Open University

Tampere

Multivariable Calculus, Online teaching

<p>Contact information<br>Email: <span class="spamspan"><span class="u">open.studies.tau</span> [at] <span class="d">tuni.fi</span></span><br>Phone: 0294 520 200</p><p>More information concerning Open University studies<br><a href="https://www.tuni.fi/open-university">tuni.fi/open-university</a></p>

Basic studies

Faculty of Information Technology and Communication Sciences

Technology and Natural Sciences

<p>Apply for Open University studies by using the following links:</p><p><ul><li><a href="https://tau-avoin.ilmoittaudu.fi/lobby/?realization=J-otm-bc8272bd-79bc-410f-9d1d-9a27ee95e862_2023-tampere-MATHAPP220" target="_blank">MATH.APP.220 Multivariable Calculus, online teaching, Tampere</a></li></ul></p><p>You can find a link to the Open University Admissions service and application instructions on the <a href="https://www.tuni.fi/en/study-with-us/open-higher-education-studies/open-university/applying-open-university">Applying to Open University studies</a> page.</p><p>Some of the studies require prior studies. For example, studying intermediate studies may require some completed basic studies. These are described on the Information about studies tab of the study unit under prior requirements.</p><p>When you have been admitted to the studies, you must enrol separately via the Sisu information system for the implementation of the unit of study and, for example if set, for a practise group of your choice. You will receive instructions on how to do this by e-mail after you have confirmed your acceptance of the study place by paying the required fee.</p>

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Hervanta Campus

Online studies

<p>Look information at <a href="https://www.tuni.fi/en/study-with-us/open-higher-education-studies/open-university/applying-open-university">Applying to Open University studies</a>.</p>

<h5>Core content</h5><ul><li>Real valued functions of several variables:<br> Graphs and contour plots of functions of two variables. Limits and <br>continuity, first and higher order partial derivatives, directed <br>derivative and gradient.</li><li>Vector-valued functions of several variables: Derivative matrix and the chain rule.</li><li>Extreme values of a function: Local and global maxima and minima.</li><li>Integrals<br> of functions of two and three variables: Computing in vertically and <br>horizontally simple domains, computing using polar, cylinder and <br>spherical coordinates.</li></ul><h5>Complementary knowledge</h5><ul><li> Linear approximation and differentiability </li><li>Hessian matrix, Taylor&amp;#39;s formula</li><li>Constrained extremal values and Lagrange&amp;#39;s method.</li><li>Center of mass, improper integrals.</li><li>Using Matlab as a tool in solving the exercise problems.</li></ul><h5>Specialist knowledge</h5><ul><li>A ball, open and closed sets<br></li><li>General change of variables, mean value theorem and average of a function</li></ul>

<h2>Groups</h2><h3>Other Event: Math Shack</h3><p>12.01.2024 12:00 - 14:00, TAU S&#228;hk&#246;talo SC203 opetustila (32)<br>19.01.2024 12:00 - 14:00, TAU S&#228;hk&#246;talo SC203 opetustila (32)<br>26.01.2024 12:00 - 14:00, TAU S&#228;hk&#246;talo SC203 opetustila (32)<br>02.02.2024 12:00 - 14:00, TAU S&#228;hk&#246;talo SC203 opetustila (32)<br>09.02.2024 12:00 - 14:00, TAU S&#228;hk&#246;talo SC203 opetustila (32)<br>16.02.2024 12:00 - 14:00, TAU S&#228;hk&#246;talo SC203 opetustila (32)<br>23.02.2024 12:00 - 14:00, TAU S&#228;hk&#246;talo SC203 opetustila (32)<br></p><h2>Voluntary</h2><h3>Exercise: </h3><p>16.01.2024 12:00 - 14:00, TAU Tietotalo TB206 opetustila (25)<br>17.01.2024 08:00 - 10:00, TAU Tietotalo TB206 opetustila (25)<br>23.01.2024 12:00 - 14:00, TAU Tietotalo TB206 opetustila (25)<br>24.01.2024 08:00 - 10:00, TAU Tietotalo TB206 opetustila (25)<br>30.01.2024 12:00 - 14:00, TAU Tietotalo TB206 opetustila (25)<br>31.01.2024 08:00 - 10:00, TAU Tietotalo TB206 opetustila (25)<br>06.02.2024 12:00 - 14:00, TAU Tietotalo TB206 opetustila (25)<br>07.02.2024 08:00 - 10:00, TAU Tietotalo TB206 opetustila (25)<br>13.02.2024 12:00 - 14:00, TAU Tietotalo TB206 opetustila (25)<br>14.02.2024 08:00 - 10:00, TAU Tietotalo TB206 opetustila (25)<br>20.02.2024 12:00 - 14:00, TAU Tietotalo TB206 opetustila (25)<br>21.02.2024 08:00 - 10:00, TAU Tietotalo TB206 opetustila (25)<br></p><h3>Lecture: Info lecture</h3><p>08.01.2024 10:00 - 11:00<br></p>

<p>On this course the students learn to study and visualize the behaviour <br>of a real valued function of two variables using its graphs and contour <br>plots, compute limits of multivariable functions, compute first <br>and higher order partial derivatives, gradients and directed <br>derivatives, and to find local and global maxima of functions. The <br>students learn to form the derivative matrix of a vector-valued function<br> and to use the chain rule of differentiation. The students learn how to <br>compute integrals of real-value functions of two and three variables <br>using cartesian, polar, cylinder and spherical coordinates. The students<br> learn how to justify their claims using mathematical methods and to <br>present their solutions orally as well as in written form.</p>

Finnish

<h2>Prerequisites</h2><p>The compulsory prerequisite knowledge is differential and integral calculus of one variable real functions, and the fundamentals of matrix algebra (Mathematics 1-3 or similar courses). <br></p><h2>Compulsory Prerequisites</h2><ul><li>Introductory Calculus, MATH.APP.111, 5 cr</li><li>Vectors and Matrices, MATH.MA.140, 5 cr</li><li>Differential and Integral Calculus, MATH.APP.160, 5 cr</li><li>Vectors and Matrices, MATH.MA.140, 5 cr</li><li>Analysis A: Limit and Continuity, MATH.MA.420, 5 cr</li><li>Differential and Integral Calculus, MATH.APP.160, 5 cr</li><li>Calculus, Part 1, MATH.MA.120, 5 cr</li><li>Calculus, Part 2, MATH.MA.160, 5 cr</li><li>Vectors and Matrices, MATH.MA.140, 5 cr</li></ul>

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<p>Materials available in Moodle. The course Moodle page can be accessed around the beginning of the year.<br></p>

<p>Levture videos. Weekly online exercises with automatic assessment and written exercises with peer review. Optional online exercise sessions to help with the exercises. An exam at the end of the course. The grade is based 50% on exercise points and 50% on exam points.<br></p>

Multivariable Calculus, Online teaching

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Multivariable Calculus, 5 cr

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Multivariable Calculus, Online teaching