Newtonian Mechanics

Newton was, without question, one of the great pioneers of modern physics. His second law of motion is encapsulated in one of the most famous equations of physics, which describes a differential relationship between the position x(t) and the force F : a := \frac{d^2 x}{dt^2} = \frac{F}{m}. While F and m are physical quantities, the acceleration a is more of a mathematical quantity, defined as the second derivative of position with respect to time. As physics became more quantitative, mathematics became increasingly enmeshed with physics. In fact, Newton had to invent a whole field of mathematics, calculus, in order to formalize his second law in precise mathematical terms. This is just one of numerous examples where the requirements for expressing the laws of physics prompted the development of new branches of mathematics. Mathematics, conversely, has also led to new insights in physics. Throughout the book, we are going to see much more of this back-and-forth interconnection and give-and-take between the two fields.