Laplace and Fourier Transforms Essay Example for Free

Laplace and Fourier Transforms Essay Laplace and Fourier Transforms are operator which when applied on a function, lead to another function in a different variable. These transforms are very useful in solving many problems in different branches of engineering. What is essentially done is that an engineering problem is modeled as a mathematical equations and these equations are generally ordinary and / partial differential equations with boundary conditions. These equations are difficult to be solved by analytical methods, however, these equations can be converted into algebraic equations by using Laplace or Fourier Transforms and then it becomes easy to solve these equations. Once these subsidiary algebraic equations are solved, the solution of these algebraic equations is transformed back and thus the solution of the engineering problem is obtained. Thus it can be said that there are following three steps involved in solving differential equations with boundary conditions. (1) Transforming the differential equations with boundary conditions into simple algebraic equations (subsidiary equations). (2) Solution of the subsidiary algebraic equations by algebraic manipulations. (3) Transforming back the result(s) of subsidiary algebraic equations to obtain the solutions. Therefore, it can be seen that the problem of solving a differential equation is simplified into solving of algebraic equations by use of Laplace or Fourier transforms and needless to say that solving an algebraic equation is much simpler than solving a differential equation. Therefore, it is not unusual that Laplace and Fourier transforms find extensive application is solving engineering problems in mechanical as well as electrical domain where the driving force has discontinuities, is impulsive and is periodic function of complex shape. Besides, this method solves the problem directly. Initial value problems are solved without determining the general solution first. Also, nonhomogeneous equations are solved without solving the homogeneous equations first. These transformations are useful in solving not only the ordinary differential equations but in solving the partial differential equations as well. In this paper, the definition, properties and applications of Laplace and Fourier transforms is discussed in detail. Laplace Transform Let us consider a function f = f(t), which is defined for all t 0. When this function is multiplied by e-st and the product is integrated from t = 0 to t = ? and if this integral exists, then this integral will be a function of s, let us say it is F(s); then F(s) is Laplace transform of f(t).

Chimpanzees Essay -- essays research papers

Chimpanzees are a genus of the great ape of Africa, with long black hair and log protruding ears. Humans know them for their intelligence and there very similarities. They have developed family ties similar to man. Over the generations they have even had developed tools out of natural materials. Food for chimpanzees is very important to them due to the excessive amount eating. Chimpanzees eat a variety of foods. They will get their food in many different ways. Bananas are one of the most favored foods of chimpanzees. They will eat it with the peal on or they will take the peal off. Researchers in Africa had video camera and had been taping the primates while eating. One day while video tapeing they caught a male chimpanzee stealing a bundle of bananas from the storage tent, and put the bundle of bananas over his shoulder and walked out. The researchers did not try to top the adult male, because they knew that the adult male are very strong and can get violent if they are bothered while eating. These primates also eat variety leaves, twigs and seeds that are found through out the jungle. Chimpanzees are nomadic they will travel up to six miles a day for food. Once food is found they will spend up to seven hours a day eating. Chimpanzee will also eat meat, but it has to be fresh meat. This means that the male’s hunt and kill there own meat in groups; some of the animals they look for are baby baboons, antelope and bush pigs. Chimpanzee’s intelligence is the one that is clos...

