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available. Most of the classes have practice problems with solutions available on the practice problems pages. using differentials to approximate error Also most classes have assignment problems for instructors to assign for

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homework (answers/solutions to the assignment problems are not given or available on the site). Algebra [Notes] differentials to approximate change [Practice Problems] [Assignment Problems] Calculus I [Notes] [Practice Problems] [Assignment Problems] Calculus II [Notes] [Practice Problems] [Assignment Problems] Calculus III [Notes] [Practice Problems] [Assignment Problems] Differential Equations differentials to approximate square root [Notes] Extras Here are some extras topics that I have on the site that do not really rise to the level of full class notes. Algebra/Trig Review Common Math Errors Complex Number Primer How To Study Math Close the Menu Current Location : Calculus I (Notes) / Applications of Derivatives / Differentials Calculus

Differentials To Approximate Volume

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nieuwe versie behouden Ongedaan maken Sluiten Deze video is niet beschikbaar. WeergavewachtrijWachtrijWeergavewachtrijWachtrij Alles verwijderenOntkoppelen Laden... Weergavewachtrij Wachtrij __count__/__total__ Errors Approximations Using Differentials IMA Videos AbonnerenGeabonneerdAfmelden33.01733K Laden... Laden... Bezig... Toevoegen aan Wil je http://tutorial.math.lamar.edu/Classes/CalcI/Differentials.aspx hier later nog een keer naar kijken? Log in om deze video toe te voegen aan een afspeellijst. Inloggen Delen Meer Rapporteren Wil je een melding indienen over de video? Log in om ongepaste content te melden. Inloggen Transcript Statistieken 17.226 weergaven 27 Vind je dit een leuke video? Log in om je mening te geven. Inloggen 28 15 Vind je dit geen leuke video? Log https://www.youtube.com/watch?v=kXkwrhdqXWg in om je mening te geven. Inloggen 16 Laden... Laden... Transcript Het interactieve transcript kan niet worden geladen. Laden... Laden... Beoordelingen zijn beschikbaar wanneer de video is verhuurd. Deze functie is momenteel niet beschikbaar. Probeer het later opnieuw. Gepubliceerd op 4 aug. 2012Errors & Approximation - Application of Derivative ( Use of Differentials) - There are many application of derivative concept in calculus mathematics. One of them is Errors and Approximation. We can easily solve question related to errors in physics as well as mathematics using the concept of derivative , using the concept of differentials.In this Calculus video, we use differential's concept to find the approximate error in calculating the volume of a sphere. For this we know the radius of the sphere and we know the error while calculating the radius of that sphere. Now we have to use the concept of differentials to find the approximate errors while calculating the entire volume the sphere.This video calculus video is created under the application of derivative ( use of differentials) playlist . For complete list of videos on use of differentials click the link below- http://www.youtube.com/playlist?list=...To play the Application of Derivative from beginning

with: (1) Functions of several variables. (2) Evaluation of partial derivatives, and the chain rules of differentiation. (3) Manipulation of summations in algebraic context. At this mathematical level our presentation can be briefer. We can dispense https://www.lhup.edu/~dsimanek/scenario/errorman/calculus.htm with the tedious explanations and elaborations of previous chapters. 6.2 THE CHAIN RULE AND DETERMINATE ERRORS If a result R = R(x,y,z) is calculated from a number of data quantities, x, y and z, then the relation: [6-1] ∂R ∂R ∂R dR = —— dx + —— dy + —— dz ∂x ∂y ∂z

holds. This is one of the "chain rules" of calculus. This equation has as differentials to many terms as there are variables.

Then, if the fractional errors are small, the differentials dR, dx, dy and dz may be replaced by the absolute errors ΔR, Δx, Δy, and Δz, and written: [6-2] ∂R ∂R ∂R ΔR ≈ —— Δx + —— Δy + —— Δz ∂x ∂y ∂z Strictly this is no longer an equality, but an approximation to DR, since the higher order terms in differentials to approximate the Taylor expansion have been neglected. So long as the errors are of the order of a few percent or less, this will not matter. This equation is now an error propagation equation. [6-3] Finally, divide equation (6.2) by R: ΔR x ∂R Δx y ∂R Δy z ∂R Δz —— = —————+——— ——+————— R R ∂x x R ∂y y R ∂z z

The factors of the form Δx/x, Δy/y, etc are relative (fractional) errors. This equation shows how the errors in the result depend on the errors in the data. Eq. 6.2 and 6.3 are called the standard form error equations. They are also called determinate error equations, because they are strictly valid for determinate errors (not indeterminate errors). [We'll get to indeterminate errors soon.] The coefficients in Eq. 6.3 of the fractional errors are of the form [(x/R)(∂R/dx)]. These play the very important role of "weighting" factors in the various error terms. At this point numeric values of the relative errors could be substituted into this equation, along with the other measured quantities, x, y, z, to calculate ΔR. Notice the character of the standard form error equation. It has one term for each error source, and that error value appears o

 

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