Derivative And Engineering
Let’s go beyond the mechanics. Differential calculus is a tool, invented to solve the most challenging problems in science and engineering. For instance, Newton used differential calculus to express the equations of planetary motion around the Sun, as well as the rate at which a warm object cools off in a colder environment. This week, you’ll become familiar with more of those applications by presenting them to your classmates.
Please research at least one source of information on engineering applications of derivatives.
Create a summary of what you found (in your own words!) and describe an example application. Keep your post clear and concise, under 500 words.
Sample Solution
Differential calculus is a mathematical tool used to solve complex problems in science and engineering. Differentiation, the process of taking derivatives, describes how a variable changes over time or with respect to another variable. In engineering applications, derivatives are often used to uncover relationships between force and motion or to find an optimal solution for a specific problem.
For example, engineers use derivatives when designing roller coasters so that they optimize safety while still creating an enjoyable experience for riders (Nakamura et al., 2017). By taking the derivative of position with respect to time (velocity) and acceleration with respect to time (acceleration), they can calculate the forces exerted on riders at different points on the track in order to design it so these forces do not exceed safe levels. They then use this information along with their own expertise in physics and mathematics to create an aesthetically pleasing design that delivers thrills without jeopardizing passenger safety.
In addition, engineers also rely heavily on derivatives when studying fluid flow around objects such as airplanes or boats. By deriving equations for velocity of air particles relative to lift coefficient and drag coefficient, engineers can estimate how much fuel is required for a plane’s wingspan or shape up its outer body properly (Bettelheim & Wang 1998). Such calculations are essential in allowing planes fly farther distances more efficiently while keeping them aerodynamically sound enough not get affected by the wind turbulence around it easily.
Overall, differential calculus has become an invaluable tool for engineers who wish to develop efficient designs that take into account all relevant variables associated with certain phenomena like motion or fluid flow (Nakamura et al., 2017). This type of mathematics allows them gain insights into complex physical processes while optimizing solutions based upon desired outcomes which makes it extremely useful both in industry and research applications
