The speaker starts by emphasizing the importance of approaching calculus not as a set of memorized rules, but as a creative process. They stress that calculus, short for infinitesimal calculus, is a broad field that encompasses everything that changes.
The speaker then delves into the historical context of calculus, tracing it back to the ancient practice of using small pebbles for calculations. The word "calculus" originates from the Latin word for small pebbles. The speaker also mentions that the field of calculus took over from mathematics in importance, suggesting that it's a fundamental aspect of mathematics.
Newton's famous apple experiment is brought up, where he observed the fall of an apple and pondered the mysteries of gravity. The speaker explains that Newton was trying to understand how gravity changes over distance, a problem that was difficult to solve due to the variable nature of the force.
The concept of the gradient of a tangent is introduced. The speaker explains that the gradient of a tangent line represents how much a quantity changes at any given point. However, calculating the gradient of a tangent is challenging because a tangent line only touches one point, making it difficult to compare it to another point.
The speaker concludes by highlighting the difficulty Newton and Leibniz faced when trying to work out the gradient of a tangent, emphasizing that calculus is more than just a set of rules to be memorized. It's a complex field that requires creative thinking and problem-solving skills.
1. The text is a lecture on calculus, a branch of mathematics.
2. The lecturer emphasizes that calculus is not just a set of rules, but a creative process.
3. The term "calculus" is an abbreviation for "infinitesimal calculus".
4. The word "calculus" comes from the Latin word for "small pebbles", reflecting its origins in ancient Rome.
5. The lecturer mentions that calculus is a very general term, and is also the root of the word "calculator".
6. The lecturer describes the history of calculus, noting that it was developed independently by Isaac Newton in England and Gottfried Wilhelm Leibniz in Germany.
7. The lecturer discusses the concept of gravity, and how Newton was inspired to study it after observing an apple fall from a tree.
8. Newton's problem was to understand how gravity changes over distance.
9. The lecturer explains that Newton needed to find a way to calculate the gradient of the tangent line at any given point.
10. The lecturer concludes by noting the challenges in calculating the gradient of a tangent line, which was a problem that Newton and Leibniz were trying to solve.