Why Calculus

Sometimes I hear, "why do we need to learn this?" What's the point of doing this? Sometimes once something is learnt we can go on to investigate something further - like Calculus.  Calculus is a branch of mathematics that deals with the study of rates of change and the accumulation of small changes. It has been an essential tool in many areas of science and engineering, including physics, engineering, economics, and statistics. The development of calculus is a fascinating story that spans centuries and involves some of the greatest minds in mathematics.

The origins of calculus can be traced back to ancient Greece, where the method of exhaustion was used to calculate the area of a circle. This method involved inscribing polygons inside and outside the circle and, calculating their areas, then using this information to approximate the area of the circle. However, it was in the 17th century that calculus began to take shape as we know it today.

One of the earliest pioneers of calculus was the English mathematician John Wallis, who, in the 1650s, developed a method of finding the area under a curve by dividing it into small rectangles. This method was further developed by the French mathematician Pierre de Fermat, who used it to solve problems in optics.

However, the work of two great mathematicians, Sir Isaac Newton and Gottfried Wilhelm Leibniz, led to the formal development of calculus. Newton, who was English, and Leibniz, who was German, independently developed a calculus system in the 1670s and 1680s. Newton's system was based on his laws of motion, while Leibniz's system was based on the concept of infinitesimals.

The development of calculus was subject to controversy, however. In the years that followed, there was a bitter dispute between Newton and Leibniz over who deserved credit for the invention of calculus. The dispute was fueled by nationalism, as Newton and Leibniz were fiercely patriotic and by personal animosity, as they had a long-standing professional rivalry. The dispute was eventually settled by a committee of the Royal Society, which ruled that both men had independently developed calculus.

Today, calculus is essential in many fields, including physics, engineering, and economics. The development of calculus has been a fascinating story of innovation and discovery, and it stands as a testament to the power of human intellect and ingenuity.

Heating Zinc Oxide

 One of the interesting things about heating Zinc Oxide is how it changes colour to yellow when hot and reverts back to white when cold. The A-Level students found it harder to determine whether Zinc should be a transition metal or not.

Spirometer

Using the @Pascoscientific spirometer and Capstone to measure my students' and my breathing rate and vital capacity. This is so much easier than using the box spirometer and chart recorder. It seems odd to do a biology experiment in Medical Physics. Still, it is interesting to see how much Physics there is in making and designing devices to measure biological systems.

 

Crushing Can

Crushing a can by the removal of air. An oldie but a goodie. The students didn't realise air and air pressure is as powerful as it is.

Engineering Physics

 Students find out that Engineering Physics is fun, looking at gyros, the drinking birds, using a manometer, water held in a glass by paper and a firestarter.

Gay-Lussacs Law

Gay-Lussac's Law: Investigating the relationship between increasing pressure as the temperature increases for a fixed volume of Gas using the @Pascoscientific pressure sensor and the wireless temperature sensor. I tried this with a Bordon gauge but didn't see enough movement. In 1802, he discovered that when a gas is heated, its volume increases at a constant rate. He also found that when a gas is compressed, its temperature also increases at a constant rate. These two discoveries led to Gay-Lussac's Law of Pressure-Temperature, which states that the pressure of a gas is directly proportional to its temperature.

Sunday is for ... drilling out bungs

 Sunday is for ... drilling out bungs and other prep work and for filming