MATH 19A Midterm: MATH19 Harvard Midterm1F0319 Spring 05

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15 Feb 2019
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You have tr,vo hours to take tiris miclterm. Any answer in decrmal fortn tnust bc acctrrate to three decirnal places. unless otherr,vise specifiecl. Pace l. ourself b-v keeping track of hou" man1, problerns you have left to go and ]rorv much time retnaius. Ytiu do uot have to ans\,rer the problems in any particular order, so tlove to auothel probletn if you iittd you are stuck or spending too rnucli tirne orr a single problem. Please be sure to r,vrite rreatly itlegible ansrvers rvili receive little or uo credit. If rnore space is neecled. use the back of the previous page to continue 1"our lr"ork. Be sure to rnake a note of this on the problem page so that the grader kuorvs u. ltere to find your answers. You may use a calculator on this exarn. but no other aids are allou"ed. Good luck!: (8 points) tright diffelential equations and folrr. krpe fields are giverr irclou-.