Dated: 30-10-2024

Introduction

Differential Calculus

It deals with problem of finding:

1. Rates of change.
2. Slopes of curves.

Applications

It can be used to find following things:

• Velocities and acceleration of moving bodies.
• Firing angles for cannons to achieve maximum height or travel distance.
• The times when planets are closest to each other.

Integral Calculus

Deals with the problem of determining a function¹ from the information of its rate of change.

Applications

1. Calculating length of curves.
2. Finding areas of irregular regions in a plane.²
3. Finding volumes and masses of arbitrary solids.
4. Knowledge about acting forces and position of a body in future, relative to present time.

Reference Axes

Just like planes,² we can define a space with 3 axes, \(x\), \(y\) and \(z\).
The planes,² \(x = 0\), \(y = 0\) and \(z = 0\) divide the space into 8 octants.
The origin of the space lies at \((0, 0, 0)\) and any point in space will have 3 coordinate values.

Following are the signs for coordinate values in each octant.

1. (+, +, +)
2. (-, +, +)
3. (-, -, +)
4. (+, -, +)
5. (+, +, -)
6. (-, +, -)
7. (-, -, -)
8. (+, -, -)

Functions¹ With Multiple Variables

A function¹ can depend on multiple variables.

Example

\[A = lw\]

\[V = lwh\]

References

Read more about notations and symbols.

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1. Read more about functions. ↩↩↩

2. Read more about planes. ↩↩↩