Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. It's used extensively in science, engineering, economics, and other fields.
Basic Concepts
- Limit: The value that a function or sequence "approaches" as the input or index approaches some value.
- Derivative: The rate at which one quantity changes with respect to another.
- Integral: The area under a curve or the sum of an infinite series of infinitely small quantities.
Key Theorems
- Mean Value Theorem: If a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one point in the open interval where the derivative is equal to the average rate of change of the function over the closed interval.
- Fundamental Theorem of Calculus: A theorem that connects differentiation and integration, and shows that differentiation and integration are inverse operations.
Applications
Calculus is used in many fields, including:
- Physics: To describe motion, forces, and energy.
- Engineering: To design and analyze structures, machines, and systems.
- Economics: To model market behavior and economic trends.
For more information on calculus concepts, you can visit our Calculus Tutorial.
Important Resources
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