{"slug": "llm-integrated-multivariable-calculus-course", "title": "LLM-Integrated Multivariable Calculus Course", "summary": "Academa launched an LLM-integrated multivariable calculus course covering vectors, partial derivatives, multiple integrals, and vector calculus. The course uses AI to enhance learning through interactive features like video lectures and chat.", "body_md": "Academa\nMultivariable Calculus\n🇺🇸\nEnglish\nVectors and the Geometry of the Space\n25:29\nLecture 1\nVectors\n33:47\nLecture 2\nDot Product\n26:17\nLecture 3\nVector Projections and Determinants\n20:07\nLecture 4\nCross Product\n37:06\nLecture 5\nPlanes and Lines\n30:02\nLecture 6\nPlanes and Lines (cont.)\nVector Functions\n28:26\nLecture 7\nParametric Curves\n28:39\nLecture 8\nParametric Curves (cont.)\nPartial Derivatives\n40:22\nLecture 9\nPartial Derivatives\n29:10\nLecture 10\nPartial Derivatives (cont.)\n9:21\nLecture 11\nTangent Plane, Normal Vector to Surface\n23:24\nLecture 12\nChain Rule\n28:29\nLecture 13\nDirectional Derivative and the Gradient\n34:42\nLecture 14\nMaximization and Minimization\n27:39\nLecture 15\nLagrange Multipliers\nMultiple Integrals\n41:43\nLecture 16\nDouble Integration\n23:02\nLecture 17\nDouble Integration over General Regions\n23:29\nLecture 18\nApplications of Double Integration\nLecture 19\nDouble Integration in Polar Coordinates\nLecture 20\nTriple Integration\nLecture 21\nApplications of Triple Integration\nLecture 22\nCylindrical and Spherical Coordinates\nLecture 23\nIntegration in Cylindrical and Spherical Coordinates\nLecture 24\nGeneral Change of Variables\nVector Calculus\nLecture 25\nVector Fields and Line Integrals\nLecture 26\nGradient Fields and the Fundamental Theorem of Line Integrals\nLecture 27\nMore on Conservative Fields\nLecture 28\nGreen's Theorem\nLecture 29\nCurl and Divergence\nLecture 30\nMore on Div and Curl\nLecture 32\nMore on Parametric Surfaces, Surface Integrals\nLecture 33\nBig Picture of Integration, Stokes' Theorem\nLecture 35\nCurl Free World, Div Free World\nToggle Sidebar\nLecture 1: Vectors\nFeedback\nVideo\nChat\nNext\nDot Product", "url": "https://wpnews.pro/news/llm-integrated-multivariable-calculus-course", "canonical_source": "https://calculus.academa.ai/", "published_at": "2026-07-19 02:55:43+00:00", "updated_at": "2026-07-19 03:21:12.826710+00:00", "lang": "en", "topics": ["large-language-models", "ai-products", "ai-tools"], "entities": ["Academa"], "alternates": {"html": "https://wpnews.pro/news/llm-integrated-multivariable-calculus-course", "markdown": "https://wpnews.pro/news/llm-integrated-multivariable-calculus-course.md", "text": "https://wpnews.pro/news/llm-integrated-multivariable-calculus-course.txt", "jsonld": "https://wpnews.pro/news/llm-integrated-multivariable-calculus-course.jsonld"}}