Calculus 3 covers advanced topics in multivariable calculus, including partial derivatives, multiple integrals, and vector calculus.
Line integrals let us sum up values along a curve, while surface integrals sum over a surface in space. These are powerful tools for measuring things like work done by a force or the flow of a fluid.
If you walk along a path and want to know the total amount of energy expended against a force, a line integral calculates this by adding up contributions at every small step.
Surface integrals extend this idea to surfaces—imagine measuring how much sunlight hits a curved solar panel.
These integrals are essential in physics, engineering, and more, helping us understand how quantities accumulate along paths and surfaces.
Calculating work done by a force field along a path using a line integral.
Measuring fluid flow across a curved surface with a surface integral.
Line and surface integrals let us sum over curves and surfaces, not just flat regions.