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diffeq1 - Appendix C Mathematical Topics §C.1 Some...

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Unformatted text preview: Appendix C Mathematical Topics §C.1 Some ordinary differential equations and their solutions §C.2 Expansions of functions in Taylor series §C.3 Differentiation of integrals (the Leibniz formula) §C.4 The gamma function §C.5 The hyperbolic functions §C.6 The error function In this appendix we summarize information on mathematical topics (other th and tensors) that are useful in the study of transport phenomena.1 §C.1 SOME ORDINARY DIFFERENTIAL EQUATIONS AND THEIR SOLUTIONS We assemble here a short list of differential e phenomena. The reader is assumed to be fami them. The quantities a, Solution Equation e _ fix) (it gig} d y _ a + fix)? - 305) _+ 2 = 332‘; ay U __ 2 :0 dx2 “3" fgdy= Ifdx + C1 y = e'ffaqefmg dx + C1) 3* = Cicomrx + Casinax y = C1 cosh ax + C2 sinhexor y = Casi-ax + C‘s—ax (31 c _ 2 - y cos ax + 3: sm ax I quations that arise frequently in " liar with these equations and 110 b, and c are real constants and f and g are functions of x, ...
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