Secondary special education of the republic of uzbekistan

Middle East. In the Middle East, Hasan Ibn al-Haytham, Latinized as Alhazen (c. 965 – c. 1040 CE) derived a formula for the sum of fourth powers. He used the results to carry out what would now be called an integration, where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid. In the 9th century mathematican Thābit ibn Qurra described the quadrative nature of the parabola and the volume of the different types of the conic section. Roshdi Rashed has argued that the 12th century mathematician Sharaf al-Dīn al-Tūsī must have used the derivative of cubic polynomials in his Treatise on Equations. Rashed's conclusion has been contested by other scholars, who argue that he could have obtained his results by other methods which do not require the derivative of the function to be known.
India. In 12th century, Indian mathematician Bhaskara II developed an earliest form of a derivative by representing an infinitesimal change and described an early form of " Rolle's theorem ". Some of Ibn al-Haytham's ideas on calculus later appeared in Indian mathematics, at the Kerala school of astronomy and mathematics suggesting a possible transmission of Islamic mathematics to Kerala following the Muslim conquests in the Indian subcontinent. Madhava of Sangamagrama in the 14th century, and later mathematicians of the Kerala school, stated components of calculus such as the Taylor series and infinite series approximations. However, they did not combine many differing ideas under the two unifying themes of the derivative and the integral, show the connection between the two, and turn calculus into the powerful problem-solving tool we have today.

The numerals used in the Bakhshali manuscript, dated between the 2nd century BC and the 2nd century AD.


Ancient Brahmi numerals in a part of India.

Indian numerals in stone and copper inscriptions.
Europe. The mathematical study of continuity was revived in the 14th century by the Oxford Calculators and French collaborators such as Nicole Oresme. They proved the "Merton mean speed theorem": that a uniformly accelerated body travels the same distance as a body with uniform speed whose speed is half the final velocity of the accelerated body.
Maya. In the Pre-Columbian Americas, the Maya civilization that flourished in Mexico and Central America during the 1st millennium AD developed a unique tradition of mathematics that, due to its geographic isolation, was entirely independent of existing European, Egyptian, and Asian mathematics. Maya numerals used a base of twenty, the vigesimal system, instead of a base of ten that forms the basis of the decimal system used by most modern cultures. The Maya used mathematics to create the Maya calendar as well as to predict astronomical phenomena in their native Maya astronomy. While the concept of zero had to be inferred in the mathematics of many contemporary cultures, the Maya developed a standard symbol for it.

The Maya numerals for numbers 1 through 19, written in the Maya script.
If we talk about the topic of Principles of calculus in general, we will start our lecture with Arithmetic. Of course, for better understanding.
Arithmetic (a term derived from the Greek word arithmos, “number”) refers generally to the elementary aspects of the theory of numbers, arts of mensuration (measurement), and numerical computation (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots). Its meaning, however, has not been uniform in mathematical usage. An eminent German mathematician, Carl Friedrich Gauss, in Disquisitiones Arithmeticae (1801), and certain modern-day mathematicians have used the term to include more advanced topics. The reader interested in the latter is referred to the article number theory.
Fundamental Definitions And Laws