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In each of 1 through 10, write the Fourier integral representation (14.1) of the

Advanced Engineering Mathematics | 7th Edition | ISBN: 9781111427412 | Authors: Peter V. O'Neill ISBN: 9781111427412 173

Solution for problem 14.2 Chapter 14

Advanced Engineering Mathematics | 7th Edition

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Advanced Engineering Mathematics | 7th Edition | ISBN: 9781111427412 | Authors: Peter V. O'Neill

Advanced Engineering Mathematics | 7th Edition

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Problem 14.2

In each of 1 through 10, write the Fourier integral representation (14.1) of the function and determine what this integral converges to.f (x) = k for 10 x 10 0 for |x| > 10

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Chapter 33 The Animal Body: Basic Form and Function  Asymmetric: sides are different when split in half  Radial symmetry: sides are same when split from any angle  Bilateral symmetry: o Anterior: front o Posterior: back o Dorsal: top o Ventral: bottom  As a cell increases in size, its surface area to volume ratio decreases  Trend towards multicellularity  Specialization o The setting spart of a particular organ for the performance of a particular function. (biology) the structural adaptation of some body part for a particular function  Animal bioenergetics o An animal's body size, activity level, and environment impacts the ways it uses and obtains energy  Animal tissues o Vertebrate animals have two major body cavities. The dorsal cavity, indicated in green, contains the cranial and the spinal cavity. The ventral cavity, indicated in yellow, contains the thoracic cavity and the abdominopelvic cavity. The thoracic cavity is separated from the abdominopelvic cavity by the diaphragm. The thoracic cavity is separated into the abdominal cavity and the pelvic cavity by an imaginary line parallel to the pelvis bones  Animals have four main categories of tissues o Epithelial  Closely packed cells that cover body surfaces and line internal organs  Three shapes  Squamous – flat; slightly irregular shape, and a small, centrally located nucleus; can be stratified into layers  Cuboidal – cube; line tubules in the mammalian kidney, where they are involved in filtering the blood  Columnar – column; absorb material from the digestive tract. Goblet cells secret mucous into the digestive tract lumen o Pseudostratified columnar epithelia line the respiratory tract. They exist in one layer, but the arrangement of nuclei at different levels makes it appear that there is more than one layer. Goblet cells interspersed between the columnar epithelial cells secrete mucous into the respiratory tract  Named by the number of cell layers they have and the shape of the cells on their apical layer o Connective  Components  Matrix  Ground Substance  Protein Fibers  Loose connective tissue is composed of loosely woven collagen and elastic fibers. The fibers and other components of the connective tissue matrix are secreted by fibroblasts  Fibrous connective tissue from the tendon has strands of collagen fibers lined up in parallel  Hyaline cartilage consists of a matrix with cells called chondrocytes embedded in it. The chondrocytes exist in cavities in the matrix called lacunae  Compact bone is a dense matrix on the outer surface of bone. Spongy bone, inside the compact bone, is porous with web-like trabeculae.  Compact bone is organized into rings called osteons. Blood vessels, nerves, and lymphatic vessels are found in the central Haversian canal. Rings of lamellae surround the Haversian canal. Between the lamellae are cavities called lacunae. Canaliculi are microchannels connecting the lacunae together.  Osteoblasts surround the exterior of the bone. Osteoclasts bore tunnels into the bone and osteocytes are found in the lacunae.  Adipose is a connective tissue is made up of cells called adipocytes. Adipocytes have small nuclei localized at the cell edge  Blood is a connective tissue that has a fluid matrix, called plasma, and no fibers. Erythrocytes (red blood cells), the predominant cell type, are involved in the transport of oxygen and carbon dioxide. Also present are various leukocytes (white blood cells) involved in immune response o Muscle tissue  Most abundant tissue in animals  Smooth muscle cells do not have striations, while skeletal muscle cells do. Cardiac muscle cells have striations, but, unlike the multinucleate skeletal cells, they have only one nucleus. Cardiac muscle tissue also has intercalated discs, specialized regions running along the plasma membrane that join adjacent cardiac muscle cells and assist in passing an electrical impulse from cell to cell o Nervous tissue  Nervous tissue senses stimuli and transmits information  Neurons are functional cells in the nervous system  Other cells in nervous tissue  Insulated axons  Nourish neurons  Regulate the fluid around neurons  The neuron has projections called dendrites that receive signals and projections called axons that send signals. Also shown are two types of glial cells: astrocytes regulate the chemical environment of the nerve cell, and oligodendrocytes insulate the axon so the electrical nerve impulse is transferred more efficiently  Homeostasis o Regulated by feedback mechanisms o Living organisms are not closed systems – exchange matter and energy with their environment o a steady state; equilibrium o The body is able to regulate temperature in response to signals from the nervous system o The birth of a human infant is the result of positive feedback Chapter 34 Animal Nutrition and the Digestive System  Takes place in many different compartments  As animals become more complex, they tend to compartmentalize things  Specialization = how cells perform different functions  Herbivores = live entirely on plant material  Carnivores = meat eaters  