Multivariable Calculus

Multivariable Calculus explores functions of multiple variables, including partial derivatives, multiple integrals, and vector calculus.

Functions of Several VariablesPartial DerivativesMultiple Integrals
Gradient, Divergence, and CurlLine and Surface IntegralsTheorems of Vector Calculus
Modeling Heat and DiffusionOptimizing Engineering DesignsData Science and Gradient Descent
Visualizing Surfaces and RegionsBreaking Problems into Steps
Functions of Several...Partial DerivativesMultiple IntegralsGradient, Divergence...Line and Surface Int...Theorems of Vector C...Modeling Heat and Di...Optimizing Engineeri...Data Science and Gra...Visualizing Surfaces...Breaking Problems in...
Study Strategies

Visualizing Surfaces and Regions

See the Math in Action

Drawing 3D graphs, contour plots, and vector fields can help you understand concepts in multivariable calculus. Use online graphing tools or sketch by hand. Visualizing complex surfaces and regions makes it easier to set up integrals and grasp how functions behave across spaces.

Tips

  • Color-code level curves or surfaces
  • Animate changes as variables move
  • Practice sketching simple shapes and regions

Examples

  • Sketching the contour map of a mountain to understand elevation changes.

  • Using a graphing calculator to plot a saddle surface.

Next
Breaking Problems into Steps