From 72f3bc757fd1fc742c5048dcf98c00b85657cad0 Mon Sep 17 00:00:00 2001 From: newt Date: Wed, 9 Oct 2024 18:02:47 +0100 Subject: [PATCH] feat: maths folder -> newtykins/maths --- .husky/pre-commit | 1 - .husky/scripts/pdfToPng.sh | 22 ------------ .vscode/extensions.json | 3 -- .vscode/settings.json | 5 +-- maths/halley's method.png | Bin 58537 -> 0 bytes maths/halley's method.tex | 53 ---------------------------- maths/nth root.png | Bin 2482 -> 0 bytes maths/nth root.tex | 12 ------- maths/style.cls | 11 ------ maths/trigometric functions/cos.png | Bin 8329 -> 0 bytes maths/trigometric functions/cos.tex | 27 -------------- maths/trigometric functions/cot.png | Bin 10792 -> 0 bytes maths/trigometric functions/cot.tex | 29 --------------- maths/trigometric functions/csc.png | Bin 10322 -> 0 bytes maths/trigometric functions/csc.tex | 28 --------------- maths/trigometric functions/sec.png | Bin 10035 -> 0 bytes maths/trigometric functions/sec.tex | 29 --------------- maths/trigometric functions/sin.png | Bin 9186 -> 0 bytes maths/trigometric functions/sin.tex | 27 -------------- maths/trigometric functions/tan.png | Bin 9992 -> 0 bytes maths/trigometric functions/tan.tex | 28 --------------- 21 files changed, 1 insertion(+), 274 deletions(-) delete mode 100755 .husky/scripts/pdfToPng.sh delete mode 100644 .vscode/extensions.json delete mode 100644 maths/halley's method.png delete mode 100644 maths/halley's method.tex delete mode 100644 maths/nth root.png delete mode 100644 maths/nth root.tex delete mode 100644 maths/style.cls delete mode 100644 maths/trigometric functions/cos.png delete mode 100644 maths/trigometric functions/cos.tex delete mode 100644 maths/trigometric functions/cot.png delete mode 100644 maths/trigometric functions/cot.tex delete mode 100644 maths/trigometric functions/csc.png delete mode 100644 maths/trigometric functions/csc.tex delete mode 100644 maths/trigometric functions/sec.png delete mode 100644 maths/trigometric functions/sec.tex delete mode 100644 maths/trigometric functions/sin.png delete mode 100644 maths/trigometric functions/sin.tex delete mode 100644 maths/trigometric functions/tan.png delete mode 100644 maths/trigometric functions/tan.tex diff --git a/.husky/pre-commit b/.husky/pre-commit index cf03b66..f8fb83c 100755 --- a/.husky/pre-commit +++ b/.husky/pre-commit @@ -2,5 +2,4 @@ . "$(dirname "$0")/_/husky.sh" npx pretty-quick --staged -.husky/scripts/pdfToPng.sh git add . diff --git a/.husky/scripts/pdfToPng.sh b/.husky/scripts/pdfToPng.sh deleted file mode 100755 index 3a2a04d..0000000 --- a/.husky/scripts/pdfToPng.sh +++ /dev/null @@ -1,22 +0,0 @@ -#!