Calculus is a very imprortant tool in science and engineering. One very useful concept is the "integral", or the "area under a curve between an upper and lower limit". The concept of integration can be used to simulate a rocket in flight or to determine the total impulse of a rocket motor (just to name two...). This module provides some enlightening insights into the concept of the integral and includes a simple experiment to demonstrate how integrating the acceleration due to gravity can be used to predict the fall time of a ball:
As a student (or teacher) of science and engineering, you will rely on mathematical equations to solve complex problems. Many times equations will have to be combined and it can be difficult to know if the equations are "compatible" from a unit perspective. One equation may involve weight, while another uses mass... If the equations are not set up to be compatible, the wrong answer will result. This sort of problem caused the demise of a NASA Mars probe a number of years ago... This problem can be avoided by applying the concept of "unit analysis" where the units are examined to make sure thay are all compatible. This module provides some useful insights that can help you master the idea of unit analysis:
A Vector Quantity has both magnitude and direction. Force is a vector because it has a magnitude and a direction of application. A upward force will make an object move upwards. An airplane flying at 200 km/hr towards the west is also a vector. In contrast, a Scalar Quantity just has size or magnitude. Speed is a scalar quantity because there is no indication of which direction the object is moving - its simply moving at 200 km/hr. The concepts of vectors and vector mathematics are very important in engineering and science. This module outlines the fundamentals of vectors and how they are mathematically manipulated.