The universe is constantly in motion, stars, planets, and galaxies are constantly changing. Elements, particles and subatomic matter bodily matter are not static either. Before the invention of calculus, Mathematics was static. Calculus is a branch of math that calculates how matter, particles and heavenly bodies actually move. Calculus is used to calculate the rate of change in real-time.
In the latter part of the 17th century, two scientists Sir Isaac Newton and Gottfried Leibniz. Leibniz developed mathematical notations used today (+, -, x, and ÷) Isaac Newton developed calculus and applied it directly to calculating physical systems.
With these tools, Mathematicians could calculate slopes, curvatures, rate of change and motion. It enabled them to understand motion and the dynamics of a changing universe and the elements in the world and the orbit of galactic planets.
‘Calculus’ singular or ‘Calculi’ plural – is a Latin word which means ‘small pebble’ – small stones used for counting in the abacus by the Romans. It was used for the counting of infinitely small numbers. Calculus is math in motion. It’s the calculation of change used to help describe the dynamic nature of our world.
It has two branches, differential calculus which calculates the behavior and rate at which quantities change e.g. distance changes over time. It involves the concept of derivatives of functions. The second branch is integration calculus; this is the reverse process of differentiation. It helps describe, for example, the volume of a 3d object with a curved boundary and many other similar applications. Differentiation is the opposite or the inverse of integration.
Integration breaks the region apart into thin unlimited vertical rectangles of equal width until they become a Limit. A process which allows mathematicians to calculate volumes, area, and precision. If you differentiate a function and then integrate it, it will always take you back to where you started.
Calculus is used in lots of fields, physics, engineering, medicine, economics, biology, engineering, space exploration, statistics, pharmacology and many more. Without calculus architects and engineers couldn’t build safe structures.
It is used to calculate changes in quantities and systems. Calculus helps to analyze, find optimal solutions and predict the future. Calculus has given us incredible power over the world because of its ability to model and control systems.
It is the language spoken by Engineers, Physicists, Economists, Quantity Surveyors, inventors, and Space explorers. Let’s look at some of the areas that calculus has a direct impact on our lives on a daily basis.
1. Quantifying Building Materials (Quantity surveyors)
Quantity surveyors use calculus integration to calculate the amount of material required to complete a construction project.
2. Calculating the weight of structures (Architectural Engineers)
Architectural engineers use calculus to calculate the shapes of curved structures like domes, sports arenas, suspended bridges, etc. They use calculus to improve on the architectural design of the structure.
3. Structural analysis – Seismic design
Structural engineers use calculus to determine complex configuration forces of structural elements that relate to seismic activities. They use calculus to create earthquake-proof structures that can withstand any level of earthquake tremors.
4. Soil structure
Calculus is also used in calculating soil structure and finding out the bearing capacity and strength of specific soil compositions. This helps determine lateral earth pressure and slope stability for complex projects before embarking on structural construction.
5. Building bridges (Civil Engineers)
Designing bridges has three structural elements; the beam, compression members and tension members. The beam links the shores. Calculus is used to calculate the elements of the forces acting on the beam. These will include anticipated traffic, pedestrians, traffic, etc. calculus helps determine which material to use while constructing the beam.
6. Building storm drains
Storm drains used to drain storm waters and open channels systems must have a surface area that is big enough and does not hinder the flow of water. Calculus is used to calculate the derivation of the basic fluid mechanics that has the optimum capacity for the drain.
7. Hydraulic Analysis Programs
Hydraulic analysis programs aid in the design of storm drains. It is calculated using numerical methods of calculus. The volume of water is calculated as the area under the curve of a plot of flow versus time.
8. Calculating Cable lengths (Electrical)
Integration Calculus is used in electrical engineering to calculate the exact length of power cables between two points which may be miles away from each other.
9. Space Exploration (Space engineers)
Space flight engineers when planning long exploratory space missions or working to launch exploratory probes use calculus to calculate the different orbiting velocities, the earth, and the distant planet being targeted to find out the gravitational influence of the sun and the moon.
The laws of planetary motion are used by astronomers to study the heavenly bodies. Calculus is used to calculate the rate at which position of moving bodies change over time to determine their orbits.
11. Analytical geometry
Calculus is used in Analytical geometry to find the tangent to an algebraic curve at a point, by finding a line with the double intersection with the curve at the point, to help invent integration
Calculus is used together with other mathematical disciplines like algebra to find the best linear approximation of a set of two points in a domain.