/bin/bash -find . -print0 | while IFS= read -r -d '' file -do - if [ -f "$file" ]; then - if [[ $file == *pdf ]]; then - mkdir temp - gm convert "$file" +adjoin temp/temp%02d.png - - for temp in ./temp/*.png - do - gm convert "$temp" -fuzz 80% -trim +repage -bordercolor white -border 50x25 "$temp" - done - - readarray -d . -t arr <<< $file - - gm convert -append ./temp/*.png "${arr[1]:1}.png" - - rm -rf temp - rm "$file" "${arr[1]:1}.synctex.gz" - fi -fi -done diff --git a/.vscode/extensions.json b/.vscode/extensions.json deleted file mode 100644 index b1b5201..0000000 --- a/.vscode/extensions.json +++ /dev/null @@ -1,3 +0,0 @@ -{ - "recommendations": ["James-Yu.latex-workshop"] -} diff --git a/.vscode/settings.json b/.vscode/settings.json index c4050b2..dcd343e 100644 --- a/.vscode/settings.json +++ b/.vscode/settings.json @@ -12,7 +12,6 @@ "commitlint.config.js": true, "**/pnpm-lock.yaml": true }, - "C_Cpp.errorSquiggles": "Disabled", "files.associations": { "*.tcc": "cpp", "complex": "cpp", @@ -33,7 +32,5 @@ "ostream": "cpp", "ratio": "cpp", "streambuf": "cpp" - }, - "latex-workshop.latex.autoBuild.run": "onSave", - "latex-workshop.latex.autoClean.run": "onBuilt" + } } diff --git a/maths/halley's method.png b/maths/halley's method.png deleted file mode 100644 index bec432b78cf62620607e7a98577ecf386ec4455a..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 58537 zcmd43cT`i+_b(Wwi6WrVM4E{7Zcsp~2uKM?3DS`&AV}{`P(ea3f`lG=Ku|z>QwRu= z8jun?geo9SI=qA5-^`o0=Djul%$qg&2XB`5o_o$ccklfvJK;|?l&@Z9ybOUruBtqF ztPO!&w1s2nQ+(PRZ;=;5d#m|UF+1J3 z&E3{;HU3r>tCR^F&u?J{roXWB=2!Eqds}nEP5N$qkz1*GUY}AvN|Au@5b1P4j{jjz 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\sum_{i=0}^{n-2}(i-n)(i-n+1)a_{n-i}x^{n-i-2} - \end{dmath*} - - After starting with an initial guess, the next iteration of Halley's method is given by $x_k - \frac{2f(x_k)f'(x_k)}{2[f'(x_k)]^2 - f(x_k)f''(x_k)}$. - - This means that we must first find $f(x)f'(x)$, $[f'(x)]^2$, and $f(x)f''(x)$. These all consist of the multiplication of two series - there is a nice general form to this problem stated below - - \begin{dmath*} - (\sum_{i=0}^{n}x_{i})(\sum_{j=0}^{m}y_{j}) = \sum_{i=0}^{n}\sum_{j=0}^{m}x_iy_j - \end{dmath*} - - \newpage - From this, we can conclude that: - - \begin{dmath*} - f(x)f'(x) = (\sum_{i=0}^{n}c_{n-i}x^{n-i})(\sum_{i=0}^{n-1}(n-i)c_{n-i}x^{n-i-1}) = \sum_{i=0}^{n}\sum_{j=0}^{n-1}(n-j)c_{n-i}c_{n-j}x^{2n-i-j-1} - \end{dmath*} - - \begin{dmath*} - [f'(x)]^2 = (\sum_{i=0}^{n-1}(n-i)c_{n-i}x^{n-i-1})(\sum_{i=0}^{n-1}(n-i)c_{n-i}x^{n-i-1}) = \sum_{i=0}^{n-1}\sum_{j=0}^{n-1}(n-i)(n-j)c_{n-i}c_{n-j}x^{2(n-1)-i-j} - \end{dmath*} - - \begin{dmath*} - f(x)f''(x) = (\sum_{i=0}^{n}c_{n-i}x^{n-i})(\sum_{i=0}^{n-2}(i-n)(i-n+1)a_{n-i}x^{n-i-2}) = \sum_{i=0}^{n}\sum_{j=0}^{n-2}(j-n)(j-n+1)c_{n-i}c_{n-j}x^{2(n-1)-i-j} - \end{dmath*} - - And all that is left to do is to plug it into the formula for Halley's method, leaving us with the following: - - \begin{align*} - x_{k+1} = x_{k} - \dfrac{2\sum_{i=0}^{n}\sum_{j=0}^{n-1}(n-j)c_{n-i}c_{n-j}x^{2n-i-j-1}}{\splitdfrac{2\sum_{i=0}^{n-1}\sum_{j=0}^{n-1}(n-i)(n-j)c_{n-i}c_{n-j}x^{2(n-1)-i-j}}{- \sum_{i=0}^{n}\sum_{j=0}^{n-2}(j-n)(j-n+1)c_{n-i}c_{n-j}x^{2(n-1)-i-j}}} - \end{align*} -\end{center} -\end{document} diff --git a/maths/nth root.png b/maths/nth root.png deleted file mode 100644 index 72b7276fb389f4883a3d2f45e3c6c220176d3751..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 2482 zcmd5;{X5eOAO0dN*&>P=nd)c~X{tF(BnlDono2edtIV>EHs+mTR43$ZB%YSHMP4_e zhEyvrDetM&X@)pX*=!?@bDryZ{(Jd(f#AgELWV(rEKc99fvU$fFSXw{sH4aAUf(;Ex-1>q0Z55smp;0 ze9MT7IJJ*0(m;b8-Y;oNpN3`@%IhL6W_4^3ZCD+oB24a8u3+-&ex}!&*r7|QLbb3? z>vD%+62n1p;E_ux)XLHjSlCfrXGYyPS?OPtc~DIblsVJm$?DLMhb?M_DcChzJqdKs zs!s3*$i?zzk#__Y7ob3XRq)53^$B}wq}a;X2FF{E6){P5sHdxCz*9^4__Rl0Pcwyh zjGrMTwr*ic4$1|%Jb{CRsYpXhqlIZe)Wx>U#35oS8K& zpgr0N(gIRvBJ;ktLxzFH9p{YT3_18dk~f`LOwLW)H-yw%;#6ne2}70r16&{4uMm#LW_^742m+u%GRX7v1{OrC>k%bA 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e^{-i\theta}} -\end{gather*} - -\begin{gather*} - \text{let} \quad \csc(\theta) = x \\ - \frac{2i}{x} = e^{i\theta} - e^{-i\theta} \\ - \frac{2i}{x}e^{i\theta} = (e^{i\theta})^2 - 1 \\ - (e^{i\theta})^2 + (-\frac{2i}{x})e^{i\theta} - 1 = 0 -\end{gather*} - -\begin{gather*} - e^{i\theta} = \frac{-(\frac{2i}{x}) \pm \sqrt{(\frac{2i}{x})^2 - 4(-1)}}{2} = x^{-1}i \pm \sqrt{1 - x^2} \\ - i\theta = \ln(x^{-1}i \pm \sqrt{1 - x^2}) \\ - \theta = -i\ln(x^{-1}i \pm \sqrt{1 - x^2}) -\end{gather*} - -\begin{gather*} - \therefore \text{arccsc}(\theta) = -i\ln(i\theta^{-1} \pm \sqrt{1 -\theta^2}) -\end{gather*} -\end{document} diff --git a/maths/trigometric functions/sec.png b/maths/trigometric functions/sec.png deleted file mode 100644 index 75793b7e227520b343d2f141622ccbdcdfe79db3..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 10035 zcmch7bx<8&)8^pr5Q1A0oIvnPun^o5oQpeL++6|$*Pyw0@QVd^P4M7c2<~n{LeTKt zHz>b4-)|Z zXAX`;0Pw6v{T>5P=;J^L{)tQozMvCaBGI-sFS8#Gpr 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e^{-i\theta}}{2i} \\ - \cos(\theta) = \frac{e^{i\theta} + e^{-i\theta}}{2} \\ - \tan(\theta) = \frac{\sin(\theta)}{\cos{\theta}} = -\frac{i(-1 + e^{2i\theta})}{1 + e^{2i\theta}} -\end{gather*} - -\begin{gather*} - \text{let} \quad \tan(\theta) = x \\ - x(1 + e^{2i\theta}) = -i(-1 + e^{2i\theta}) \\ - x + xe^{2i\theta} = i - ie^{2i\theta} \\ - xe^{2i\theta} + ie^{2i\theta} = i - x \\ - e^{2i\theta}(i + x) = i - x \\ - e^{2i\theta} = \frac{i - x}{i + x} \\ - 2i\theta = \ln(\frac{i - x}{i + x}) \\ - i\theta = \frac{1}{2}\ln(\frac{i - x}{i + x}) \\ - \theta = -\frac{i}{2}\ln(\frac{i - x}{i + x}) -\end{gather*} - -\begin{gather*} - \therefore \arctan(\theta) = -\frac{i}{2}\ln(\frac{i - \theta}{i + \theta}) -\end{gather*} -\end{document}