In mathematics, the symmetric derivative is an operation generalizing the ordinary derivative. It is defined as The expression under the limit is sometimes called the symmetric difference quotient. A function is said to be symmetrically differentiable at a point x if its symmetric derivative exists at that point. If a function is differentiable (in the usual sense) at a point, then it is also symmetrically differentiable, but the converse is not true. A well-known counterexample is the absolute value function f(x) = |x|, which is not differentiable at x = 0, but is symmetrically differentiable here with symmetric derivative 0. For differentiable functions, the symmetric difference quotient does provide a better numerical approximation of the derivative than the usual difference quotient. The symmetric derivative at a given point equals the arithmetic mean of the left and right derivatives at that point, if the latter two both exist. Neither Rolle's theorem nor the mean-value theorem hold for the symmetric derivative; some similar but weaker statements have been proved. (Wikipedia).
Symmetric matrices - eigenvalues & eigenvectors
Free ebook http://tinyurl.com/EngMathYT A basic introduction to symmetric matrices and their properties, including eigenvalues and eigenvectors. Several examples are presented to illustrate the ideas. Symmetric matrices enjoy interesting applications to quadratic forms.
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From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?
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We use the definition of derivative to find the derivative of x^-2. For more calculus tutorials, please see my new "just calculus" channel: 👉https://www.youtube.com/justcalculus If you find my videos helpful, then consider supporting me on Patreon: 👉 https://www.patreon.com/blackpenred
From playlist Sect 2.7, Definition of Derivative
Derivatives are the main object of study in differential calculus. They describe rates of change of functions. That makes them incredibly useful in all of science, as many models can be expressed by describing the changes over time (e.g. of physical quantities). However, the abstract defin
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From playlist Symmetric Matrices
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Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
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Visit http://ilectureonline.com for more math and science lectures! In this video I will describe the physical meaning of a derivative.
From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?
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From playlist Calculus Ch 3 - Derivatives
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From playlist Rings and modules