numerical analysis

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Word: Numerical Analysis

Part of Speech: Noun

Definition: Numerical analysis is a branch of mathematics that focuses on developing and studying algorithms (which are step-by-step procedures) that help find approximate solutions to problems involving calculations, especially in calculus. It is used when exact answers are difficult to find, and instead, we look for close or approximate answers.

Usage Instructions:

• You can use "numerical analysis" when discussing topics related to mathematics, engineering, computer science, or any field that involves solving complex problems.
• It is usually used in academic or technical contexts.

Example:

• "In my mathematics class, we learned about numerical analysis to solve complicated equations that can't be solved exactly."

Advanced Usage:

• In higher education or research, numerical analysis can involve sophisticated methods such as finite element analysis, numerical integration, and error analysis to ensure the accuracy of the approximated solutions.

Word Variants:

• Numerical (adjective): Relating to numbers or calculations.
  • Example: "Numerical data is essential for the experiment."
• Analysis (noun): The detailed examination of the elements or structure of something.
  • Example: "The analysis of the data revealed interesting trends."

Different Meanings:

• While "numerical analysis" primarily refers to mathematics, "analysis" on its own can mean examining or studying anything in detail, not just numbers.

Synonyms:

• Computational mathematics
• Algorithmic analysis

Idioms and Phrasal Verbs:

While "numerical analysis" does not have specific idioms or phrasal verbs associated with it, you might encounter phrases like: - "Crunch the numbers": This means to perform calculations, which is a part of numerical analysis. - "Run the numbers": Similar to "crunch the numbers," it means to calculate or analyze data.

Summary:

Numerical analysis is an important field in mathematics that helps us find approximate solutions to complex problems, especially when exact answers are not possible.

Academic

Noun

1. (mathematics) the branch of mathematics that studies algorithms for approximating solutions to problems in the infinitesimal calculus