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calculus on parameterized curves, derivatives of functions of several variables, multiple integrals, vector calculus.<br/> </p> <button class="notinpdf cb-extras-toggle" aria-expanded="false" onclick="toggleCourseBlockInfo(this); return false;"><svg aria-hidden="true"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#uw-symbol-caret-down"></use></svg>View details</button><div class="cb-extras" aria-hidden="true"><p class="courseblockextra noindent clearfix"><span class="cbextra=label"><strong><span class="cbextra-label"><strong>Requisites: </strong></span></strong></span><span class="cbextra-data"><a href="/search/?P=MATH%20222" title="MATH 222" class="bubblelink code" onclick="return showCourse(this, 'MATH 222');">MATH 222</a></span></p><p class="courseblockextra noindent clearfix"><span class="cbextra=label"><strong><span class="cbextra-label"><strong>Course Designation: </strong></span></strong></span><span class="cbextra-data">Breadth - Natural Science<br/> Level - Intermediate<br/> L&S Credit - Counts as Liberal Arts and Science credit in L&S</span></p><p class="courseblockextra noindent clearfix"><span class="cbextra=label"><strong><span class="cbextra-label"><strong>Repeatable for Credit: </strong></span></strong></span><span class="cbextra-data">No</span></p><p class="courseblockextra noindent clearfix"><span class="cbextra=label"><strong><span class="cbextra-label"><strong>Last Taught: </strong></span></strong></span><span class="cbextra-data">Fall 2024</span></p><p class="courseblockextra noindent clearfix"><span class="cbextra=label"><strong></strong></span><span class="cbextra-data"><div class="bubblehide"><p class="courseblockextra noindent clearfix"><span class="cbextra-label"><strong>Learning Outcomes: </strong></span><span class="cbextra-data">1. Analyze the behavior of functions of several variables, including their asymptotic behavior, local behavior, and existence of extrema with the tools of calculus (e.g., limits and continuity of multidimensional functions, derivatives and integrals of vector valued functions, arc length and curvature, partial derivatives, tangent planes, etc.).<br/>Audience: Undergraduate<br/><br/>2. Describe and analyze motion in space with the tools of calculus (velocity vector and acceleration, directional derivatives and the gradient vector, etc.).<br/>Audience: Undergraduate<br/><br/>3. Represent and compute areas and volumes by means of multiple integrals (e.g., integration over rectangles and more general spaces, average values, integration with polar, cylindrical, and spherical coordinates, general changes of variables, etc.).<br/>Audience: Undergraduate<br/><br/>4. Derive relations between different physical phenomena and their integral representations (e.g., using Green's theorem, the Divergence theorem, and Stokes' theorem).<br/>Audience: Undergraduate<br/><br/>5. Describe physical, biological, and/or economic phenomena using mathematical models (e.g., topographical maps and level curves, Lagrange multipliers, etc.).<br/>Audience: Undergraduate<br/><br/>6. Offer informal mathematical arguments and formal computations in English using appropriate mathematical terminology, notation, and grammar.<br/>Audience: Undergraduate</span></p></div></span></p></div></div></div></article> <article class="searchresult search-pageresult"><a href="/undergraduate/letters-science/mathematics/mathematics-bs/"><h3>Mathematics, BS</h3> <cite class="displaypath">https://guide.wisc.edu/undergraduate/letters-science/mathematics/mathematics-bs/</cite></a><h4 class="search-catdesc">Undergraduate</h4> <div class="search-summary">Mathematics is about understanding the world through studies of quantity, structure, pattern, and change to create logical solutions that make life more meaningful