Sir Isaac Newton (1642–1727) was one of the greatest mathematicians and physicists in history. His contributions to calculus and other branches of mathematics laid the foundation for much of modern science.

His work in calculus includes:

• Concept of limits, although not formally defined.

• Introduction of derivatives (rate of change) and integrals (area under a curve) as inverse operations.

• Used calculus to:

  • Calculate instantaneous velocity and acceleration.

  • Solve problems in motion and gravitation.

  • Explain planetary motion and orbits.

Binomial Theorem

• He extended the binomial theorem to fractional and negative exponents.

• This led to infinite series expansions like:

  $$(1 + x)^n = 1 + nx + \frac{n(n-1)}{2!}x^2 + \cdots$$

  He developed power series expansions for functions like:

  • Sine, cosine, exponential, and logarithmic functions.

  • A funny story

  •  One day, Newton was resting under an apple tree in his mother’s garden. Suddenly — thud! — an apple landed right on his head.

    Newton shouted:

    "Ouch! Who threw that?!"

    Looking around and seeing no one, he realized:

    "Wait a minute… everything falls down. Why not sideways or upward?"

    He didn’t get angry. Instead of thinking it was a prank by a squirrel, he started thinking about the forces of nature!

    And thus, what would have made a normal person just rub their head and complain, made Newton invent the law of universal gravitation.

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    😊 Moral of the Story:

    While most of us would just be annoyed by falling fruit, Newton turned it into a discovery that changed the world. So next time you get hit by something — maybe think harder before getting angry!