Omnivores = feed upon animal and plant material  Sponges- food vacuoles o Bunches of cells o Most simple organism  Incomplete systems- gastrovascular cavity o Singular cavity organism o Food enters mouth and undigested food is expelled back out of the mouth o These organisms tend to live in aquatic environments o Also cnidarians and flat worms  Humans have a complete digestive system o Opening for nutrients to go in o Opening for waste to come out o Allows of compartmentalization  Human digestion components o Oral cavity, salivary glands, stomach, gall-bladder, liver, pancreas, small intestine, large intestine, rectum, anus  Oral cavity o Where digestion begins o Mechanical (chewing-which breaks down the food into smaller particles which increases the surface area) and chemical digestion o The tongue  Tastes  Shapes food into a ball called a bolus  Moves bolus towards the pharynx o Salivary glands release  A glycoprotein that moistens and lubricates food  Buffers that neutralize acids  Salivary amylase-an enzyme that begins the hydrolysis of starch  Antibacterial agents that kill some bacteria ingested with food  Lingual lipase-triglycerides broken down; released by tongue o As we swallow, the epiglottis closes the respiratory system o Peristalsis  Moves food through the esophagus into the stomach  Muscular movement (series of contractions) of material from the mouth to the stomach (through the esophagus) o Esophagus does not carry on any type of digestion, only a passageway for food to get into the stomach o Stomach  Some chemical digestion occurs  Lined with cells that release materials  pH of stomach is really low, around 2  contents are very acidic  gastric juice consists of  mucus-protects stomach from damage; coats stomach  protein digesting enzyme-  strong acid-  where consumption of alcohol takes place  ulcer happens to regions of the stomach aren’t protected, so gastric juices create holes in stomach o Chemical digestion in the stomach  pepsinogen (inactive form of pepsin) and HCl are secreted into the lumen of the stomach  HCl converts pepsinogen to pepsin  pepsin helps activate more pepsinogen  pepsin begins the chemical digestion of proteins  sphincters in stomach help to regulate how much food enters and exits stomach  Small intestine o major organ of chemical digestion and absorption o absorption-absorbing materials into the blood system o highly vascularized o chyme mixes with the digestive juices from the pancreas, liver, and gland cells in the intestinal wall o pancreas- structure where insulin is produced; has cells that produce enzymes; main structure that regulates our glucose o alkaline pH (8 or 9) o small intestine is well adapted for absorption o surface area increased by  folds in the intestinal lining  fingerlike projections called villi  tiny projections on the surface of the intestinal cells called microvilli o arterial blood system-red o venus system-blue o veins lead to heart o arteries lead away from the heart  Large intestine o Also called the colon o Has a pouch (cecum) near its junction with the small intestine which bears the appendix o Contains large populations of E. coli which produce important vitamins o Absorbs these vitamins and water into the blood stream o No chemical digestion occurs here  Appendix o Vestibular organ- something left in our body that does not have a purpose  Food processing o Occurs in 4 stages: o Ingestion-occurs through mouth o Digestion-mechanical & chemical breakdown o Absorption-nutrient molecules enter body cells o Elimination- gets rid of undigested material  Breakdown of macromolecules o Protein  protein-digesting enzymes  amino acids o Polysaccharide/disaccharide  carb-digesting enzymes  monosaccharides o Nucleic acid  nucleic acid-digesting enzymes  nucleotides o Fat  fat-digesting enzymes  fatty acids/glycerol  Digestion of carbs o Digestion of carbohydrates is performed by several enzymes. Starch and glycogen are broken down into glucose by amylase and maltase. Sucrose (table sugar) and lactose (milk sugar) are broken down by sucrase and lactase, respectively  Digestion of proteins o Protein digestion is a multistep process that begins in the stomach and continues through the intestines  Digestion of lipids o Lipids are digested and absorbed in the small intestine o Mechanical and chemical digestion of food takes place in many steps, beginning in the mouth and ending in the rectum  Know compartments of digestive system, what each compartment does, where mechanical and chemical breakdown begins, know enzymes involved & what they do, memorize macromolecules, & about eh digestive system  https://www.youtube.com/watchv=zr4onA2k_LY Chapter 35 Neurons and Nervous Systems  Review structure of cell membranes  Review diffusion and active transport  Neuron—functional cells in nervous system o Know structure of the neuron o Cell body—normal cell activities o Dendrites, axon, synapse o Some axons are bare, and some have a sheath o Myelin sheath—enable quick responses o Sometimes have strange looking anatomies  Unipolar, bipolar, multipolar, pseudopolar o Glial cells support neurons and maintain the environment of the nervous system  Nervous systems have two main anatomical divisions o The central nervous system (CNS) consists of the brain and spinal cord (vertebrates)  Decisions are made by nervous system; discriminates between important info and no important info o The peripheral nervous system (PNS) is located outside the CNS and consists of nerves (bundles of neurons wrapped in connective tissue) and ganglia clusters of cell bodies  The Nervous System o Obtains sensory info, sensory input o Processes sensory info, integration o Sends commands to effector cells (muscles and glands) that carry out appropriate responses, motor output  Sensory neurons o Convey signals from sensory receptors to the CNS  Interneurons o Located entirely in the CNS and