Junwen Wayne Peng - 台大 NCTS 數學組研究員

In the 8th class, we went over a few examples to practice the technique of definite and indefinite integrating a function. The order of integration won’t change the value of an integral. However, we discussed how the order of integration can sometimes be important, and that it is essential to... [Read More]

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Calculus 3 Worksheet 3

Double Integral, Fubini Theorem

Posted on March 27, 2023 · 1 minute read

Compute the following double integral $\int\int_{\Omega}\frac{1}{1+x+y}dxdy$, $\Omega: [0,1]\times[0,2]$. (Hint: it requires integration by part for $\int\ln(x)dx$.) $\int\int_{\Omega}\frac{xy}{(x^2+y^2)^2}dxdy$, $\Omega:[1,2]\times[1,3]$. (Hint: we are going to apply integration by part twice.) Explain $\int\int_{\Omega}1dxdy$ is the area of $\Omega$. Examine the region $\Omega$ bounded by the lines $x=4$, $y=\frac{1}{2}x+2$, and $y=-x$, as depicted in... [Read More]

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test

Posted on March 24, 2023 · 1 minute read

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test

Calculus 3-7 Overview

Lagrange Multipliers, Application of Integral, Double Integration

Posted on March 23, 2023 · 1 minute read

Method of Lagrange Multipliers In our seventh class, we began by reviewing Lagrange multipliers and discussing finding extreme values on a surface with an open relation. [Read More]

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