{"id":15410629,"url":"https://github.com/damienbod/math-docs","last_synced_at":"2026-02-23T18:07:39.738Z","repository":{"id":66359449,"uuid":"497268128","full_name":"damienbod/math-docs","owner":"damienbod","description":"docs for some math equations","archived":false,"fork":false,"pushed_at":"2022-05-28T18:30:03.000Z","size":59,"stargazers_count":8,"open_issues_count":0,"forks_count":12,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-10-25T04:23:52.004Z","etag":null,"topics":["math","mathjax","tex"],"latest_commit_sha":null,"homepage":"","language":null,"has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/damienbod.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2022-05-28T09:10:10.000Z","updated_at":"2024-11-29T13:22:15.000Z","dependencies_parsed_at":"2023-02-23T04:15:59.494Z","dependency_job_id":null,"html_url":"https://github.com/damienbod/math-docs","commit_stats":{"total_commits":68,"total_committers":1,"mean_commits":68.0,"dds":0.0,"last_synced_commit":"07641fe392c56e6e19e4feccde26174b401ff1f7"},"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/damienbod/math-docs","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/damienbod%2Fmath-docs","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/damienbod%2Fmath-docs/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/damienbod%2Fmath-docs/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/damienbod%2Fmath-docs/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/damienbod","download_url":"https://codeload.github.com/damienbod/math-docs/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/damienbod%2Fmath-docs/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":29749987,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-02-23T07:44:07.782Z","status":"ssl_error","status_checked_at":"2026-02-23T07:44:07.432Z","response_time":90,"last_error":"SSL_read: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["math","mathjax","tex"],"created_at":"2024-10-01T16:45:27.135Z","updated_at":"2026-02-23T18:07:39.716Z","avatar_url":"https://github.com/damienbod.png","language":null,"funding_links":[],"categories":[],"sub_categories":[],"readme":"# Exploring github markdown for math\n\n## Quadratic equations\n\n$$x = {-b \\pm \\sqrt{b^2-4ac} \\over 2a}$$\n\n$(a+b)^2$\n\n$$\\eqalign{\n(a+b)^2 \u0026= (a+b)(a+b) \\\\\n        \u0026= a^2 + ab + ba + b^2 \\\\\n        \u0026= a^2 + 2ab + b^2\n}$$\n\n$(a-b)^2$\n\n$$\\eqalign{\n(a-b)^2 \u0026= (a-b)(a-b) \\\\\n        \u0026= a^2 - ab - ba + b^2 \\\\\n        \u0026= a^2 - 2ab + b^2\n}$$\n\n$(a-b)(a+b)$\n\n$$\\eqalign{\n(a+b)(a-b)  \u0026= a^2 - ab + ba - b^2 \\\\\n        \u0026= a^2 - b^2\n}$$\n\n## Functions\n\n$$ f(x) = {\\sqrt{5x^2+2x-1}+(x-2)^2 } $$\n\n\n$$ g(x) = {\\\\frac{a}{1-a^2} }$$\n\n$$ f(x) = {(x + 2) \\over (2x + 1)} $$   \n\n\n$$ f(x) = { \\sqrt[3]{x^2} }$$\n  \n$$ \\sqrt[5]{34}$$\n  \n## Trigonometry\n\n$$ cos^2 \\theta + sin^2 \\theta  = 1  $$\n\n$$ tan 2 \\theta = {2tan \\theta  \\over 1 - tan^2 \\theta}  $$\n\n$$\\eqalign{\ncos 2 \\theta = cos^2 \\theta - sin^2 \\theta \\\\\n                       \u0026=  2 cos^2  \\theta -1 \\\\\n                       \u0026= 1 - 2sin^2 \\theta \n}$$\n\nProve $ \\sqrt{ 1 - cos^2 \\theta \\over 1- sin^2 \\theta} = tan \\theta $\n\n$$ \\sqrt{ 1 - cos^2 \\theta \\over 1- sin^2 \\theta} = \\sqrt{ sin^2 \\theta \\over cos^2 \\theta} = {sin \\theta \\over cos \\theta}  = Tan \\theta $$\n\n## Calculus\n\n$$\\eqalign{\nf(x) = {3x^4} \\implies {dy \\over dx} = 12x^3\n}$$\n\n$$\\eqalign{\nf(x) = {2x^{-3/2}} \\implies  {dy \\over dx} = -3x^{-5/2} \u0026= - {3 \\over \\sqrt{x^5}}\n}$$\n\nIf $x = 2t + 1$ and $ y = t^2$ find ${dy \\over dx}$ ?\n\n$$\\eqalign{\nx = 2t + 1 \\implies  {dx \\over dt} = 2 \\\\\n        y = t^2 \\implies  {dy \\over dt} = 2t \\\\\n        {dy \\over dx} = {dy \\over dt} \\div {dx \\over dt} \\\\\n         \\implies 2t \\div 2 = t\n}$$\n\n## Integration\n\nEvaluate $\\int_1^2 (x + 4)^2 dx $\n\n$$\\eqalign{\n\\int_1^2 (x + 4)^2 dx =  \\int_1^2 (x^2 + 8x + 16) dx \\\\\n        \u0026= \\left\\lbrack {x^3 \\over 3} + {8x^2 \\over 2}  + 16x \\right\\rbrack_1^2 \\\\\n        \u0026= \\left\\lbrack {8 \\over 3} + {8 * 4 \\over 2}  + 16 * 2 \\right\\rbrack - \\left\\lbrack {1 \\over 3} + {8 \\over 2}  + 16  \\right\\rbrack \n}$$\n\n## Matrix\n\n$$ {\\left\\lbrack \\matrix{2 \u0026 3 \\cr 4 \u0026 5} \\right\\rbrack} * \\left\\lbrack \\matrix{1 \u0026 0 \\cr 0 \u0026 1} \\right\\rbrack = \\left\\lbrack \\matrix{2 \u0026 3 \\cr 4 \u0026 5} \\right\\rbrack $$\n\n## Sum\n\n$$\\sum_{n=1}^n n = {n \\over 2} (n + 1) $$\n\n$$\\sum_{n=1}^n n^2 = {n \\over 6} (n + 1)(2n + 1) $$\n\n# Links\n\nhttps://github.blog/changelog/2022-05-19-render-mathematical-expressions-in-markdown/\n\nhttps://www.mathjax.org/\n\nhttp://docs.mathjax.org/en/latest/\n\nhttps://docs.mathjax.org/en/v2.7-latest/tex.html\n\nhttps://www.onemathematicalcat.org/MathJaxDocumentation/TeXSyntax.htm\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdamienbod%2Fmath-docs","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fdamienbod%2Fmath-docs","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdamienbod%2Fmath-docs/lists"}