{"id":15728269,"url":"https://github.com/mikeroyal/calculus-guide","last_synced_at":"2026-01-08T09:06:39.033Z","repository":{"id":47271752,"uuid":"403407762","full_name":"mikeroyal/Calculus-Guide","owner":"mikeroyal","description":"Calculus Guide","archived":false,"fork":false,"pushed_at":"2021-09-05T21:55:32.000Z","size":29,"stargazers_count":15,"open_issues_count":0,"forks_count":2,"subscribers_count":3,"default_branch":"main","last_synced_at":"2025-02-06T07:14:07.542Z","etag":null,"topics":["calculus","calculus-2","calculus-of-variations","integrals","math","mathematics","theorems"],"latest_commit_sha":null,"homepage":"","language":null,"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/mikeroyal.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}},"created_at":"2021-09-05T20:35:51.000Z","updated_at":"2025-01-22T23:34:21.000Z","dependencies_parsed_at":"2022-09-04T09:31:16.998Z","dependency_job_id":null,"html_url":"https://github.com/mikeroyal/Calculus-Guide","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mikeroyal%2FCalculus-Guide","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mikeroyal%2FCalculus-Guide/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mikeroyal%2FCalculus-Guide/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mikeroyal%2FCalculus-Guide/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/mikeroyal","download_url":"https://codeload.github.com/mikeroyal/Calculus-Guide/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":246403902,"owners_count":20771527,"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":["calculus","calculus-2","calculus-of-variations","integrals","math","mathematics","theorems"],"created_at":"2024-10-03T23:01:50.622Z","updated_at":"2026-01-08T09:06:38.969Z","avatar_url":"https://github.com/mikeroyal.png","language":null,"funding_links":[],"categories":[],"sub_categories":[],"readme":"\u003ch1 align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132140810-9aad1ff2-f5b9-4f68-963f-06fa30b04aa6.png\"\u003e\n  \u003cbr /\u003e\n  Calculus Guide\n\u003c/h1\u003e\n\n#### A guide covering Calculus including the Formulas, Equations and Theorems that will help you a better understand practical applications of Calulus.\n\n**Note: You can easily convert this markdown file to a PDF in [VSCode](https://code.visualstudio.com/) using this handy extension [Markdown PDF](https://marketplace.visualstudio.com/items?itemName=yzane.markdown-pdf).**\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132140811-a92ceeea-faa4-4953-a29e-25adc41ce9d9.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\n# Table of Contents\n\n1. [Calculus Learning Resources](https://github.com/mikeroyal/Calculus-Guide#calculus-learning-resources)\n\n2. [Introduction to Calculus](https://github.com/mikeroyal/Calculus-Guide#introduction-to-calculus)\n\n   - Velocity and Distance\n   - Calculus Without Limits\n   - The Velocity at an Instant\n   - Circular Motion\n   - Trigonometry Review\n   - Thousand Points of Light\n   - Computing in Calculus\n\n3. [Derivatives](https://github.com/mikeroyal/Calculus-Guide#derivatives)\n\n   - The Derivative of a Function\n   - Powers and Polynomials\n   - The Slope and the Tangent Line\n   - Derivative of the Sine and Cosine\n   - Product and Quotient and Power Rules\n   - Limits\n   - Continuous Functions\n\n4. [Applications of the Derivative](https://github.com/mikeroyal/Calculus-Guide#applications-of-the-derivative)\n\n   - Linear Approximation\n   - Maximum and Minimum Problems\n   - Second Derivatives: Minimum vs. Maximum\n   - Graphs\n   - Ellipses, Parabolas, and Hyperbolas\n   - Iterations x,+ ,= F(x,)\n   - Newton's Method and Chaos\n   - Mean Value Theorem and L 'Hôpital's Rule\n\n5. [The Chain Rule](https://github.com/mikeroyal/Calculus-Guide#the-chain-rule)\n\n   - Derivatives by the Charin Rule\n   - Implicit Differentiation and Related Rates\n   - Inverse Functions and Their Derivatives\n   - Inverses of Trigonometric Functions\n\n6. [Integrals](https://github.com/mikeroyal/Calculus-Guide#integrals)\n\n   - What is an Integral\n   - Antiderivatives\n   - Summation vs. Integration\n   - Indefinite Integrals and Substitutions\n   - The