Physics, like other branches of science, would not be explained without experimental observations and quantitative measurements. The core purpose of physics is to discover those limited number of those fundamental laws that are related to some natural phenomena, and to use them to create new theories that can help predict the consequences of other experiments. These fundamental laws are often in the form of some mathematical expressions, those expressions which help us understand and analyse the results of new experiments.
When an experiment cannot be explained using one or more than one of the existing theories, there is a need to devise or update the existing theories to the level where they can explain and analyse the experiment. Some theories have limitations while other which are general are not limited to some specifications. "For example, the laws of motion discovered by Isaac Newton (1642–1727) in the 17th century accurately describe the motion of bodies at normal speeds but do not apply to objects moving at speeds comparable with the speed of light." (Quoted From "Fundamentals of Physics" by Halliday and Resnick,) "In contrast, the special theory of relativity developed by Albert Einstein (1879–1955) in the early 1900s gives the same results as Newton’s laws at low speeds but also correctly describes motion at speeds approaching the speed of light." Here we say that Newton's theory was specific to the bodies moving with normal speeds, while, Einstein's theory was more general that can describe the motion of bodies moving with normal speeds as well as high speeds.
The physics which was developed before 20th Century is called Classical Physics. It includes all the experimental and theoretical work done in classical mechanics, electromagnetism and thermodynamics. The major contributions in the classical physics are provided by Newton. He is known to be one of the originators of the calculus.
The physics which began to develop near the end of 19th century is called Modern Physics. The motivation behind the discovery of this new era physics or modern physics was, that, many natural phenomena occurring in the nature were still undefined in scope of Classical Physics. This led to the development of new theories i.e. Theory of Relativity and Quantum Mechanics. Theory of relativity was developed by Einstein and it gave the scientists new ways to think about space, time, and energy. The quantum mechanics is the results of the hard work of number of distinguished scientists. It applies on both, microscopic and macroscopic worlds.
Thus, Physics is the core subject for many engineering courses, because it provides both experimental and mathematical explanation of the physical phenomena occurring in nature. It is important because it provides the explanation of other sciences as well. Our motivation towards studying this course is to understand and analyze many physical phenomena around us, which should be a hobby for an engineer.