13. Bacterial growth
Biologists use differential calculus to determine the exact bacterial growth rate in a culture, in different variables e.g. temperature and food source. Logistics differential equations together with exponential equations are used to calculate the rate of bacterial growth.
14. Patient Diagnosis
Physicians estimate the rate of change at which a patient gets sick or is cured. This estimation helps drive dangerous conditions and determine appropriate action to deal with the prognosis. Calculus helps calculate these changes and make predictions.
15. Epidemiology – Calculate the rate of disease spread
Epidemiologists, people who study the spread of infectious diseases rely heavily on calculus. Which they use to determine how far and how fast a disease can spread. It helps them determine where the disease originated and how to contain it.
16. Cardiac output – Blood Flow
Calculus is also used to determine cardiac output- the rate of blood flow in an artery or vein at any given time. Calculus with the help of a dye is used to calculate the rate of blood pumped through the heart.
17. Cancer – Monitor Tumor
Calculus is also used to calculate the growth or shrinkage of a tumor, it can also be used to calculate the total number of cells in the tumor. It is used to analyze the progression or reversion of the disease using an exponential function.
18. Surgery- Controlling Red Blood Cells
The blood volume in the human body also called hematocrit consists of red blood cells. during surgery the patient’s blood volume has to be maintained by injection of saline solution which mixes quickly with blood but dilutes it so that the hematocrit decreases as time passes Calculus is used to calculate the patient’s volume of red blood cells of which a certain percentage is extracted and returned with the saline solution during surgery.
Calculus is used to calculate the velocity of blood flow in an artery or vein at a given point and the volume of blood flowing through the artery, to help keep the patient under anesthesia.
Cardiologists use differential calculus to describe blood flow dynamics that will help them build artificial computer model aorta and determine where to place it in a transplant.
Pharmacologists use calculus to determine the derivative optimization strength of drugs. Drug sensitivity is used to find the right dosage that will provide a maximum output of drug integration.
Integrated calculus can also be used to calculate drugs side effects brought about by other factors like body temperature changes.
Calculus helps determine the variable changes at varying health levels. Pharmacologists can designate the kidney as a changing function in a calculus equation using the Cockcroft-Gault equation which uses the level of creatine in a patient’s blood to find the level of the kidney’s functional ability that helps Doctors determine appropriate drug dosage.
Physiologists study how the body works, they seek to understand the chemistry and physics behind body functions, these include molecule behavior, cell growth and organ functional coordination in a healthy body and what happens when a person gets ill.
Physiologists use calculus to determine the rate of change in the shortening velocity with respect to the modeling of muscle contractions and body responses.
Neurologists study the nervous system, its disorders, and treatments. The nervous system is a complex and sophisticated network of neurons that regulates and coordinates body activities, it has two major divisions the central nervous system and the brain and spinal cord.
Integration calculus is used to calculate the voltage of a neuron at a certain point in time. Whilst differential calculus is used to calculate the change of voltage in a neuron with respect to time.
Parasitology is a branch of medicine that studies parasites, their relationship with their hosts. Parasitology is not determined by organisms or environment but the organism’s way of life.
The Nicholson Bailey model uses partial fractions and integrated calculus to model dynamics of a host-parasitoid system.
Entomology is a branch of zoology that studies insects. Entomologists seek to classify species and determine how to control insect infestations in homes and in the environment.
Crawling larvae can be modeled with partial derivatives in calculus to help determine the insect’s proficiency.
Physicists use integration calculus in many areas e.g. to calculate the center of mass, the center of gravity, mass moment of inertia and many other applications.
26. Calculate the center of mass
The center of mass is a defined position relative to an object or system of objects. It’s the average position of all parts of the system. Weighted according to their masses. Rigid objects with uniform densities have their center of mass located at the centroid.
Calculus is used to calculate the center of mass, for example, the center of mass of a ring will fall in the middle where there isn’t any material.
27. Calculate Center of gravity
The center of gravity is the point through which the force of gravity is exerted on an object. When the gravitational field is assumed to be uniform, then the center of gravity is exactly in the same position as the center of mass.
Integration calculus is used to calculate the center of mass.
28. Mass moment of inertia – sports vehicles, etc.
Moment of inertia is an object’s resistance to change in its rotational motion. Inertia is always measured by a reference line the axis of rotation.
