Math
Multivariable and Vector Calculus
Train on Multivariable and Vector Calculus with 316 published problems. Preview a problem, explore the course outline, and work through one problem at a time.
Training
Try 5 problems free
Course and path
No account needed for these. The full course is 316 problems for $19 USD a month. What's included
A free account opens the first unit of every course, with hints and solutions.
Preview a course problem
See a problem from Multivariable and Vector Calculus before you begin.
Course topics
Course topics
Geometry, vectors, and vector-valued functions
Multivariable limits, continuity, and differentiation
Constrained optimization and Lagrange multipliers
Multiple integration and change of variables
Vector fields, line integrals, and Green's theorem
Surface integrals, divergence theorem, and Stokes' theorem
Practice problems
Try a few Multivariable and Vector Calculus problems, each with a hint.
- Let A=(1,-2,4) and B=(5,2,-2) Free with an accountGeometry, vectors, and vector-valued functions
- Let C be the curve of intersection of the surfaces y=x³ and z=x² Multivariable limits, continuity, and differentiation
- A closed rectangular box has measured edge lengths x=8 cm, y=5 cm, and z=3 cm Constrained optimization and Lagrange multipliers
- Let D be the closed region in the xy-plane bounded by the parabola y=x² and the line y=x+2 Multiple integration and change of variables
- Locate the shortest connector between two skew lines Free with an accountGeometry, vectors, and vector-valued functions
- Differentiate normalization as a tangent projection Multivariable limits, continuity, and differentiation
- Diagnose a constrained minimum missed by multiplier equations Constrained optimization and Lagrange multipliers
- Straighten a product-ratio region with logarithms Multiple integration and change of variables
- Check outward flux across a parabolic cap Vector fields, line integrals, and Green's theorem
- Orient a triangular Stokes calculation Surface integrals, divergence theorem, and Stokes' theorem