Transcription of Chapter 7 Riemann-Stieltjes Integration
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Chapter 7 Riemann-Stieltjes Integration
Chapter 7 Riemann-Stieltjes IntegrationCalculus provides us with tools to study nicely behaved phenomena using smalldiscrete increments for information collection. The general idea is to (intelligently)connect information obtained from examination of a phenomenon over a lot of tinydiscrete increments of some related quantity to close in on or approximate some-thing that behaves in a controlled ( , bounded, continuous, etc.) way. The clos-ing in on approach is useful only if we can get back to information concerning thephenomena that was originally under study. The bene t of this approach is mostbeautifully illustrated with the elementary theory of integral calculus us to adapt some limiting formulas that relate quantities of physical interestto study more realistic situations involving the three formulas that are encountered frequently in most standard phys-ical science and physics classes at the pre-college level:A l *d r tm d the space that is provided to indicate what you know about these use of these formulas is limited to situations where the quantities on theright are constant.
276 CHAPTER 7. RIEMANN-STIELTJES INTEGRATION wish to study, by making certain assumptions and applying the known formulas incrementally. Note that except for the units, the formulas are indistinguishable. Consequently, illustrating the “closing in on" or approximating process with any one of them car-
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