elementary functions

USAGE SUMMARY

The phrase "elementary functions" is correct and usable in written English.
It is typically used in mathematics to refer to basic functions such as polynomials, exponentials, logarithms, and trigonometric functions. Example: "In calculus, we often study the properties of elementary functions to understand more complex equations."

✓ Grammatically correct

Science

Encyclopedias

News & Media

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Table 2 lists the integrals of a small number of elementary functions.

Encyclopedia Britannica

The elementary functions of real analysis, such as polynomials, trigonometric functions, and exponential functions, can be extended to complex numbers.

Encyclopedia Britannica

In its elementary functions and rudimentary characteristics, however, a city is not clearly distinguishable from a town or even a large village.

Encyclopedia Britannica

SAINT would take its problem given to it in the language of elementary functions, which had to be defined as well and then begin a search among its algorithms.

The New Yorker

Elementary functions.

Protein Physics A Course of Lectures

Their solutions can be written in elementary functions.

Advances in Difference Equations

Different kinds of algorithms can be chosen so as to compute elementary functions.

Mathematical and Computer Modelling

Finally, we apply these bounds to some elementary functions in Section 5.

Journal of Inequalities and Applications

Conjecture 12 The solution of equation (16) cannot be solved in elementary functions.

Boundary Value Problems

(27) Let us now discuss some general applications of (N_{q}) to some elementary functions.

Advances in Difference Equations

The following lemma establishes the relationship between (Phi r,xi)) and some basic elementary functions.

Boundary Value Problems

Expert writing Tips

Best practice

When discussing mathematical models or equations, clearly define the "elementary functions" involved to ensure clarity and avoid ambiguity.

Common error

Avoid assuming that all functions are "elementary functions". Many complex mathematical functions, like special functions or solutions to differential equations, cannot be expressed using only elementary operations.

Linguistic Context

The phrase "elementary functions" functions primarily as a noun phrase, referring to a specific category of mathematical functions. As Ludwig AI confirms, it’s correctly used in mathematics to denote basic functions like polynomials, exponentials, and trigonometric functions. The examples provided by Ludwig illustrate this usage across various contexts.

Expression frequency: Very common

Frequent in

Science

76%

Encyclopedias

5%

News & Media

3%

Less common in

Wiki

1%

Formal & Business

0%

Social Media

0%

Ludwig's WRAP-UP

In summary, "elementary functions" is a noun phrase denoting a fundamental set of mathematical functions, including polynomials, trigonometric functions, exponentials, and logarithms. Ludwig AI confirms its grammatical correctness and common usage in mathematical contexts. The phrase is predominantly used in formal and scientific settings, as demonstrated by its prevalence in academic papers and encyclopedias. When writing, define the specific "elementary functions" when necessary to maintain clarity and avoid confusing them with more complex functions. Related terms include "basic functions" and "fundamental functions". Be mindful that not all integrals can be expressed using only "elementary functions".

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

basic functions

Focuses on the fundamental nature of the functions, emphasizing their simplicity and foundational role.

fundamental functions

Highlights the essential and underlying character of these functions in mathematical analysis.

standard functions

Emphasizes the conventional and well-established nature of these functions in mathematical practice.

common functions

Indicates the widespread use and familiarity of these functions across different mathematical disciplines.

simple functions

Underscores the straightforward and easily understood nature of these functions.

polynomial functions

Refers specifically to functions involving polynomial expressions, which are a subset of elementary functions.

trigonometric functions

Highlights a specific category of elementary functions related to angles and ratios in triangles.

exponential functions

Focuses on functions where a constant is raised to a variable power, another key type of elementary function.

logarithmic functions

Emphasizes the inverse of exponential functions, another essential component of elementary functions.

algebraic functions

Includes functions that can be expressed using algebraic operations, encompassing a broader set than just elementary functions.

FAQs

What are some examples of "elementary functions"?

Examples of "elementary functions" include polynomials, trigonometric functions (sine, cosine, tangent), exponential functions, logarithmic functions, and their inverses. These functions can be combined using arithmetic operations and composition.

How are "elementary functions" used in calculus?

"Elementary functions" are fundamental in calculus. They are often used to build more complex functions, and their derivatives and integrals are studied extensively. Many calculus problems involve finding the derivatives or integrals of "elementary functions".

Are all integrals expressible in terms of "elementary functions"?

No, not all integrals can be expressed in terms of "elementary functions". Some integrals, such as the integral of exp(-x^2), require special functions like the error function to express their solutions. These are known as non-elementary integrals.

What's the difference between "elementary functions" and "special functions"?

"Elementary functions" are functions that can be constructed from basic arithmetic operations, exponentials, logarithms, and trigonometric functions. "Special functions" are more complex functions that are typically defined as solutions to differential equations or integrals that cannot be expressed in terms of elementary functions. Examples of "special functions" include Bessel functions and the Gamma function.