Definite Integral\n   - Properties of the Integral and the Average Value\n   - The Fundamental Theorem and Its Consequences\n   - Numerical Integration\n\n7. [Exponentials and Logarithms](https://github.com/mikeroyal/Calculus-Guide#exponentials-and-logarithms)\n\n   - The Exponential e^x\n   - Growth and Decay in Science and Economics\n   - Logarithms\n   - Separable Equations Including the Logistic Equation\n   - Powers Instead of Exponentials\n   - Hyperbolic Functions\n\n8. [Techniques of Integration](https://github.com/mikeroyal/Calculus-Guide#techniques-of-integration)\n\n   - Integration by Parts\n   - Trigonometric Integrals\n   - Trigonometric Substitutions\n   - Partial Fractions\n   - Improper Integrals\n\n\n9. [Applications of the Integral](https://github.com/mikeroyal/Calculus-Guide#applications-of-the-integral)\n\n   - Areas and Volumes by Slices\n   - Length of a Plane Curve\n   - Area of a Surface of Revolution\n   - Probability and Calculus\n   - Masses and Moments\n   - Force, Work, and Energy\n\n10. [Polar Coordinates and Complex Numbers](https://github.com/mikeroyal/Calculus-Guide#polar-coordinates-and-complex-numbers)\n\n   - Polar Coordinates\n   - Polar Equations and Graphs\n   - Slope, Length, and Area for Polar Curves\n   - Complex Numbers\n\n11. [Infinite Series](https://github.com/mikeroyal/Calculus-Guide#infinite-series)\n\n   - The Geometric Series\n   - Convergence Tests: Positive Series\n   - Convergence Tests: All Series\n   - The Taylor Series for e^x, sin x, and cos x\n   - Power Series\n\n12. [Vectors and Matrices](https://github.com/mikeroyal/Calculus-Guide#vectors-and-matrices)\n\n   - Vectors and Dot Products\n   - Planes and Projections\n   - Cross Products and Determinants\n   - Matrices and Linear Equations\n   - Linear Algebra in Three Dimensions\n\n\n13. [Motion along a Curve](https://github.com/mikeroyal/Calculus-Guide#motion-along-a-curve)\n\n   - The Position Vector\n   - Plane Motion: Projectiles and Cycloids\n   - Tangent Vector and Normal Vector\n   - Polar Coordinates and Planetary Motion\n\n\n14. [Partial Derivatives](https://github.com/mikeroyal/Calculus-Guide#partial-derivatives)\n\n   - Surface and Level Curves\n   - Partial Derivatives\n   - Tangent Planes and Linear Approximations\n   - Directional Derivatives and Gradients\n   - The Chain Rule\n   - Maxima, Minima, and Saddle Points\n   - Constraints and Lagrange Multipliers\n\n\n15. [Multiple Integrals](https://github.com/mikeroyal/Calculus-Guide#multiple-integrals)\n\n   - Double Integrals\n   - Changing to Better Coordinates\n   - Triple Integrals\n   - Cylindrical and Spherical Coordinates\n\n16. [Vector Calculus](https://github.com/mikeroyal/Calculus-Guide#vector-calculus)\n\n   - Vector Fields\n   - Line Integrals\n   - Green's Theorem\n   - Surface Integrals\n   - The Divergence Theorem\n   - Stokes' Theorem and the Curl of F\n\n# Calculus Learning Resources\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n[Calulus](https://en.wikipedia.org/wiki/Calculus) is the mathematical study of continuous change where there is two major branches, [Differential calculus](https://en.wikipedia.org/wiki/Differential_calculus) and [Integral calculus](https://en.wikipedia.org/wiki/Integral).\n\n[Wolfram Course Assistant Apps: Calculus Step-by-Step](http://products.wolframalpha.com/courseassistants/calculus.html)\n\n[Wolfram Course Assistant Apps: multivariable Step-by-Step](https://products.wolframalpha.com/courseassistants/mvcalculus.html)\n\n[Calculus - Math is Fun](https://www.mathsisfun.com/calculus/)\n\n[Calculus 1 | Khan Academy](https://www.khanacademy.org/math/calculus-1)\n\n[Differential Calculus | Khan Academy](https://www.khanacademy.org/math/differential-calculus)\n\n[Top Calculus Courses Online | Coursera](https://www.coursera.org/courses?query=calculus)\n\n[Introduction to Calculus | Coursera](https://www.coursera.org/learn/introduction-to-calculus)\n\n[Mathematics for Machine Learning: Multivariate Calculus | Coursera](https://www.coursera.org/learn/multivariate-calculus-machine-learning)\n\n[Calculus - Mathematics for Data Science - Machine Learning](https://www.udemy.com/course/deep-learning-calculus-data-science-machine-learning-ai/)\n\n[Calculus