Open Adoption vs. Closed Adoption

Many children are adopted each year, and with these children being adopted there are adoptions. There are many forms of adoption used throughout the world, but the biggest forms of adoption are closed adoption and open adoption. Open adoptions are adoptions in which the birthmother, the biological mother of an adoptee, is allowed contact with the adoptee. Closed adoption is an adoption where the birthmother of the adoptee is not present in the child’s life in any way shape or form. The birth family is completely cut off and cannot give or receive any information regarding their welfare or the adoptee’s.Closed adoptions are a better option than open adoption and should be mandatory because it would prevent confusion the child may face, allow children to actually fit into their adoptive family, provide privacy and closure and protect families from unstable birthparents. Having multiple sets of parents creates confusion in a family, and mostly for the child. â€Å"Adoptio n was created out of the recognition that children need to feel secure about who their parents are and what their parent’s role is† (Harnack 84). This is what’s best for the child in most if not all adoptions.The child needs to know who exactly is their parent, not a birthparent but the adoptive parent. Adoptive parents are permanent and a child may not grasp that idea with a tentative parent; the birth parent. When a child does not know who their parent is, it creates trouble. The child may even seek out trouble. Children are developing and such an unstable family creates really harsh developmental issues within the adoptee. All children need to know who their parents are and be able to trust that their parents are not going to leave them. Having a birth parent around makes things difficult for everyone, but most importantly the adoptee. The adoptee may have a reduced ability to assimilate into family-Interaction with the birth family may make it harder for the child to assimilate into the adoptive family† (â€Å"Open Adoption: Disadvantages†). This is one of many examples of how adoptive families are not as whole and full as they could potentially be because of problems with the birth parent. The feeling of rejection from a birthmother can seriously impact the intellectual growth and development of an adoptee. A recent interview of an adoptee provided more evidence and demonstrated how the privacy provided with a closed adoption would give the adoptive parents more closure.The fourteen year old adoptee learned about her closed adoption ten years ago when she was four, her parents wanted to wait to tell her until she was eighteen but the adoptee found out through another family member. So then the adoption became open allowing the adoptee contact with her birth mother. â€Å"Now,† said the adoptee â€Å"I speak with my birthmother more than I do my mom† (Anonymous). Her birthmother being a big part of her life, t he adoptee is losing her relationship with her adoptive parents. Her adoptive parents feel that if the birthmother wasn’t so intrusive in their lives that they would have a better relationship with their daughter.This is why the closure and privacy involved in a closed adoption is so critical. Although there are so many benefits in a closed adoption some people still argue that open adoption is not completely the worst option in some cases. Among those arguing are adoptees who develop clinical illnesses in their lifetime. One thing a doctor may ask when a patient is diagnosed with a disease is for medical history. An adoptee in a closed adoption does not have access to their medical history, that information is sealed at a court house as with the contact information of the birthfamily.In some cases the birth family is contacted and refuses to give up the vital information that would be beneficial in the treatment of a patient. â€Å"When an adoptee is denied medical informat ion†¦ he may feel like and adult who has no rights whatsoever† (Eldridge 269). An open adoption would ensure a medical history and prevent the scandal of being without, but this positive factor of open adoption does not outweigh the benefits of the closed adoption. One of those benefits includes escaping the risk of â€Å"an unstable birthparent [who] could cause problems† (Adamec).Many times adoptions occur because the birthparent is unsuited to raise the child. This includes birthparents who abuse drugs, are unemployed or even felonious. Unstable birthparents provide bad examples for adoptees and much of the time influence adoptees. Children have very malleable minds; this is why it is so easy for children to learn. They pick up traits and learn bad habits through the time they spend with their birthparents. There have also been worse cases, for example there are cases where birthparents kidnap the adoptee.The adoptive parents and the adoptee should never have to face the stress or trauma an unstable birth parent would cause. Open adoption has become conventional, almost a standard for adoptions. Closed adoptions are almost unheard of in this day and age. One would think with all the benefits of a closed adoption it would be the standard, but such is not the case. Closed adoptions are a better option because it helps adoptees to actually fit into their adoptive family, helps prevent confusion in an adoptee, provides privacy and closure, and protect the adoptive families from unstable birthfamilies.Work Cited Adamec, Christine. â€Å"†Open† or â€Å"Closed† Adoption? † Family Education. Pearson Education, Inc. , 2004. Web. 23 Feb. 2013. . Anonymous. Personal interview. 22 February 2013. Eldridge, Sherrie. Twenty Things Adopted Kids Wish Their Adoptive Parents Knew. New York: Dell Publishing, 1999. Print. Harnack, Andrew. Adoption Opposing Viewpoints. Miami: San Val Incorporated, 1995. Print. â€Å"Open Adoption: Di sadvantages. † American Pregnancy Association. N. p. , Oct. 2008. Web. 7 Feb. 2013. .

FAQs About Purchasing and Maintaining a Chainsaw

Small chainsaws  are commonly purchased by rural property owners, tree and timber owners, firewood users and farmers. Often, a new chainsaw owner can become frustrated at the learning curve associated with chainsaw ownership. Here are answers to many questions asked by people planning to buy and operate a chainsaw. This Frequently Asked Questions page is for the new chainsaw owner and addresses the most common concerns about purchasing and maintaining a chainsaw. How to Select a New Chainsaw You should buy only the chainsaw you feel comfortable with. Chainsaw manufacturers are using newer  and lighter materials to build more powerful but durable machines.   Where to Purchase Most foresters and loggers agree and suggest purchasing chainsaws like Stihl, Jonsered or Husqvarna with strong local dealers.  Any reputable brand of chainsaw you purchase with a local dealership servicing that brand can last a long time. How to Learn Operating One There are many great resources on the Internet that can help you operate your saw. The best way is  to place it on flat ground, pull the start control to the on position, and hold the front handle with your left hand as you place your right foot on the rear handle. Make sure to safely review hazards before operating a chainsaw. According to saw expert Carl Smith: If you place your hands on a chainsaw, you must keep in mind that it is like grabbing  a hand grenade without a pin in it. It is very likely to go off in your face. From the moment that you take it out of storage to the time that it goes back to the same place, you can be hurt by either it, or by whatever you will be cutting. Chainsaw Kickbacks and Prevention One in every 12 timbering accidents is caused by chainsaw kickback. If a professional tree feller is at risk, it can definitely happen to a less experienced chainsaw user.  The main focus is to be aware and alert and always wear chainsaw safety clothing. Notice the position of the chainsaw bars nose and chains. Chainsaw Protection Equipment Wearing the proper clothing is one of the best safeguards for you to reduce the possibility of serious injury. Wear sturdy, snug-fitting clothing that gives you complete freedom of movement. The Most Important Parts of a Chainsaw OSHA requires you to have  10 parts on a chainsaw including the chain catcher, flywheel, and the clutch. It is also wise to not buy a  chainsaw bar  thats too short for your average trunk or limb diameter. Mixing Oil With Gas All 2-cycle engines require gas to be mixed with oil. The oil tank is for bar and chain lubricant. Additionally, you really do need to use a quality bar oil as your chainsaw bar oil rather than regular motor oil. This is because the bar and chain oil have a high-tack additive that prevents it from slinging off the chain as it travels. Chainsaw Chipper Vs. Chisel Chain A chipper is a round tooth, round filled chain. It maintains its edge better in dirty cutting. The chisel chain is a square tooth, often ground round and older in design. Filing a Chain When the chips it cuts are no longer chips but dust, or when you have to physically push or force it to cut, you need to sharpen your chain. Depth Gauge Depth gauges are the metal point in front of each tooth on a chainsaw chain. They determine how large a chip the tooth can be taken by the cutter.