Calculus Sketch

When calculus was invented, has always been a question in Math. The first signs of calculus were done by Greek mathematicians. Zeno of Elea of about 450 B.C. gave a number of problems which were based on the infinite. His argument was that motion is impossible. Other Greek mathematicians that contributed to the method of exhaustion are Leucippus, Democritus and Antiphon. The method of exhaustion is so called because one thinks of the areas measured expanding so that they account for more and more of the required area. Archimedes made one of the greatest contributions of the Greek. One advancement he made was to show that the area of a segment of a parabola is 4/3 the area of a triangle with the same base and vertex and 2/3 of the area of the circumscribed parallelogram. Archimedes also “invented” the volume and surface area of a sphere, the volume and area of a cone, the surface area of an ellipse, and the volume of any segment of a parabolic. No progress or advancements were made in calculus until the 17th century. One great mathematician that was born in Barsa, Persia is Abu Ali-Hasan ibn al-Haytham. He integrated a fourth-degree polynomial. In the 3rd century AD Liu Hui of China used the method of exhaustion in order to fin the area of a circle. In the 5th century AD Zu Chongzhi also used it to find the volume of a sphere. In the 12th century Bhaskara II of India developed an early derivative representing infinitesimal change and described an early form of “Rolle’s theorem”. Seki Kowa expanded the method of exhaustion in the early 17th century in Japan. In AD 1668 James Gregory provided a special case of the second fundamental theorem of calculus. Some applications of calculus are used by biologist, electrical engineers, architects, space flight engineers, statisticians, graphic artist and so much more. Biologists use differential calculus. They use it to determine the exact rate of growth in a bacterial culture when different variables are changed such as

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