and Optimization for Machine Learning Course | Coursera](https://www.coursera.org/learn/calculus-and-optimization-for-machine-learning)\n\n[Learn Calculus 1 and Become a Calculus Master Course | Udemy](https://www.udemy.com/course/calculus1/)\n\n[Become a Calculus 2 Master Course | Udemy](https://www.udemy.com/course/calculus-2/)\n\n[Become a Calculus 3 Master Course | Udemy](https://www.udemy.com/course/calculus-3/)\n\n[Calculus 3 (multivariable calculus) | Udemy](https://www.udemy.com/course/calculus-3-multivariable-calculus-part-1-of-2/)\n\n[Learn Calculus with Online Courses | edX](https://www.edx.org/learn/calculus)\n\n[Online Calculus Courses | Harvard University](https://online-learning.harvard.edu/subject/calculus)\n\n[Calculus 1 | Harvard University - Harvard Online Courses](https://online-learning.harvard.edu/course/calculus-1)\n\n[Mathematics | MIT OpenCourseWare | Free Online Courses](https://ocw.mit.edu/courses/mathematics/)\n\n[Single Variable Calculus | Mathematics | MIT OpenCourseWare](https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/)\n\n[The Organic Chemistry Tutor - Calculus Video Playlist | YouTube](https://www.youtube.com/playlist?list=PL0o_zxa4K1BWYThyV4T2Allw6zY0jEumv)\n\n[Calculus I - Pauls Online Math Notes](https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx)\n\n[Calculus II - Pauls Online Math Notes](https://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx)\n\n[Calculus III - Pauls Online Math Notes](https://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx)\n\n# Introduction to Calculus\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n### Velocity and Distance\n\n### Calculus Without Limits\n\n### The Velocity at an Instant\n\n### Circular Motion\n\n### Trigonometry Review\n\n### Thousand Points of Light\n\n### Computing in Calculus\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141978-dcb03fe5-ab48-43e7-ad30-c44410635847.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nDistance and Velocity Formulas.\n\n# Derivatives\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n### The Derivative of a Function\n\n### Powers and Polynomials\n\n### The Slope and the Tangent Line\n\n### Derivative of the Sine and Cosine\n\n### The Product and Quotient and Power Rules\n\n### Limits\n\n### Continuous Functions\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132140821-1870bd8b-28db-4026-97b4-31dec590c732.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nDerivative Rules. Source: [onlinemathlearning](https://www.onlinemathlearning.com/derivative-rules.html)\n\n\n# Applications of the Derivative\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n### Linear Approximation\n\n### Maximum and Minimum Problems\n\n### Second Derivatives: Minimum vs. Maximum\n\n### Graphs\n\n### Ellipses, Parabolas, and Hyperbolas\n\n### Iterations x,+ ,= F(x,)\n\n### Newton's Method and Chaos\n\n### The Mean Value Theorem and L'Hôpital's Rule\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132140823-a5ab549e-28f5-4f91-a28d-0ec4964b3ab5.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nDerivatives and Limits. Source: [EEWeb](https://www.eeweb.com/tools/online-scientific-calculator/)\n\n# The Chain Rule\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n### Derivatives by the Charin Rule\n\n### Implicit Differentiation and Related Rates\n\n### Inverse Functions and Their Derivatives\n\n### Inverses of Trigonometric Functions\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141393-a0ce6be9-cc37-43a8-ae1b-bbaedec64e13.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nChain Rule. Source: [onlinemathlearning](https://www.onlinemathlearning.com/chain-rule.html)\n\n\n# Integrals\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n### What is an Integral\n\n### Antiderivatives\n\n### Summation vs. Integration\n\n### Indefinite Integrals and Substitutions\n\n### The Definite Integral\n\n### Properties of the Integral and the Average Value\n\n### The Fundamental Theorem and Its Consequences\n\n### Numerical Integration\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141982-cf89ede1-7939-453a-9406-f6989323d734.