the preceding equation

USAGE SUMMARY

The phrase "the preceding equation" is correct and usable in written English.
It can be used when referring to an equation that was mentioned earlier in the text or discussion. Example: "To solve for x, we can use the values from the preceding equation."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

19 human-written examples

With U regarded as a function U S, V), its differential dU is      (40) A comparison with the preceding equation shows immediately that the partial derivatives are     (41) Furthermore, the cross partial derivatives,     (42) must be equal because the order of differentiation in calculating the second derivatives of U does not matter.

Encyclopedia Britannica

We use the identity m ( m − 1 i − 1 ) = i ( m i ). in the third line of the preceding equation.

Advances in Difference Equations

Unfortunately, the preceding equation cannot be solved independently because the surface heat flux is unknown and coupled to transient conduction of the rock mass surrounding the fracture.

Geothermal Energy

The preceding equation means that it is possible to predict the financial situation of firm i at time t using its situation at time t-1 and some exogenous variables z it.

Journal of Statistical Distributions and Applications

Furthermore, from the preceding equation, we have f ′ ( x n ) = c 1 + 2 c 2 e n + 3 c 3 e n 2 + 4 c 4 e n 3 + O e n 4. Open image in new window (9).

Mathematical Sciences

Neglecting the higher order terms, the preceding equation reduces to: φ u T Δ K φ u = Λ d - Λ u - φ u T K u Δ φ - Δ φ T K u φ u (18).

International Journal of Advanced Structural Engineering (IJASE)

Human-verified similar examples from authoritative sources

Similar Expressions

41 human-written examples

Accordingly, there must be a sudden change in the amount of,, and, from zero to a certain positive value which is determined by the preceding equations: (21).

EURASIP Journal on Wireless Communications and Networking

To generate uniform [0,1] random vectors X ± = X 1 ±, X 2 ±, X 3 ± with correlation matrices ρ±, one uses two times the preceding equations.

Journal of Statistical Distributions and Applications

In order for the later use, we express the preceding equations in vector format that x ̄ n = [ x n ( t 1 ), x n ( t 2 ), …, x n ( t I ) ] T and ψ ̄ n = [ e j 2 Π n I t 1, e j 2 Π 2 n I t 2, …, e j 2 Π nI I t I ] T = [ ψ 1 n, ψ 2 n, …, ψ In ] T.

EURASIP Journal on Wireless Communications and Networking

The addition of feedback changes only the functional form of x in the preceding equations, as detailed below.

Biology Direct

So the terms p ^ u, i in the preceding equations represent the probabilities that the mate of the focal parent is contributing an i allele.

Genetics

Expert writing Tips

Best practice

When using "the preceding equation", ensure the equation is clearly identifiable and not too distant from the reference point to avoid confusion. If there are multiple equations in the section, consider numbering them for clarity.

Common error

Avoid using "the preceding equation" if several equations are presented in close proximity. Instead, label or number equations for precise referencing. Without clear labeling, readers may misinterpret which equation is being referenced.

Linguistic Context

The phrase "the preceding equation" functions as a determiner phrase, specifically a noun phrase acting as an adjective, that modifies an implicit noun or clause. It identifies a specific equation mentioned before in the text. Ludwig examples show this phrase clearly indicating a previously referenced equation.

Expression frequency: Common

Frequent in

Science

94%

Encyclopedias

3%

News & Media

3%

Less common in

Formal & Business

0%

Wiki

0%

Reference

0%

Ludwig's WRAP-UP

In summary, the phrase "the preceding equation" is a grammatically sound and frequently used expression, especially in scientific and academic contexts. Ludwig AI confirms its correctness and usability. It serves to provide a clear and concise reference to an equation introduced earlier in the text, avoiding redundancy. While alternatives like "the previous equation" or "the earlier equation" exist, maintaining clarity in referencing is crucial. When using this phrase, ensure the referenced equation is easily identifiable to prevent misinterpretation. The prevalence of academic and scientific sources emphasizes its formal nature, making it most suitable for technical writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

the previous equation

Replaces "preceding" with "previous", indicating the equation that came immediately before.

the prior equation

Synonym of previous using 'prior' for a more formal tone.

the earlier equation

Substitutes "preceding" with "earlier", broadly referencing an equation mentioned at some earlier point.

the above equation

Uses "above" to indicate that the equation appeared earlier in the text.

the equation above

Rearranges the phrase to place "above" after "equation", still indicating the equation that came before.

the former equation

Employs "former" to specify the first of two equations being discussed.

the equation mentioned earlier

Uses a more descriptive phrase to indicate the equation referenced earlier.

the equation referenced above

Similar to "the above equation" but includes the explicit act of referencing.

the aforementioned equation

Replaces with a more formal tone and signifies that the equation has been previously cited.

the equation in question

Refers to the equation that is currently under discussion or analysis, which was previously introduced.

FAQs

How can I use "the preceding equation" in a sentence?

You can use "the preceding equation" to refer to an equation that has already been introduced in your text. For example, "Substituting the values from "the preceding equation", we can solve for x."

What's the difference between "the preceding equation" and "the previous equation"?

"The preceding equation" and "the previous equation" are largely interchangeable. Both refer to the equation that came immediately before the current point of discussion. "Preceding" is slightly more formal than "previous."

What are some alternatives to using "the preceding equation"?

Some alternatives include "the earlier equation", "the above equation", or "the aforementioned equation", depending on the context and your desired level of formality.

Is it ever incorrect to use "the preceding equation"?

It would be incorrect to use "the preceding equation" if no equation has been mentioned prior in the text or if the reference is unclear due to the presence of multiple unlabeled equations. Ensure that the referenced equation is easily identifiable.