Math: High school & college Ages 14-18 ● Media ready

Multivariable calculus

Learn multivariable calculus—derivatives and integrals of multivariable functions, application problems, and more.

5 units 51 lessons 175 videos 11 on CDN

First 3 lessons are free Unlock every lesson with Pro —
watch the rest of this course and all others. Create free account Go Pro

Unit 2 Thinking about multivariable functions

1 Introduction to multivariable calculus Free 1 video(s) ● 2 Vectors and matrices Free 3 Visualizing scalar-valued functions Free 4 video(s) ● 4 Visualizing vector-valued functions 🔒 Pro 6 video(s) ● 5 Transformations 🔒 Pro 3 video(s) 6 Visualizing multivariable functions (articles) 🔒 Pro

Unit 3 Derivatives of multivariable functions

1 Partial derivatives 🔒 Pro 4 video(s) 3 Gradient and directional derivatives 🔒 Pro 7 video(s) 4 Partial derivative and gradient (articles) 🔒 Pro 6 Differentiating parametric curves 🔒 Pro 2 video(s) 7 Multivariable chain rule 🔒 Pro 5 video(s) 9 Curvature 🔒 Pro 9 video(s) 10 Partial derivatives of vector-valued functions 🔒 Pro 5 video(s) 11 Differentiating vector-valued functions (articles) 🔒 Pro 12 Divergence 🔒 Pro 6 video(s) 14 Curl 🔒 Pro 10 video(s) 15 Divergence and curl (articles) 🔒 Pro 17 Laplacian 🔒 Pro 4 video(s) 18 Jacobian 🔒 Pro 5 video(s) 14 Green's, Stokes', and the divergence theorems: Unit test 🔒 Pro

Unit 4 Applications of multivariable derivatives

1 Tangent planes and local linearization 🔒 Pro 4 video(s) 2 Quadratic approximations 🔒 Pro 7 video(s) 4 Optimizing multivariable functions 🔒 Pro 7 video(s) 5 Optimizing multivariable functions (articles) 🔒 Pro 7 Lagrange multipliers and constrained optimization 🔒 Pro 8 video(s) 8 Constrained optimization (articles) 🔒 Pro

Unit 5 Integrating multivariable functions

1 Line integrals for scalar functions 🔒 Pro 4 video(s) 2 Line integrals for scalar functions (articles) 🔒 Pro 3 Line integrals in vector fields 🔒 Pro 9 video(s) 4 Line integrals in vector fields (articles) 🔒 Pro 6 Double integrals 🔒 Pro 6 video(s) 7 Double integrals (articles) 🔒 Pro 1 video(s) 9 Triple integrals 🔒 Pro 3 video(s) 10 Change of variables 🔒 Pro 12 Polar, spherical, and cylindrical coordinates 🔒 Pro 13 Surface integral preliminaries 🔒 Pro 3 video(s) 14 Surface integrals 🔒 Pro 13 video(s) 15 Surface integrals (articles) 🔒 Pro 17 Flux in 3D 🔒 Pro 3 video(s) 18 Flux in 3D (articles) 🔒 Pro

Unit 6 Green's, Stokes', and the divergence theorems

1 Formal definitions of div and curl (optional reading) 🔒 Pro 2 Green's theorem 🔒 Pro 4 video(s) 3 Green's theorem (articles) 🔒 Pro 4 2D divergence theorem 🔒 Pro 3 video(s) 6 Stokes' theorem 🔒 Pro 11 video(s) 7 Stokes' theorem (articles) 🔒 Pro 8 3D divergence theorem 🔒 Pro 3 video(s) 9 Divergence theorem (articles) 🔒 Pro 11 Proof of Stokes' theorem 🔒 Pro 7 video(s) 12 Types of regions in three dimensions 🔒 Pro 3 video(s) 13 Divergence theorem proof 🔒 Pro 5 video(s)