and more beautiful. Mathematics bridges the humanities and the sciences. Its position among the humanities is based on the study of mathematics as one of the liberal arts for more than two thousand years. The natural sciences have invariably turned to mathematics for techniques needed to explore the consequences of scientific theories. In the last few decades, social scientists have increasingly found higher mathematics of value in their training and research. Still an expanding subject, mathematics is a part of more new and challenging frontiers than at any time in its long history — with many new fields, from data science to quantum computing, requiring new techniques and inspiring ideas for exploration.</div></article> <article class="searchresult search-pageresult"><a href="/undergraduate/letters-science/mathematics/mathematics-ba/"><h3>Mathematics, BA</h3> <cite class="displaypath">https://guide.wisc.edu/undergraduate/letters-science/mathematics/mathematics-ba/</cite></a><h4 class="search-catdesc">Undergraduate</h4> <div class="search-summary">Mathematics is about understanding the world through studies of quantity, structure, pattern, and change to create logical solutions that make life more meaningful and more beautiful. Mathematics bridges the humanities and the sciences. Its position among the humanities is based on the study of mathematics as one of the liberal arts for more than two thousand years. The natural sciences have invariably turned to mathematics for techniques needed to explore the consequences of scientific theories. In the last few decades, social scientists have increasingly found higher mathematics of value in their training and research. Still an expanding subject, mathematics is a part of more new and challenging frontiers than at any time in its long history — with many new fields, from data science to quantum computing, requiring new techniques and inspiring ideas for exploration.</div></article> <article class="searchresult search-pageresult"><a href="/undergraduate/letters-science/chemistry/chemistry-bs/"><h3>Chemistry, BS</h3> <cite class="displaypath">https://guide.wisc.edu/undergraduate/letters-science/chemistry/chemistry-bs/</cite></a><h4 class="search-catdesc">Undergraduate</h4> <p class="search-snippet"><b>...</b>majors also take <b>MATH</b> <b>234</b> Calculus--Functions of Several Variables and <b>MATH</b> 320 Linear Algebra<b>...</b></p></article> <article class="searchresult search-pageresult"><a href="/undergraduate/letters-science/chemistry/chemistry-ba/"><h3>Chemistry, BA</h3> <cite class="displaypath">https://guide.wisc.edu/undergraduate/letters-science/chemistry/chemistry-ba/</cite></a><h4 class="search-catdesc">Undergraduate</h4> <p class="search-snippet"><b>...</b>majors also take <b>MATH</b> <b>234</b> Calculus--Functions of Several Variables and <b>MATH</b> 320 Linear Algebra<b>...</b></p></article> <article class="searchresult search-pageresult"><a href="/undergraduate/letters-science/physics/physics-bs/"><h3>Physics, BS</h3> <cite class="displaypath">https://guide.wisc.edu/undergraduate/letters-science/physics/physics-bs/</cite></a><h4 class="search-catdesc">Undergraduate</h4> <p class="search-snippet"><b>...</b><b>MATH</b> 221 , <b>MATH</b> 222 , <b>MATH</b> <b>234</b> , <b>MATH</b> 319 , <b>MATH</b> 340 , <b>MATH</b> 321 , <b>MATH</b> 322 . <b>MATH</b><b>...</b></p></article> <article class="searchresult search-pageresult"><a href="/undergraduate/letters-science/physics/physics-ba/"><h3>Physics, BA</h3> <cite class="displaypath">https://guide.wisc.edu/undergraduate/letters-science/physics/physics-ba/</cite></a><h4 class="search-catdesc">Undergraduate</h4> <p class="search-snippet"><b>...</b><b>MATH</b> 221 , <b>MATH</b> 222 , <b>MATH</b> <b>234</b> , <b>MATH</b> 319 , <b>MATH</b> 340 , <b>MATH</b> 321 , <b>MATH</b> 322 . <b>MATH</b><b>...