Open University

Tampere

Differential and Integral Calculus

<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-3f4e5e22-b009-4835-95a4-68806ebe1491-tampere-MATHAPP160" target="_blank">MATH.APP.160 Differential and Integral Calculus, 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>

English

Hervanta Campus

<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>Antiderivative and basic integration techniques. Proper and improper integrals.</li><li>Ordinary linear differential equations of first and second order. Separable first order differential equations.</li><li>Limit of a sequence, increasing and decreasing sequences.</li><li>Series (geometric, with positive terms, alternating, Taylor series) and their convergence.</li></ul><h5>Complementary knowledge</h5><ul><li>Applications of integration in, e.g., determining areas and volumes of geometrical shapes, and computing the length of a curve.</li><li>Higher &nbsp;order differential equations. Modeling specific real world problems, &nbsp;such as growth of populations, with differential equations.</li><li>Approximating a function with a polynomial.</li><li>Using Matlab as a tool in solving the exercise problems.</li></ul><h5>Specialist knowledge</h5><ul><li>Numerical integration, trapezoid rule and Simpson&amp;#39;s formula. Computing the Riemann sums.</li><li>Existence and uniqueness results, matrix notation for linear systems.</li><li>Testing &nbsp;convergence. Computing limits and integrals using series. Estimating &nbsp;the error in polynomial approximations of functions.</li></ul>

<h2>Groups</h2><h3>Other Event: &nbsp;/ Laskutupa (in English)</h3><p>01.09.2023 12:00 - 14:00, TAU S&#228;hk&#246;talo SC105B opetustila (48)<br>08.09.2023 12:00 - 14:00, TAU S&#228;hk&#246;talo SC105B opetustila (48)<br>15.09.2023 12:00 - 14:00, TAU S&#228;hk&#246;talo SC105B opetustila (48)<br>22.09.2023 12:00 - 14:00, TAU S&#228;hk&#246;talo SC105B opetustila (48)<br>29.09.2023 12:00 - 14:00, TAU S&#228;hk&#246;talo SC105B opetustila (48)<br>06.10.2023 12:00 - 14:00, TAU S&#228;hk&#246;talo SC105B opetustila (48)<br>13.10.2023 12:00 - 14:00, TAU S&#228;hk&#246;talo SC105B opetustila (48)<br>27.10.2023 12:00 - 14:00, TAU S&#228;hk&#246;talo SG312 opetustila (48)<br>03.11.2023 12:00 - 14:00, TAU S&#228;hk&#246;talo SG312 opetustila (48)<br>10.11.2023 12:00 - 14:00, TAU S&#228;hk&#246;talo SG312 opetustila (48)<br>17.11.2023 12:00 - 14:00, TAU S&#228;hk&#246;talo SG312 opetustila (48)<br>24.11.2023 12:00 - 14:00, TAU S&#228;hk&#246;talo SG312 opetustila (48)<br>01.12.2023 12:00 - 14:00, TAU S&#228;hk&#246;talo SG312 opetustila (48)<br>08.12.2023 12:00 - 14:00, TAU S&#228;hk&#246;talo SG312 opetustila (48)<br></p><h2>Voluntary</h2><h3>Lecture: Online teaching</h3><p>29.08.2023 14:00 - 16:00<br>05.09.2023 14:00 - 16:00<br>12.09.2023 14:00 - 16:00<br>19.09.2023 14:00 - 16:00<br>26.09.2023 14:00 - 16:00<br>03.10.2023 14:00 - 16:00<br>10.10.2023 14:00 - 16:00<br>24.10.2023 14:00 - 16:00<br>31.10.2023 14:00 - 16:00<br>07.11.2023 14:00 - 16:00<br>14.11.2023 14:00 - 16:00<br>21.11.2023 14:00 - 16:00<br>28.11.2023 14:00 - 16:00<br></p>

<p>On this course the students learn basic techniques such as integration <br>by parts and changing of integration variables in integration of simple <br>functions. The students learn to compute antiderivatives of rational <br>functions and to analyze and compute improper integrals. The students <br>also learn to solve simple separable differential equations, compute <br>general solutions of homogeneous second order differential equations <br>with constant coefficients, and to compute the particular solution of a <br>nonhomogeneous differential equation using the method of undetermined coefficients After the course the students are capable of analyzing the <br>limit of a sequence, computing the sum of a geometric series, and <br>testing the convergence of a series with positive terms. The students <br>also learn how to determine the interval of convergence of a power <br>series, form Taylor polynomials of functions, and simple Taylor series. <br>The students learn present their solutions orally as well as in written <br>form.</p>

Finnish

<h2>Prerequisites</h2><h5>Prerequisite</h5><ul><li>Code:&#160;MAT-01130</li><li>Name: Fundamentals of Engineering Mathematics<br></li><li>ECTS credits:&#160;5</li><li>Mandatory: Mandatory<br></li></ul><h5>Prerequisite</h5><ul><li>Code:&#160;MAT-01230</li><li>Name: Vectors and matrices</li><li>ECTS credits:&#160;5</li><li>Mandatory:&#160;Mandatory</li></ul><h2>Recommended Prerequisites</h2><ul><li>Vectors and Matrices, MATH.MA.140, 5 cr</li><li>Introductory Calculus, MATH.APP.111, 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>Introduction to University Mathematics, MATH.APP.010, 5 cr</li></ul>

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<h5>Material</h5><ul><li>Type:&#160;Book</li><li>Name:&#160;Calculus 6e, Early Transcendentals, Matrix Version</li><li>Author:&#160;Edwards &amp;amp; Penney</li><li>Language:&#160;English</li><li>Info: Chapters 5, 7, 8 and 10<br></li></ul>

Differential and Integral Calculus

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