Numerical Calculus: Differentiation and Integration

Numerical calculus is a branch of mathematics that deals with the numerical approximation of derivatives and integrals. It is a powerful tool that can be used to solve a wide variety of problems in mathematics, engineering, and physics.

Numerical Calculus: Differentiation and Integration

by D. James Benton

4.6 out of 5

Language	:	English
File size	:	2663 KB
Text-to-Speech	:	Enabled
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Differentiation

Differentiation is the process of finding the derivative of a function. The derivative of a function is a measure of how fast the function is changing at a given point.

There are a variety of numerical methods that can be used to approximate the derivative of a function. One common method is the forward difference formula:

$$f'(x) \approx \frac{f(x+h) - f(x)}{h}$$

where $h$ is a small number.

Integration

Integration is the process of finding the integral of a function. The integral of a function is a measure of the area under the curve of the function.

There are a variety of numerical methods that can be used to approximate the integral of a function. One common method is the trapezoidal rule:

$$∫_a^b f(x) dx \approx \frac{h}{2}[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]$$

where $h$ is the width of the intervals.

Applications of Numerical Calculus

Numerical calculus has a wide variety of applications in mathematics, engineering, and physics. Some of the most common applications include:

• Solving differential equations
• Finding the area under a curve
• Calculating the volume of a solid
• Solving problems in fluid dynamics
• Solving problems in heat transfer

Numerical calculus is a powerful tool that can be used to solve a wide variety of problems in mathematics, engineering, and physics. This comprehensive guide will provide you with all the essential formulas and techniques you need to get started.

Numerical Calculus: Differentiation and Integration

by D. James Benton

4.6 out of 5

Language	:	English
File size	:	2663 KB
Text-to-Speech	:	Enabled
Screen Reader	:	Supported
Enhanced typesetting	:	Enabled
Print length	:	111 pages
Lending	:	Enabled

FREE