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nProperties of Integrals \u0026 Integration Rules. Source: [OSU.edu](https://mslc.osu.edu/sites/mslc.osu.edu/files/Integral%20Calculus%20Formula%20Sheet_0.pdf)\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132140812-e5467311-aba5-41bb-ae9b-503fa3362116.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nFund. Theorem of Calulus, Riemann Sums, and Net Change. Source: [OSU.edu](https://mslc.osu.edu/sites/mslc.osu.edu/files/Integral%20Calculus%20Formula%20Sheet_0.pdf)\n\n\n# Exponentials and Logarithms\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n### The Exponential e^x\n\n### Growth and Decay in Science and Economics\n\n### Logarithms\n\n### Separable Equations Including the Logistic Equation\n\n### Powers Instead of Exponentials\n\n### Hyperbolic Functions\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141407-76cd6160-9c2a-4862-93cb-adcefdef3081.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nExponents and Logarithms. Source: [onlinemathlearning](https://www.onlinemathlearning.com/logarithms-exponents.html)\n\n# Techniques of Integration\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n### Integration by Parts\n\n### Trigonometric Integrals\n\n### Trigonometric Substitutions\n\n### Partial Fractions\n\n### Improper Integrals\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141450-6d54da79-37fc-419a-b2bf-d339b6da3446.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nTechniques of Integration. Source: [OSU.edu](https://mslc.osu.edu/sites/mslc.osu.edu/files/Integral%20Calculus%20Formula%20Sheet_0.pdf)\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141455-2faf8c02-0201-4228-986e-1d49a5381d59.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nTechniques of Integration Part 2. Source: [OSU.edu](https://mslc.osu.edu/sites/mslc.osu.edu/files/Integral%20Calculus%20Formula%20Sheet_0.pdf)\n\n# Applications of the Integral\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n### Areas and Volumes by Slices\n\n### Length of a Plane Curve\n\n### Area of a Surface of Revolution\n\n### Probability and Calculus\n\n### Masses and Moments\n\n### Force, Work, and Energy\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141495-70fc0a00-8c3b-4c79-b75d-7a19da480b11.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nSurface Area of Revolution of Parametric Equations. Source: [YouTube](https://www.youtube.com/watch?v=USiKDtILhmc)\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141496-c034c3a2-70a5-4258-a8e2-e9837f53fa88.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nAreas and Volumes. Source: [OSU.edu](https://mslc.osu.edu/sites/mslc.osu.edu/files/Integral%20Calculus%20Formula%20Sheet_0.pdf)\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141500-c42c32f6-aaa7-40a1-979a-921f3c2999c2.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nPhysical Applications. Source: [OSU.edu](https://mslc.osu.edu/sites/mslc.osu.edu/files/Integral%20Calculus%20Formula%20Sheet_0.pdf)\n\n# Polar Coordinates and Complex Numbers\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n### Polar Coordinates\n\n### Polar Equations and Graphs\n\n### Slope, Length, and Area for Polar Curves\n\n### Complex Numbers\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141505-d7fe6ddc-aa41-4d6b-8851-871efbf498fa.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nPolar Coordinates - Rectangular. Source: [getcalc](https://getcalc.com/geometry-rectangle-polar-calculator.htm)\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132142408-3f2b8920-6867-4cff-9c27-f70cec43473c.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nArea in Polar Coordinates. Source: [Calcworkshop](https://calcworkshop.com/polar-functions/area-polar-coordinates/)\n\n# Infinite Series\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n### The Geometric Series\n\n### Convergence Tests: Positive Series\n\n### Convergence Tests: All Series\n\n### The Taylor Series for e^x, sin x, and cos x\n\n### Power Series\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141539-f05442a0-cfc8-427d-8419-90ca8cb40e3a.