
Seats Taken: 8/25
|
|
</span>
|
|
</div>
|
|
</td>
|
|
<td colspan="2" class="term summer not-offered">
|
|
</td>
|
|
<td class="term fall not-offered">
|
|
</td>
|
|
</tr>
|
|
<tr>
|
|
<th class="year">2002</th>
|
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<td class="term spring not-offered">
|
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</td>
|
|
<td colspan="2" class="term summer not-offered">
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|
</td>
|
|
<td class="term fall not-offered">
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|
</td>
|
|
</tr>
|
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<tr>
|
|
<th class="year">2001</th>
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<td class="term spring not-offered">
|
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</td>
|
|
<td colspan="2" class="term summer not-offered">
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|
</td>
|
|
<td class="term fall not-offered">
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|
</td>
|
|
</tr>
|
|
<tr>
|
|
<th class="year">2000</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">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>
|