Titlebook: Calculus and Analysis in Euclidean Space; Jerry Shurman Textbook 2016 Springer International Publishing AG 2016 derivative.implicit functi

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Inverse and Implicit Functionspecifies some of the variables as functions of the others. The Lagrange multiplier condition follows, giving a method to solve optimization problems with constraints, i.e., to begin doing calculus in curved spaces.

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0172-6056 tics resourcefully by marshaling the skills of...geometric intuition (the visual cortexbeing quickly instinctive)..algebraic manipulation (symbol-patternsbeing precise and robust)..incisive use of natural langu978-3-319-84130-4978-3-319-49314-5Series ISSN 0172-6056 Series E-ISSN 2197-5604

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The Derivativeting the original mapping near the point of approximation. The derivative properties are established using the Bachmann–Landau notat–on scheme, allowing a range of ideas from calculus to be handled uniformly. The chapter then computes the derivative in coordinates, and it studies the multivariable c