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Calculus

Calculus is a mathematical discipline focused on studying change and motion, divided into differential calculus (rates of change) and integral calculus (accumulation). It is widely applicable across various fields such as science, engineering, economics, biology, physics, and computer science. Key concepts include derivatives for understanding speed and integrals for calculating total quantities.

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10 views2 pages

Calculus

Calculus is a mathematical discipline focused on studying change and motion, divided into differential calculus (rates of change) and integral calculus (accumulation). It is widely applicable across various fields such as science, engineering, economics, biology, physics, and computer science. Key concepts include derivatives for understanding speed and integrals for calculating total quantities.

Uploaded by

Sherįl Alexx
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Calculus is a branch of mathematics that studies how things change.

It's essentially the


mathematics of motion and change, dealing with quantities that are continuously varying.

What Is Calculus?

Calculus is divided into two main branches:

1. Differential Calculus

• Focuses on rates of change (like speed, growth, slopes).

• Main tool: Derivative – tells you how a function is changing at any point.

2. Integral Calculus

• Focuses on accumulation (like area under a curve, total distance).

• Main tool: Integral – sums up small pieces to find whole quantities.

Bonus: Multivariable and Vector Calculus

• Extends the ideas of calculus to functions with more than one variable.

• Used in physics, engineering, economics, etc.

Why Is Calculus Useful?

1. Science & Engineering

• Describes motion, heat, light, fluids, and electricity.

• Used in designing everything from cars and planes to bridges and electronics.

2. Economics & Finance

• Used to find maximum profit or minimum cost.

• Helps in modeling market trends and predicting future values.

3. Biology & Medicine

• Models how diseases spread, how populations grow, or how drugs break down in
the body.

4. Physics

• Virtually all physics – from classical mechanics to quantum theory – uses calculus.

• Think: velocity, acceleration, gravity, wave motion.


5. Computer Science & AI

• Calculus underpins machine learning algorithms and graphics rendering.

• Used in data analysis, modeling, and simulation.

Simple Example

If a car’s position over time is given by a function:

• Differentiation tells you its speed (rate of position change).

• Integration tells you the distance it traveled over time.

Would you like a simple real-life example worked out (e.g., how fast water fills a tank or how
to maximize profit)?

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