Publications by Dimas Atha Putra
Integration: Case Study
As we know, integration is about finding the anti-derivative of a function. The theory is, every function is a derivative of something. If we have a function, f(x) = x^2 + 8x + 7 then that would be the derivative of the following function \begin{align*} \int_{}^{} f(x) \; dx &= {\int_{}^{} x^2 \; dx} + {\int_{}^{} 8x \; dx} + {\int_{}^{} 7 \;...
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Differentiation: Case Study
We have learned basic things about differentiaton. Taking the derivative of a function is basically just going through all its “elements,” deriving it with a rule (for example, the power rule), and putting them all back together. Let’s do a little bit of refreshing. What’s the derivative of the following function? f(x) = 2x^2 - x - 6 Le...
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Integration: Finding the function that a function could be the derivative of with the mosaicCalc library
As we talked about in previous article, the derivative of a function is expressed with this thing someone might have seen somewhere and be intimidated by it (it’s me, I’m that one who used to be intimidated by it): \[{\frac{d}{dx}} [f(x)]\] For example, if we have the function \(f(x) = x^3\), the definition of its derivative would be expres...
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Differentiation: Defining the derivative of a function with the mosaicCalc library
In my previous article I talked a little bit about optimization. Where we took a random function, and brute forced our computer to iterate through a range of values to find the maximum and minimum result of that function. Now, differentiation actually has a part in optimization, which we were not using in that article. Defining the derivative o...
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Optimization: Plotting the local ranges of a basic function with the mosaicCalc library
Optimization is used to find the highest peaks in an area of a function. When we graph out a function, for example, with a function picked randomly with mosaicCalc’s rfun(): h <- rfun(~ x, seed=720) we can get this graph: You can see that the highest peak is somewhere on the \(x = {-1}\) area. And the lowest is in near the \(x = {2}\) area. L...
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Iteration: Finding the square root of a number with the mosaicCalc library
Finding the square root of a number usually involves this function: \({\sf better}(guess) = \frac{1}{2}(guess + \frac{x}{guess})\) This is how you can define it in R. better <- makeFun((guess + x/guess)/2 ~ guess) The function takes two arguments: \(guess\) and \(x\). The algorithm starts with dividing \(x\) by a number for \(guess\), and adding...
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Zero-finding: Tracing back your steps with the mosaicCalc library
Zero-finding is like when you get ahold of a treasure map. And you need to find where the “X” spot in the map is. You use the trees and rocks as your reference points until… you find it. The treasure is yours. It’s like tracing back your steps. Exponentials Let’s say you have a number, \(5\). What could the exponent for this number ...
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