17 dierential equations many physical phenomena can be modeled using the language of calculus for example observational evidence suggests that the temperature of a cup of tea or some other ...
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...Dierential equations many physical phenomena can be modeled using the language of calculus for example observational evidence suggests that temperature a cup tea or some other liquid in roomofconstant temperaturewillcoolovertimeatarateproportionaltothedierence between room and symbols if t is time m f at then k where constant which will depend on kind more generally but not this newton s law cooling equation we just wrote down an ideally would like to solve namely nd function describes over though often turns out impossible case various approximation techniques must used use solution important eld mathematics here see how simple useful types informally one derivatives appear typically scientic theory produce system governs process desired functions directly recall from section when variable derivative y sometimes written as instead quite common study chapter first order differential westartbyconsidering only rst appears definition arstorderdierentialequationisanequationoftheform makes ...