Basic Calculus: Introduction to Calculus

Short introduction to calculus 11

1. Applications of Calculus in Real life

2. WHAT IS CALCULUS??? The ideas of Calculus were discovered at the same time by NEWTON in England and LEIBNIZ in Germany in the 17th century. There was a lot of ill feeling between them because each one wanted to take the credit for discovering Calculus. Newton had a particular interest in the orbits of planets and gravity. He “invented” calculus to help him study such topics. His theory was used extensively in putting the first men on the moon and his equations of motion clearly describe the paths of objects thrown through the air.

3. CALCULUS The very basic idea of CALCULUS is how to find the changing steepness of curves.

4. CALCULUS

5. CALCULUS

6. WHAT IS CALCULUS??? Calculus can be applied to many subjects: finding equations to model the growth of animals, plants or bacteria; finding maximum profits in economics; finding the least amount of material to make boxes and cylinders; all sorts of velocity and acceleration problems

7. Fields that Calculus is used in : 1. Engineering 2. Economics 3. biology 4. Astronomy 5. And lots of other fields

8. Calculus in Engineering : Engineering is the field in which calculus is used most often in a real-world context. 1. Calculus is necessary to determine distances with precision, such as the length of a cable supported by two poles. 2. Calculus is also required by engineers and architects to calculate the size of curved or dome-style surfaces. 3.Without the accuracy afforded by the use of calculus, bridges, roads and tunnels would not be as safe as they are today.

9. Constructing burj khalifa This calculus integral was used to calculate the energy needed to raise all the 180 floors up to a height h which is 828.8 m

10. Calculus in Astronomy : Calculus has been used in astronomy since the 17th century to calculate the orbits of the planets around stars. Calculus is also necessary to accurately calculate the variable speed of moving objects in space, including asteroids, comets and other celestial bodies. Many of today's most interesting astronomical insights were gained with the use of calculus.

11. It is worth mentioning that one of the more famous applications of calculus is its application in projecting a path of the Apollo capsule  to arrive at the moon at the precise location in its orbit above the earth. You can't just point to the moon and fire, by the time you get there, the moon will have moved along at about 1/6th of its orbit around the earth. You have to factor in escape velocity to achieve escape of earth's orbit with the minimum use of liquid fuel, and the precise combination of acceleration and velocity to get to the moon. And this was all achieved using calculus !!!

12. This is the trajectory of the appollo mission and the capsule which landed on the moon.

13. Calculus in biology : Calculus is also used in biology. Some applications include : modeling enzyme reactions as a function of nutrient concentration and the growth rate for bacteria. modeling population growth of a certain species. modeling the relationship between related physical traits, such as backbone.

14. Calculus in Economics : Calculus is routinely used in economics. Economists use calculus to determine the right time to buy or sell something The marginal value of a particular action How much the price of an item affects How many people buy it Or any other instance that requires measuring change over time in two or more related variables.

15. Calculus in other fields : Calculus is also used indirectly in a number of other fields including public policy applied physics computer science graphic arts and more.

16. CALCULUS The study of CHANGE. Basically focusing on RATE OF CHANGE and ACCUMULATION

17. DIFFERENTIAL AND INTEGRAL CALCULUS

18. DIFFERENTIAL Determines the rate of change in quantity

19. ALGEBRA VS CALCULUS

20. DIFFERENTIAL CALCULUS A differential equation can simply be termed as an equation with one or more functions and its derivatives. The functions usually represent physical quantities, and derivatives of these functions give the rate of change of the quantities, and the differential equation describes the relationship between them. The simplest way to calculate quantities is by using differential equations formulas.

21. EQUATIONS Here are some few differential equations

22. INTEGRAL Determines the quantity where the rate of change is known.

23. ALGEBRA VS CALCULUS

24. equations