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nGeometric Series. Source: [onlinemathlearning](https://www.onlinemathlearning.com/geometric-series.html)\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141542-30b7f8d9-ab94-4632-9949-eeecf9f5e364.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nTaylor and MacLaurin Series. Source: [onlinemathlearning](https://www.onlinemathlearning.com/taylor-maclaurin-series.html)\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141540-cf6c84d9-466d-40b2-8b2a-df58f339fc33.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nPower Series. Source: [onlinemathlearning](https://www.onlinemathlearning.com)\n\n# Vectors and Matrices\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n### Vectors and Dot Products\n\n### Planes and Projections\n\n### Cross Products and Determinants\n\n### Matrices and Linear Equations\n\n### Linear Algebra in Three Dimensions\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141578-81028690-d33e-4b07-8944-754e6e4ec630.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nScalar, Vector, Matrix. Source: [mathisfun](http://www.mathsisfun.com/algebra/scalar-vector-matrix.html)\n\n\n# Motion along a Curve\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n### The Position Vector\n\n### Plane Motion: Projectiles and Cycloids\n\n### Tangent Vector and Normal Vector\n\n### Polar Coordinates and Planetary Motion\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141580-86d71ab4-8180-472d-8fd8-281d6e996d9b.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nPosition Vectors. Source [YouTube](http://www.youtube.com/watch?v=v3uhB6LhXis)\n\n# Partial Derivatives\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n### Surface and Level Curves\n\n### Partial Derivatives\n\n### Tangent Planes and Linear Approximations\n\n### Directional Derivatives and Gradients\n\n### The Chain Rule\n\n### Maxima, Minima, and Saddle Points\n\n### Constraints and Lagrange Multipliers\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141617-de61fe77-e536-4e6a-a9dd-4c4c30f70e01.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nChain Rule With Partial Derivatives. Source: [YouTube](https://www.youtube.com/watch?v=XipB_uEexF0)\n\n\n# Multiple Integrals\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n\n### Double Integrals\n\n### Changing to Better Coordinates\n\n### Triple Integrals\n\n### Cylindrical and Spherical Coordinates\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141623-018c8a05-3a0e-428a-afa2-7b51a8f85891.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nDouble Integrals. Source: [YouTube](https://www.youtube.com/watch?v=BJ_0FURo9RE)\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141624-b27fb107-e899-4f3b-9ac7-310585196a81.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nTriple Integrals. Source: [YouTube](https://www.youtube.com/watch?v=7iy83x8bv6o)\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132142124-27571c7f-1565-4f8f-8445-d965331e7828.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nCylindrical and Spherical Coordinates.\n\n# Vector Calculus\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\n### Vector Fields\n\n### Line Integrals\n\n### Green's Theorem\n\n### Surface Integrals\n\n### The Divergence Theorem\n\n### Stokes' Theorem and the Curl of F\n\n\u003cp align=\"center\"\u003e\n \u003cimg src=\"https://user-images.githubusercontent.com/45159366/132141648-66e77401-bda8-4165-99ee-1b4429682088.png\"\u003e\n  \u003cbr /\u003e\n\u003c/p\u003e\n\nVector Calculus Forumlas. Source: [vectorified](https://vectorified.com/vector-calculus-formulas)\n\n\n## Contribute\n\n- [x] If would you like to contribute to this guide simply make a [Pull Request](https://github.com/mikeroyal/Calculus-Guide/pulls).\n\n\n## License\n[Back to the Top](https://github.com/mikeroyal/Calculus-Guide#table-of-contents)\n\nDistributed under the [Creative Commons Attribution 4.0 International (CC BY 4.0) Public License](https://creativecommons.org/licenses/by/4.0/).\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmikeroyal%2Fcalculus-guide","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmikeroyal%2Fcalculus-guide","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmikeroyal%2Fcalculus-guide/lists"}