Maybe I will write the obvious answer:
Isaac Newton and Gottfried Leibniz are said to have invented calculus independently (even if there is a priority dispute). Both were working on the math but also on applications.
Isaac Newton used calculus to reformulate the concepts of motion and dynamics (position, velocity, acceleration, force) in terms of derivatives (or fluxions as he called it, see Newton's De Methodis Serierum et Fluxionum published in 1763). He also applied calculus to describe the motion of astronomical bodies and in optics. These steps led to the development of what we now call classical physics (and all of its derivatives like planetary motion prediction and mechanical engineering). Newton's Principia may have avoided to use calculus, but there is some of it, for more details check answers here: Why is calculus missing from Newton's Principia?
As for Leibniz, I cannot provide a complete idea of everything he did but he certainly applied calculus to physics like the brachistochrone problem (Newton also got a solution for it) and rigid beams calculations (see here).