क्यों असंभव था Calculus को बनाना | Calculus is impossible without these 9 discoveries

Explore the fascinating history of calculus in this in-depth video, tracing its evolution through nine groundbreaking discoveries that shaped modern mathematics, physics, and technology. From Archimedes’ ancient techniques to Lebesgue’s 20th-century innovations, learn how calculus became essential for fields like quantum mechanics, engineering, and artificial intelligence.

What You’ll Discover in This Video:
1. Archimedes’ Method of Exhaustion (3rd Century BC): How ancient Greek mathematician Archimedes used polygons to approximate pi, introducing infinitesimals to calculate areas.

2. Cavalieri’s Method of Indivisibles (17th Century): Bonaventura Cavalieri’s revolutionary idea of slicing shapes into infinite thin layers to compute areas and volumes.

3. Descartes and Fermat’s Coordinate Geometry (17th Century): The fusion of algebra and geometry, enabling curves to be represented as equations.

4. Fermat’s Tangents and Optimization (17th Century): Pierre de Fermat’s pioneering work on tangents, laying the groundwork for derivatives and optimization techniques.

5. Newton and Leibniz’s Fundamental Theorem (17th Century): How Isaac Newton and Gottfried Wilhelm Leibniz unified differentiation and integration, creating calculus as we know it.

6. Cauchy and Weierstrass’ Limits and Continuity (19th Century): The rigorous foundation of limits, resolving paradoxes and defining derivatives and integrals precisely.

7. Real Analysis (19th Century): A framework for studying complex functions, including those continuous but non-differentiable, expanding calculus’ scope.

8. Complex Analysis (19th Century): Cauchy and Riemann’s extension of calculus to complex numbers, introducing powerful tools like Riemann surfaces.

9. Lebesgue Integration (20th Century): Henri Lebesgue’s innovative integration method, handling irregular functions with the Lebesgue measure.

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Archimedes pi calculation- https://youtu.be/nB9V_MpmwW0

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क्यों असंभव था Calculus को बनाना | Calculus is impossible without these 9 discoveries

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