{"id":27128193,"url":"https://github.com/k-karna/multivariable_calculus","last_synced_at":"2025-07-30T06:12:54.591Z","repository":{"id":211712612,"uuid":"708194084","full_name":"k-karna/multivariable_calculus","owner":"k-karna","description":"Solutions to Multivariable Calculus by Don Shimamoto | Solved step by step through LaTeX","archived":false,"fork":false,"pushed_at":"2024-01-31T19:39:53.000Z","size":643,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2024-01-31T20:38:50.699Z","etag":null,"topics":["multivariable-calculus","real-valued-functions"],"latest_commit_sha":null,"homepage":"","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/k-karna.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"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}},"created_at":"2023-10-21T20:02:26.000Z","updated_at":"2023-10-21T20:08:55.000Z","dependencies_parsed_at":"2023-12-14T14:25:28.324Z","dependency_job_id":"e18931f5-04f9-4ed2-b107-fba53b40bff7","html_url":"https://github.com/k-karna/multivariable_calculus","commit_stats":null,"previous_names":["k-karna/multivariable_calculus"],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/k-karna%2Fmultivariable_calculus","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/k-karna%2Fmultivariable_calculus/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/k-karna%2Fmultivariable_calculus/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/k-karna%2Fmultivariable_calculus/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/k-karna","download_url":"https://codeload.github.com/k-karna/multivariable_calculus/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":247713275,"owners_count":20983680,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","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":["multivariable-calculus","real-valued-functions"],"created_at":"2025-04-07T18:47:49.691Z","updated_at":"2025-04-07T18:47:50.257Z","avatar_url":"https://github.com/k-karna.png","language":"Jupyter Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"\u003ccenter\u003e\u003ch2\u003e Multivariable Calculus\u003c/h2\u003e\u003c/center\u003e \n\u003ccenter\u003e\u003ch4\u003eAuthor: Don Shimamoto\u003c/h4\u003e\u003c/center\u003e\n\n### I: Preliminaries\n\n### II: Vector-valued function of one variable\n\n#### Chapter 2: Path and Curves\n- Parametrizations\n- Velocity, acceleration, speed, arclength\n- Intgrals with respect to arclength\n- The geometry of curves: tangent and normal vectors\n- The cross product\n- The geometry of space curves: Frenet vectors\n- Curvature and torsion\n- The Frenet-Serret formulas\n- The classification of space curves\n- **Exercise for Chapter 2**\n\n### III: Real-Valued Functions\n#### Chapter 3: Real-valued functions: Preliminaries\n- Graphs and level sets\n- More surface in $\\mathbb{R}^3$\n- The equation of a plane in $\\mathbb{R}^3$\n- Open sets\n- Continuity\n- Some properties of continuous functions\n- The Cauchy-Schwarz and triangle inequalities\n- Limits\n- **Exercise for chapter 3**\n\n#### Chapter 4: Real-valued functions: Differentiation\n- The first-order approximation\n- Conditions for differentiability\n- The mean value theorem\n- The $C^1$ test\n- The Little Chain Rule\n- Directional derivatives\n- $\\nabla f$ as normal vector\n- Higher-order partial derivatives\n- Smooth functions\n- Max/Min: Critical points\n- Classifying nondegenrate critical points\n- Max/Min: Lagrange Multipliers\n- **Exercise for chapter 4**\n\n#### Chapter 5: Real-valued fuctions: Integration\n- Volume and iterated integrals\n- The double integral\n- Interpretations of the double integral\n- Parametrization of surfaces\n  - Polar Coordinates $(r, \\theta)$ in $\\mathbb{R}^2$\n  - Cylindrical coordinates $(r, \\theta, z)$ in $\\mathbb{R}^3$\n  - Spherical coordinates $(p, \\phi , \\theta)$ in $\\mathbb{R}^3$\n- Integrals with respect to surface area\n- Triple integrals and beyond\n- **Exercise for chapter 5**\n\n### IV: Vector-valued Functions\n#### Chapter 6: Differentiability and the Chain rule\n- Continuity revisited\n- Differentiability revisited\n- The chain rule : a conceptual approach\n- The chain rule : a computational approach\n- **Exercise for chapter 6**\n\n#### Chapter 7: Change of Variables\n- Change of vaiables for double integrals\n- A word about substitution\n- Examples : Linear changes of variables, symmetry\n- Change of variables for $n-$fold integrals\n- **Exercise for chapter 7**\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fk-karna%2Fmultivariable_calculus","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fk-karna%2Fmultivariable_calculus","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fk-karna%2Fmultivariable_calculus/lists"}