--- title: Multivariable Calculus description: Multivariable calculus extends single-variable calculus to functions of several variables. You will understand partial derivatives, multiple integrals, and optimization in three-dimensional space, allowing you to model and analyze complex physical systems and multi-dimensional data. category: mathematics subcategory: calculus difficulty: beginner, intermediate, advanced url: /subject/multivariable-calculus --- # Multivariable Calculus Multivariable calculus extends single-variable calculus to functions of several variables. You will understand partial derivatives, multiple integrals, and optimization in three-dimensional space, allowing you to model and analyze complex physical systems and multi-dimensional data. ## Available Resources 3 Books • 4 Courses • 2 Websites ## Websites ### 1. Paul's Online Math Notes - Calc III Complete Calculus III lecture notes from Lamar University, with worked examples and practice problems on 3D vectors, partial derivatives, multiple integrals in cylindrical and spherical coordinates, line and surface integrals, and the theorems of Green and Stokes. **Difficulty:** Beginner | **Price:** Free **Link:** https://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx **Tags:** calculus, vector-calculus, partial-derivatives, multiple-integrals, lecture-notes ### 2. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry ## Courses ### 1. Multivariable Calculus Master multivariable calculus! Explore functions of several variables, gradients, and more with this comprehensive course. **Difficulty:** Advanced | **Price:** Free **Link:** https://www.khanacademy.org/math/multivariable-calculus **Tags:** calculus, vector-calculus, partial-derivatives, vector-fields, video-lessons ### 2. Calculus Revisited: Multivariable Calculus (MIT RES.18-007) **Author:** Herbert Gross A lecture series first released in 1971 reviewing multivariable calculus: vector arithmetic and vector functions, partial derivatives, multiple and line integrals, and matrix and linear algebra ideas. Includes 26 lecture videos, study guides, supplementary notes and problem solutions, suited to first-time learners and review. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/res-18-007-calculus-revisited-multivariable-calculus-fall-2011/ **Tags:** multivariable-calculus, vector-calculus, partial-derivatives, multiple-integrals, linear-algebra ### 3. Multivariable Calculus (MIT 18.02SC) **Author:** Denis Auroux Differential, integral and vector calculus in several variables: vectors and matrices, partial derivatives, optimization, double and triple integrals, line integrals, and the theorems of Green, Stokes and Gauss. Includes 106 lecture and recitation videos, notes, and problems and exams with solutions, built for independent study. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/ **Tags:** multivariable-calculus, partial-derivatives, multiple-integrals, vector-calculus, line-integrals ### 4. Multivariable Calculus This course provides an overview of bachelor-level calculus of multivariable functions (Calculus II). You will review many basic concepts related to differentiation and integration of multivariable functions. **Difficulty:** Advanced | **Language:** English | **Price:** Free **Link:** https://www.edx.org/learn/calculus/delft-university-of-technology-calculus-ii-multivariable-functions **Tags:** courses, mathematics-statistics, calculus ## Books ### 1. Calculus Vol II - Tom M. Apostol **Author:** Tom M. Apostol Covers multi-variable calculus, linear algebra applications, and differential equations. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://amzn.to/3Z6hSgE **Tags:** calculus, multivariable-calculus, linear-algebra, differential-equations, textbook ### 2. Calculus: Multivariable **Author:** William L. Briggs, Lyle Cochran Pearson's multivariable half of the Briggs-Cochran sequence, covering vectors, curves in space, partial derivatives, multiple integration, and vector fields through Green's, Stokes', and divergence theorems, with large graded exercise sets and figures that build geometric intuition before the formal statements. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0321664159?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, calculus ### 3. Vector Calculus **Author:** Susan Jane Colley Third edition of Colley's multivariable calculus textbook, written in the language of vectors and matrices. Covers vectors, differentiation in several variables, multiple integrals, line and surface integrals, and theorems of Green, Gauss and Stokes. Readers with single-variable calculus gain fluency with multidimensional derivatives and integrals. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0131858742?tag=edmonddante07-20 **Tags:** vector-calculus, multivariable-calculus, line-integrals, surface-integrals, stokes-theorem --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/multivariable-calculus