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Get Full Access to Elementary Differential Equations And Boundary Value Problems - 10 Edition - Chapter 6.2 - Problem 28
Get Full Access to Elementary Differential Equations And Boundary Value Problems - 10 Edition - Chapter 6.2 - Problem 28

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# The Laplace transforms of certain functions can be found

ISBN: 9780470458310 168

## Solution for problem 28 Chapter 6.2

Elementary Differential Equations and Boundary Value Problems | 10th Edition

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Problem 28

The Laplace transforms of certain functions can be found conveniently from their Taylorseries expansions.(a) Using the Taylor series for sin tsin t = n=0(1)nt2n+1(2n + 1)!,and assuming that the Laplace transform of this series can be computed term by term,verify thatL{sin t} =1s2 + 1, s > 1.(b) Letf(t) =(sin t)/t, t = 0,1, t = 0.Find the Taylor series for f about t = 0. Assuming that the Laplace transform of thisfunction can be computed term by term, verify thatL{f(t)} = arctan(1/s), s > 1(c) The Bessel function of the first kind of order zero, J0, has the Taylor series (seeSection 5.7)J0(t) = n=0(1)nt2n22n(n!)2 .Assuming that the following Laplace transforms can be computed term by term, verifythatL{J0(t)} = (s2 + 1)1/2, s > 1andL{J0(t)} = s1e1/(4s), s > 0.

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Lecture Notes March 9 , 2016 Reproduction and Development  Anatomy and Physiology o Gametogenesis- the production of gametes  Spermatogenesis- production of sperm- in the testes located in a sack like structure called the scrotum- occurs continuously throughout a male’s reproductive life  Testes have two functional components o Seminiferous tubules- where the sperm is produced o Interstitial Cells- secrete the male sex hormone- testosterone  During spermatogenesis the cells lining the seminiferous tubules are called 1° spermatocytes (2N)  2° spermatocytes (N)  become spermatids ----differentiation (lose cytoplasm and grow tail) Sperm (Spermatozoa)  Sperm have little food reserve and die within 72 hours, but in very low temperatures they can survive for years  Men must release 100 million sperm during intercourse to be considered fertile- some men release 1 billion per ejaculation  Oogenesis- production of eggs in the ovaries- suspended in the abdominal cavity  Two functions of ovaries o Produce the oocytes o Secrete female sex hormones- estrogen and progesterone  Begins before the female is born o Oogonia 1° oocytes (2N) (born with 3-400K) 2° oocytes o Happens once a month only one created  During cytokinesis one of the two cells formed during meiosis gets less cytoplasm- polar body 1  Secondary oocytes are in a sack structure called the follicle  At puberty ovaries begin to release one 2° oocyte every 28 days- ovulation  Ovulation begins when a follicle near the surface of the ovary begins to grow and fill with fluid  Eventually the pressure inside the follicle becomes so great that it ruptures and the 2° oocyte is released into the abdominal cavity  Meiosis II only occurs if the 2° oocyte is penetrated by a sperm  During Meiosis II another polar body is formed- three of the four eggs disintegrate  Once the true egg is formed- fertilization can take place and the zygote 2N is formed Lecture Notes  Since the female has been carrying 1° oocyte for many years the chances that mutations have occurred is much higher than for male sperm o Of the 3-400K oocytes only 13 are ovulated each year o Not very many are released throughout a females life and they will all disintegrate around the age of 50 o Male Reproductive Tract  A coiled tube called the epididymis lies on the surface of the testes and carries the sperm to the vasteferens  That’s what gets cut when you have a vasectomy  Vasteferens (2) run into the abdominal cavity and join the urethra just beyond the point where it leaves the bladder  The urethra passes through the penis and empties to the outside  As the sperm passes through the vasterferens and the urethra seminal fluids added to form semen (seminal fluid + sperm = semen)  Seminal fluid is produced by three glands o Seminal vesicles o Prostate o Cowper’s  Seminal Fluid has four main functions o Vehicle for the transport of sperm o Lubrication of passages o Chemical buffer against the acids in the female reproductive tract o Contains sugars- provide sugars which provide energy to the sperm o Female Reproductive Tract  From the ovary 2° oocyte travels through the abdominal cavity and is swept into the oviduct/ fallopian tube  The swept down the fallopian tube into the uterus  Uterus- pair shaped and muscular  If 2° oocyte is entered by a sperm meiosis II occurs, egg is fertilized and implants on uterine wall  If egg is not penetrated it passes through the cervix into the vagina during menstruation

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##### ISBN: 9780470458310

The full step-by-step solution to problem: 28 from chapter: 6.2 was answered by , our top Math solution expert on 12/23/17, 04:36PM. This textbook survival guide was created for the textbook: Elementary Differential Equations and Boundary Value Problems, edition: 10. The answer to “The Laplace transforms of certain functions can be found conveniently from their Taylorseries expansions.(a) Using the Taylor series for sin tsin t = n=0(1)nt2n+1(2n + 1)!,and assuming that the Laplace transform of this series can be computed term by term,verify thatL{sin t} =1s2 + 1, s > 1.(b) Letf(t) =(sin t)/t, t = 0,1, t = 0.Find the Taylor series for f about t = 0. Assuming that the Laplace transform of thisfunction can be computed term by term, verify thatL{f(t)} = arctan(1/s), s > 1(c) The Bessel function of the first kind of order zero, J0, has the Taylor series (seeSection 5.7)J0(t) = n=0(1)nt2n22n(n!)2 .Assuming that the following Laplace transforms can be computed term by term, verifythatL{J0(t)} = (s2 + 1)1/2, s > 1andL{J0(t)} = s1e1/(4s), s > 0.” is broken down into a number of easy to follow steps, and 130 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 76 chapters, and 2039 solutions. Since the solution to 28 from 6.2 chapter was answered, more than 241 students have viewed the full step-by-step answer. Elementary Differential Equations and Boundary Value Problems was written by and is associated to the ISBN: 9780470458310.

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