Calculus 3

Calculus 3 covers advanced topics in multivariable calculus, including partial derivatives, multiple integrals, and vector calculus.

Functions of Several VariablesPartial DerivativesMultiple Integrals
Vector Fields and GradientLine and Surface IntegralsDivergence, Curl, and the Big Theorems
Modeling Weather and ClimateEngineering and Physics ApplicationsEconomics and Resource Management
Visualization and SketchingBreaking Down Problems
Functions of Several...Partial DerivativesMultiple IntegralsVector Fields and Gr...Line and Surface Int...Divergence, Curl, an...Modeling Weather and...Engineering and Phys...Economics and Resour...Visualization and Sk...Breaking Down Proble...
Study Strategies

Visualization and Sketching

Drawing Your Way to Understanding

Sketching graphs, surfaces, and vector fields helps you truly see what equations mean. Whenever possible, draw level curves, surfaces, or field diagrams. This makes complicated ideas much more approachable and memorable.

  • Use color to distinguish different features.
  • Try drawing by hand or with graphing software.
  • Visuals help you check your work and spot mistakes early.

Examples

  • Sketching the level curves of a function before calculating partial derivatives.

  • Drawing a vector field to understand the direction of fluid flow.

Next
Breaking Down Problems