Multivariable Calculus explores functions of multiple variables, including partial derivatives, multiple integrals, and vector calculus.
Sometimes, we want to add up values not just over flat regions or volumes, but along curves (paths) or across surfaces.
A line integral sums a function along a curve. In physics, it can represent work done by a force along a path.
A surface integral adds up a function's values over a surface—imagine calculating the sunlight hitting a curved rooftop.
Finding the total electric flux through a spherical surface.
Calculating the work needed to drag a sled along a winding path.
Line and surface integrals let us add up quantities along curves and across surfaces, vital in physics and engineering.