</b></p></article> <article class="searchresult search-pageresult"><a href="/undergraduate/letters-science/astronomy/astronomy-physics-bs/"><h3>Astronomy–Physics, BS</h3> <cite class="displaypath">https://guide.wisc.edu/undergraduate/letters-science/astronomy/astronomy-physics-bs/</cite></a><h4 class="search-catdesc">Undergraduate</h4> <p class="search-snippet"><b>...</b>typical <b>math</b> sequence is: <b>MATH</b> 221 , <b>MATH</b> 222 , <b>MATH</b> <b>234</b> , <b>MATH</b> 319 , <b>MATH</b> 340 , <b>MATH</b><b>...</b></p></article> <article class="searchresult search-pageresult"><a href="/undergraduate/letters-science/astronomy/astronomy-physics-ba/"><h3>Astronomy–Physics, BA</h3> <cite class="displaypath">https://guide.wisc.edu/undergraduate/letters-science/astronomy/astronomy-physics-ba/</cite></a><h4 class="search-catdesc">Undergraduate</h4> <p class="search-snippet"><b>...</b>typical <b>math</b> sequence is: <b>MATH</b> 221 , <b>MATH</b> 222 , <b>MATH</b> <b>234</b> , <b>MATH</b> 319 , <b>MATH</b> 340 , <b>MATH</b><b>...</b></p></article> <article class="searchresult search-pageresult"><a href="/undergraduate/engineering/electrical-computer-engineering/electrical-engineering-bs/"><h3>Electrical Engineering, BS</h3> <cite class="displaypath">https://guide.wisc.edu/undergraduate/engineering/electrical-computer-engineering/electrical-engineering-bs/</cite></a><h4 class="search-catdesc">Undergraduate</h4> <p class="search-snippet"><b>...</b><b>MATH</b> 375 and <b>MATH</b> 376 taken in sequence will fulfill the requirement for <b>MATH</b> <b>234</b><b>...</b></p></article> <article class="searchresult search-pageresult"><a href="/undergraduate/engineering/"><h3>College of Engineering</h3> <cite class="displaypath">https://guide.wisc.edu/undergraduate/engineering/</cite></a><h4 class="search-catdesc">Undergraduate</h4> <p class="search-snippet"><b>...</b>through <b>MATH</b> <b>234</b> Calculus--Functions of Several Variables , then additional <b>math</b> courses numbered <b>MATH</b> 217<b>...</b></p></article> <article class="searchresult search-pageresult"><a href="/undergraduate/letters-science/mathematics/applied-mathematics-engineering-physics-bs-amep/"><h3>Applied Mathematics, Engineering, and Physics, BS AMEP</h3> <cite class="displaypath">https://guide.wisc.edu/undergraduate/letters-science/mathematics/applied-mathematics-engineering-physics-bs-amep/</cite></a><h4 class="search-catdesc">Undergraduate</h4> <p class="search-snippet"><b>...</b><b>MATH</b> 221 , <b>MATH</b> 222 , and <b>MATH</b> <b>234</b> with at least a 2.75 GPA. <b>MATH</b><b>...</b></p></article> <article class="searchresult search-pageresult"><a href="/undergraduate/engineering/electrical-computer-engineering/computer-engineering-bs/"><h3>Computer Engineering, BS</h3> <cite class="displaypath">https://guide.wisc.edu/undergraduate/engineering/electrical-computer-engineering/computer-engineering-bs/</cite></a><h4 class="search-catdesc">Undergraduate</h4> <p class="search-snippet"><b>...</b><b>MATH</b> 375 and <b>MATH</b> 376 taken in sequence will fulfill the requirement for <b>MATH</b> <b>234</b><b>...</b></p></article> </div> </section> </div> </div>  </div>  <div id="right-col"> <button class="tabs-expand" onclick="toggleTabs();"><svg aria-hidden="true"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#uw-symbol-caret-down"></use></svg> Select a section…</button> <div id="print-options-box"> <button aria-expanded="false" aria-controls="print-options-list" data-toggle="#print-options-list"> <svg class="main-printer" viewBox="0 0 24 24" aria-hidden="true"> <path d="M18 3v3.984h-12v-3.984h12zM18.984 12c0.563 0 1.031-0.422 1.031-0.984s-0.469-1.031-1.031-1.031-0.984 0.469-0.984 1.031 0.422 0.984 0.984 0.984zM15.984 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