Metalogic | Logic symbols | Variables (mathematics)

Metavariable

In logic, a metavariable (also metalinguistic variable or syntactical variable) is a symbol or symbol string which belongs to a metalanguage and stands for elements of some object language. For instance, in the sentence Let A and B be two sentences of a language ℒ the symbols A and B are part of the metalanguage in which the statement about the object language ℒ is formulated. John Corcoran considers this terminology unfortunate because it obscures the use of schemata and because such "variables" do not actually range over a domain. The convention is that a metavariable is to be uniformly substituted with the same instance in all its appearances in a given schema. This is in contrast with nonterminal symbols in formal grammars where the nonterminals on the right of a production can be substituted by different instances. Attempts to formalize the notion of metavariable result in some kind of type theory. (Wikipedia).

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11_3_6 Continuity and Differentiablility

Prerequisites for continuity. What criteria need to be fulfilled to call a multivariable function continuous.

From playlist Advanced Calculus / Multivariable Calculus

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11_2_1 The Geomtery of a Multivariable Function

Understanding the real-life 3D meaning of a multivariable function.

From playlist Advanced Calculus / Multivariable Calculus

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Multivariable Calculus | Differentiability

We give the definition of differentiability for a multivariable function and provide a few examples. http://www.michael-penn.net https://www.researchgate.net/profile/Michael_Penn5 http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus

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Multivariable Calculus | Definition of partial derivatives.

We give the definition of the partial derivative of a function of more than one variable. In addition, we present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus

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Multivariable Calculus | What is a vector field.

We introduce the notion of a vector field and give some graphical examples. We also define a conservative vector field with examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus

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Vector form of multivariable quadratic approximation

This is the more general form of a quadratic approximation for a scalar-valued multivariable function. It is analogous to a quadratic Taylor polynomial in the single-variable world.

From playlist Multivariable calculus

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Partial derivatives of vector fields, component by component

Here we step through each partial derivative of each component in a vector field, and understand what each means geometrically.

From playlist Multivariable calculus

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How to Evaluate a Multivariable Function Defined by an Integral

How to Evaluate a Multivariable Function Defined by an Integral If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)

From playlist Calculus 3

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11_4_1 The Derivative of the Composition of Functions

The composition of a multivariable function and a vector function and calculating its derivative.

From playlist Advanced Calculus / Multivariable Calculus

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0420 -- Rust: rustfmt / HTTP server

This is #420 in my series of live (Twitch) coding streams. This stream I figured out how to configure rustfmt to automatically format my Rust code more or less how I like, and then moved on to complete more of my HTTP server in Rust. Notebook page: https://tinyurl.com/y3c48hm6 -- Wat

From playlist Excalibur

Related pages

Type theory | Symbol (formal) | John Corcoran (logician) | Explicit substitution | Metalanguage