Inertia is the measure of resistance that a body of a certain mass when pushed in motion or stopped from moving. Inertia calculates the difficulty of the object to resist change. For example, heavier objects have difficulty in accelerating and difficulty in stopping.
Calculus is used to calculate the moment of inertia due to its ease of use in continuous variables.
29. Calculate Velocity of an object
Calculus uses Newton’s second and third laws of motion to calculate the orbital velocity of a rocket around the earth and its ability to escape the earth’s gravitational pull. The thrust of a rocket into space is based on the calculus of motion.
30. Calculate the Trajectory of an object
Calculus is used to calculate the trajectory of a rocket. As the rocket propellant ignites the rocket experiences extreme acceleration. The backward thrust exerts a push force on the rocket in the opposite direction, upwards.
The change of momentum which is the first derivative of momentum is calculated using calculus.
31. Predict positions of planets
Calculus is used in astronomy to find out the rate at which planets move over time. The planetary laws of motion are used by astronomers to study planet orbits derived by using calculus.
Since the 17th-century calculus has been used to accurately calculate the variable speed of moving the planet in space and their orbits around stars in equal time.
Electromagnetism works on the principle that an electric current allows electrons to flow in a circuit and generate a small magnetic field at the same time. When a coiled wire carries the electric current, the magnetism becomes stronger.
Vector calculus is used to calculate electromagnetism.
Astronomers use calculus to study the different motions of planets and meteorites. It is used to find the rate at which the position of a moving body changes over time, based on the laws of planetary motion.
Calculus is used to determine the dynamics of particles. Fractional calculus in fields presents, integral and differential equations of non-integer orders.
35. Determining Frictional forces
Calculus is also used in mechanical engineering computing the surface area of complex objects to determine frictional forces.
36. Pump Flow rate
When designing a pump, the flow rate of the head is calculated using calculus
37. Power Output in Batteries
The power output provided by a battery system can be calculated using calculus.
38. Considering variables in the manufacturing
Research analysts use calculus when observing different processes, and studying different variables in manufacturing processes to determine operational efficiency, production and profits.
39. Evaluate survey data
Statisticians use calculus to evaluate survey data which involves many different questions with a range of possible answers, Calculus helps get more accurate predictions and take the right action.
Land surveyors work to calculate the area of the land surface, they measure air, water bodies and other variables like power lines electrical and sewer lines. They use calculus to solve variables in calculating the surface area.
40. Calculating birth and death rates
Population ecologists use calculus to model population dynamics that represent growth without environmental constraints Calculus can be used to accurately predict population changes and. the future when taking into account birth and death rates.
41. Determine 3 D Behavioral pattern
Graphic designers use calculus to determine how different three-dimensional models behave when subjected to changing conditions. It is used to create a realistic environment for video games and movies.
42. Rate of Chemical reaction
Calculus is used to determine the rate of chemical reaction in compounds.
43. Radioactive decay reaction
Radioactive material disintegrates at a rate proportional to the amount present. Calculus is used to calculate the rate of decay of radioactive isotopes.
44. Calculating Weather patterns
By using differential calculus equations, you can calculate the effects of changing weather conditions in the atmosphere by applying such variables as temperature, pressure changes. These help meteorologists to predict the weather.
Calculus is used to calculate damped harmonic motion. An oscillation cannot go on indefinitely, friction and air resistance dissipate the energy of the oscillation. Common dissipative forces encountered is the damped force which is proportional to the velocity of the object. This is calculated using calculus.
Forced Oscillation and resonance can be calculated using calculus. A body is displaced, in this case, air, and then released subject to frictional forces. Using an independent force, you can drive oscillation at different frequencies. Calculus helps establish this frequency.
47. Credit card payments
Calculus is used by credit card companies to set payment structures, they consider different variables such as changing interest rates and fluctuating balances to calculate the minimum amount due on a credit card.
48. Planning prosecution cases
Lawyers use calculus to build the discipline necessary to solve complex problems while prosecuting cases.
49. Calculate costs
Economists use calculus to calculate the costs of production.
50. Calculate revenue
Calculus can be used to calculate the increase in revenue while increasing production. The businessman can then maximize their profits based on the rate of production.
Economics use calculus to calculate the price elasticity of demand and supply. They consider such variables as the supply-demand curve, to calculate elasticity, which is the exact measure of elasticity at a particular point on a supply and demand curve, and changes according to price.
Calculus is encompassed in every aspect of our lives helping solve problems, predict the future, explore the unknown and understand our world and the universe.