Application of calculus in our daily life
- 1. Assignment No 1 B S C S 1 C R o l l n o . 1 2 1 R e h a n u l h a q Use of calculus in daily life Use of calculus in science and engineering
- 2. Application of calculus in our daily life Among the disciplines that utilize calculus include physics, engineering, economics, statistics, and medicine. It is used to create mathematical models in order to arrive into an optimal solution. For example, in physics, calculus is used in a lot of its concepts. Algorithms are used every day by major search engine companies to help refine searches for the person behind the keyboard. Algorithms are calculations used to compile a large amount of data and variables into an equation, spitting out the best possible answer. These algorithms are what makes search engines so adept at finding the precise answer quickly. They take into account variables such as the user's geographic location, web history and how useful other users have found similar webpages to create an appropriate search result. All of these variables are utilized to define the rules and constraints of sequent calculus equations that produce the most logical and effective results.
- 3. Weather is more accurately predicted than ever before. Part of the improvement is thanks to technology, such as computer modelling that uses calculus and is able to more meticulously predict upcoming weather. These computer programs also use types of algorithms to help assign possible weather outcomes in a region. Much like in the computer algorithms, weather forecasts are determined by considering many variables, such as wind speed, moisture level and temperature. Though computers do the heavy lifting of sifting through massive amounts of data, the basics of meteorology are grounded in differential equations, helping meteorologists determine how changes in the temperatures and pressures in the atmosphere may indicate changes in the weather. The field of epidemiology -- the study of the spread of infectious disease -- relies heavily on calculus. Such calculations have to take three main factors into account: those people who are susceptible to a disease, those who are infected with the disease and those who have already recovered from it. With these three variables, calculus can be used to determine how far and fast a disease is spreading, where it may have originated from and how to best treat it. Calculus is especially important in cases such as this because rates of infection and recovery change over time, so the equations must be dynamic enough to respond to the new models evolving every day. Calculus is used to improve the architecture not only of buildings but also of important infrastructures such as bridges. Bridges are complex constructions because they have to be able to support varying
- 4. amounts of weight across large spaces. When designing a bridge, one must take into account factors including weight, environmental factors and distance. Because of this, maths such as differential calculus and integral calculus are often used to create the most robust design. The use of calculus is also creating a change in the way other architecture projects are designed, pushing the frontier of what sorts of shapes can be used to create the most beautiful buildings. For example, though many buildings have arches with perfect symmetry, calculus can be used to create archways that are not symmetric along with other odd shapes that are still able to be structurally sound. Calculus is used in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modelled and an optimal solution is
- 5. desired. It allows one to go from (non-constant) rates of change to the total change or vice versa, and many times in studying a problem we know one and are trying to find the other. Calculus, defined as the mathematical study of change, was developed independently by Isaac Newton and Gottfried Wilhelm von Leibniz in the 17th century. Engineering is defined as "the profession in which a knowledge of the mathematical and natural sciences gained by study, experience, and practice is applied with judgment to develop ways to utilize, economically, the materials and forces of nature for the benefit of mankind." Some engineers directly use calculus in their daily practice and some use computer programs based on calculus that simplify engineering design. Two methods of calculus, differentiation and integration, are particularly useful in the practice of engineering, and are generally used for optimization and summation, respectively.
- 6. Many aspects of civil engineering require calculus. Firstly, derivation of the basic fluid mechanics equations requires calculus. For example, all hydraulic analysis programs, which aid in the design of storm drain and open channel systems, use calculus numerical methods to obtain the results. In hydrology, volume is calculated as the area under the curve of a plot of flow versus time and is accomplished using calculus.
- 7. In structural engineering, calculus is used to determine the forces in complex configurations of structural elements. Structural analysis relating to seismic design requires calculus. In a soil structure context, calculations of bearing capacity and shear strength of soil are done using calculus, as is the determination of lateral earth pressure and slope stability in complex situations. Many examples of the use of calculus are found in mechanical engineering, such as computing the surface area of complex objects to determine frictional forces, designing a pump according to flow rate and head, and calculating the power provided by a battery
- 8. system. Newton's law of cooling is a governing differential equation in HVAC design that requires integration to solve. Numerous examples of the use of calculus can be found in aerospace engineering. Thrust over time calculated using the ideal rocket equation is an application of calculus. Analysis of rockets that function in stages also requires calculus, as does gravitational modelling over time and space. Almost all physics models, especially those of astronomy and complex systems, use some form of calculus.