chapter 2 dierential calculus in many dimensions descriptions of physical systems can have many state variables the state variables don t always assume arbitrary independent values for instance suppose there ...
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...Chapter dierential calculus in many dimensions descriptions of physical systems can have state variables the don t always assume arbitrary independent values for instance suppose there are three x y and z physically admissible triples live on some surface as depicted figure a is graph if one variable say function other two this case role dependent typically composed graphs glued together at most points choose or remaining shaded patch we represent magnied picture b curve ab intersection with plane constant its derivative respect to denoted more traditionally called partial project onto you get represents slopes tangent lines similar meaning cd yz higher derivatives clear meanings means dierentiate then xx xy seems backward inherited from traditional notation time order dierentiations mixed does not matter both continuous they equal yx ve seen before what ll concentrate here interchangeability roles between certain sciences mechanics thermodynamics particular notorious changing their mi...