Newton

Definition

Sir Isaac Newton was a mathematician and physicist who made significant contributions to calculus, including the development of the concept of derivatives. His work laid the foundation for many principles in calculus, particularly those involving rates of change and motion.

5 Must Know Facts For Your Next Test

1. Newton's notation for derivatives uses a dot over the function, e.g., $\dot{y}$ represents the derivative of $y$ with respect to time.
2. Newton independently developed calculus at the same time as Leibniz, though their notations and approaches differed.
3. The Fundamental Theorem of Calculus connects differentiation and integration, concepts that Newton helped formalize.
4. Newton's method is an iterative numerical technique for finding successively better approximations to the roots (or zeroes) of a real-valued function.
5. His contributions are foundational to physics as well; Newton's laws of motion rely heavily on calculus.

Review Questions

• What notation did Newton use to represent derivatives?
• How does Newton’s contribution relate to the Fundamental Theorem of Calculus?
• Describe how Newton's method is used in calculus.

Related terms

Derivative: A measure of how a function changes as its input changes. In other words, it represents an instantaneous rate of change.

Fundamental Theorem of Calculus: This theorem links the concept of differentiating a function with integrating a function, showing that they are essentially inverse operations.

Newton's Method: An iterative numerical technique used to find approximations to the roots (zeroes) of a real-valued function.