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What makes Torus Special
For the past couple of days I have been encountering the word "Torus" quite often. I would like to know what special properties does the Torus possess tha...
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What is meant by a purely real number?
I am a bit confused about this question: I understand that a purely real complex number is where the 'a' value is 0, But how would you go about ...
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How to integrate $\cos^3x$ by parts
I've converted $\cos^3(x)$ into $\cos^2(x)\cos(x)$ but still have not gotten the answer. The answer is $\dfrac{\sin(x)(3\cos^2x + 2\sin^2x)}{3}$ My a...
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Give some example of linear functional?
Give some example of linear functional ? My attempt : I know the definition of linear functional linear functional on $V$ is a function $ f : V \to F$ suc...
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Euler's Method Global Error: How to calculate $C_1$ if $error = C_1 h$
My textbook claims that, for small step size $h$, Euler's method has a global error which is at most proportional to $h$ such that error $= C_1h$. It...
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Average in a rating between 1 and 5
A user can vote on these numbers: 1, 2, 3, 4, 5 Then it's displayed as groups like this: 1 - 5 votes 2 - 3 votes 3 - 1 vote 4 - 17 votes 5 - 2 votes ...
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approximating second derivative from Taylor's theorem
I have been having trouble coming up with an approximation formula for numerical differentiation (2nd derivative) of a function based on the truncation of...
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$n$-th derivative of $f(x)=x\cos(x)$
Can someone help me prove that the $n$-th derivative of $f(x)=x\cos(x)$ is: $$f^n(x)=x\cos\left(x+\frac{n\pi}{2}\right)+n\cos\left(x+(n-1)\frac{\pi}{2}\ri...
Read Journal![Calculate Fourier series of $f(x)=x^2$ , $x \in \ [-\pi,\pi]$](https://ly.shilpakalanarail.gov.bd/uploads/calculate-fourier-series-of-f-x-x-2-x-in-pi-pi_720.jpg)
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Calculate Fourier series of $f(x)=x^2$ , $x \in \ [-\pi,\pi]$
Calculate Fourier series of $f(x)=x^2$ , $x \in \ [-\pi,\pi]$ and determine module and phase spectrum $$f(x)=\frac{a_0}{2}+\sum_{n=1}^{+\infty} a_n \ \cos...
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Why is the line between two points called the line of the "secant"?
The definition of the slope of the line of the secant is: slope = $\frac{y2-y1}{x2-x1}$ The definition of the slope of the tangent line is: $\lim_{h->0...
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