by calculus

USAGE SUMMARY

The phrase "by calculus" is correct and usable in written English.
It can be used when referring to something that is determined, calculated, or derived through the use of calculus in mathematics. Example: "The area under the curve can be found by calculus, providing a precise measurement of the region."

✓ Grammatically correct

Science

News & Media

Academia

Human-verified examples from authoritative sources

Exact Expressions

19 human-written examples

And it's not because women are stumped by calculus; it's that they lack the confidence to succeed in furthering their calculus studies.

University of California, Berkeley

As a Ph.D. student, the young Elizabeth Loftus wasn't captivated by calculus: "I used to sit in the back of the seminars, kind of bored, writing letters to my Uncle Joe, or hemming skirts or whatever".

The Guardian

Using target operators that specify the control objective, the pulse design is reduced to the maximization/minimization problem of the expectation values subject to additional requirements if needed, which can be solved by calculus of variations.

Reference Module in Chemistry, Molecular Sciences and Chemical Engineering

The partial differential equation, describing the transverse vibration of the cantilever beam, and the transversality condition, describing the contact position between the beam and the cylindrical foundation, are derived by calculus of variation and Hamilton's principle.

Journal of Sound and Vibration

If we are bored by calculus, muddling through on a combination of memorization, technique, and brutal willpower, we may well end up earning the exact same grade as someone who sees the equations as beautiful illustrations of how the world works.

The New Yorker

The left-hand inequality is easily proved by calculus.

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

41 human-written examples

For this, Kepler was put into a so-called "earth-traling orbit," engineered according to specifications determined by calculus-based tools.

Huffington Post

With this definition, the Recursive functions are exactly the same as the set of partial functions computable by the Lambda calculus, by Kleene Formal systems, by Markov algorithms, by Post machines, and by Turing machines.

SEP

By six, he was well versed in geometry; by ten, calculus; and by twelve, relativity.

Huffington Post

In an interview, he said he was swayed not by political calculus, but by discussions over two months with both advocates and opponents of the measure.

The New York Times

Left ventricular dP/dt is the first derivative of left ventricular pressure, which is computed by software algorithms by using calculus.

Journal of Pharmacological and Toxicological Methods

Expert writing Tips

Best practice

When writing about mathematical or scientific topics, use "by calculus" to clearly indicate that a result was obtained through the application of calculus methods. Ensure the context makes it clear what specific aspect of calculus is being referenced (e.g derivative, integral).

Common error

Avoid using "by calculus" in non-mathematical contexts where it doesn't accurately describe the method or process used. For instance, don't say "the decision was made by calculus" unless you literally mean a calculus-based model was used to make the decision. Use a more suitable alternative such as "by careful consideration".

Linguistic Context

The phrase "by calculus" primarily functions as an adverbial phrase modifying a verb, indicating the method or means by which an action is performed or a result is obtained. Ludwig shows this usage is frequent in scientific and academic writing.

Expression frequency: Common

Frequent in

Science

60%

News & Media

20%

Academia

13%

Less common in

Wiki

3%

Encyclopedias

2%

Formal & Business

2%

Ludwig's WRAP-UP

In summary, the phrase "by calculus" is a grammatically sound and relatively common construction used to indicate that a result or understanding was obtained through the application of calculus. Ludwig confirms its primary usage in scientific, academic, and technical contexts, where precision is important. While alternatives like "through calculus" or "using calculus" exist, "by calculus" remains a direct and clear way to specify the method used. Avoid overgeneralizing its use to non-mathematical scenarios where other phrases may be more appropriate.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

through calculus

Replaces the preposition "by" with "through", maintaining the same meaning.

using calculus

Substitutes "by" with "using", focusing on the method employed.

via calculus

Replaces "by" with "via", indicating a means or route.

derived with calculus

Emphasizes the derivation process using calculus.

calculated through calculus

Highlights the calculation aspect using calculus.

determined by calculus

Focuses on calculus as the determining factor.

computed using calculus

Highlights the computation aspect using calculus.

assessed by calculus

Indicates calculus is used as a mean for evaluation.

analysed via calculus

Suggests calculus is the tool to conduct analysis.

modeled by calculus

Indicates calculus is used as a mean for modeling.

FAQs

How can I use "by calculus" in a sentence?

You can use "by calculus" to indicate that a result, value, or understanding was obtained through the application of calculus. For example, "The area under the curve was determined "by calculus"".

What are some alternatives to "by calculus"?

Alternatives include "through calculus", "using calculus", or "via calculus", each subtly shifting the emphasis on the method used.

Is it appropriate to use "by calculus" in non-mathematical contexts?

Generally, "by calculus" is most appropriate in mathematical, scientific, or technical contexts. In other contexts, using phrases like "by careful consideration" or "by logical deduction" may be more fitting.

What does "by calculus of variations" mean?

"By calculus of variations" refers to solving optimization problems where the unknown is a function, using a specific branch of calculus. It is often used in physics and engineering to find functions that minimize or maximize certain integrals.