they integrate info and send it to the motor neurons  Motor neurons o Convey signals to effector cells  Simple reflex arc o Demonstrates the relationship between neurons and nervous system structure and function  Resting potential o In order for a neuron to be stimulated, must be at resting potential  Gated channels o When stimulus is applied, these open up and allow sodium to move in o Inside loses its negative charge  Threshold response o Minimum amount of stimulation needed to generate action potential  Action potential o Threshold o Depolarization o Repolarization o Hyperpolarization  Propagation and synapse o The movement of an action potential down the neuron (propagation) o One area of a neuron depolarizes  A stimulus o any factor that causes a nerve signal to be generated o Alters the permeability of a portion of the neuron membrane o Allows ions to pass through o Changes the membrane’s voltage  A nerve signal, action potential, is o A change in the membrane voltage o From the resting potential o To a maximum level, and o Back to the resting potential  Action potentials are o Self-propagated in a one-way chain along a neuron all-or-none events o Threshold versus non-threshold o Frequency of action potentials, but not their strength changes with the strength of the stimulus  Myelin sheath o Covers up a part of the axon o This area of membrane cannot be stimulated o Nodes of Ranvier—gaps in myelin coverage along axons  Synapse o Relay points between a synaptic terminal of a sending neuron and a receiving cell o Polarizations:  Depolarization  Repolarization  Hyperpolarization o The receiving cell can be:  Another neuron  An effector cell such as a muscle or endocrine cell  Chemical synapses o The ending (presynaptic) cell secretes a chemical signal, a neurotransmitter o The neurotransmitter crosses the synaptic cleft o The neurotransmitter binds to a specific receptor on the surface of the receiving (postsynaptic) cell o Responsible for the determination of if cell moves on or not o Action potential triggers neurotransmitter o Neuron that has decision—postsynaptic neuron o Has action potential—presynaptic neuron o Bonding of neurotransmitter makes the decision o Postsynaptic neuron begins to depolarize if Na channel opens (gains Na) o Postsynaptic neuron begins to hyperpolarize if K channel opens (loses K)  Synapse o Some neurotransmitters excite a receiving cell (EPSP) o Some inhibit a receiving cell (IPSP) o A receiving neuron’s membrane may receive excitatory and inhibitory signals from different sending neurons o The summation of excitation and inhabitation determines if a neuron will transit a nerve signal o One the action potential is generated, everything is done and goes through the process o A single neuron can receive both excitatory and inhibitory inputs from multiple neurons, resulting in local membrane depolarization (EPSP input) and hyperpolarization (IPSP input). All these inputs are added together at the axon hillock. If the EPSPs are strong enough to overcome the IPSPs and reach the threshold of excitation, the neuron will fire.  Presynaptic/postsynaptic neurons, IPSP, EPSP, polarizations  Nervous System Overview o The flow of information in the nervous system relies on synaptic integration; how many neurons are organized in the body o The brain has thousands and thousands of neurons arranged in blocks all receiving either excitatory or inhibitory signals o There are divergent circuits-neurons in one block fan out to form connections with other blocks o There are also convergent circuits-signals from many blocks are relayed to a few blocks  Evolutionary Trends o The nervous systems of invertebrates are not as complex as that those of vertebrates; however they are still able to respond to stimuli and carryout some complex behavior o Behavior is controlled by nervous system and hormone system o Trends to look for  Whole body response to more local response  Cephalization – the formation of a head  Specialized functions of sensory, integrating, and responding  Radial Symmetry o Radial symmetrical animals have a nervous system arranged in a web-like system of neurons called a nerve net  Cephalization and Centralization o Most bilaterally symmetrical animals evolved o Cephalization – the concentration of the nervous system at the head end o Centralization – the presence of a central nervous system distinct from a peripheral/nervous system o Presence of ganglia—aggregates of neurons that receive info & respond  The Human Nervous System o CNS—receives and processes info; initiates action o Brain—receives and processes sensory info; initiates responses; stores memories; generates thoughts and emotions o Spinal Cord—conducts signals to and from brain; controls reflex activities o PNS—transmits signals between CNS and the rest of the body o Sensory neurons—carry signals from sensory organs to CNS o Motor neurons—carry signals from CNS; control activities of muscles and glands o Somatic Nervous System—controls voluntary movements; activates skeletal muscles o Autonomic Nervous System—controls involuntary responses; influences organs, glands, and smooth muscles o Sympathetic Division—prepares body for stress or energetic activity; “Fight-or-Flight” responses o Parasympathetic Division—dominates during times of “rest or rumination”; directs maintenance activities  Human Peripheral Nervous System o The PNS can be divided into two functional components o Motor system – mostly voluntary o Autonomic nervous system – mostly involuntary o The motor nervous system  Carries signals to and from skeletal muscles  Mainly respond to external stimuli o The autonomic nervous system  Regulates the internal environment  Controls smooth and cardiac muscle and organs and glands of the digestive, cardiovascular, excretory, and endocrine systems o The sympathetic and parasympathetic nervous systems often have opposing effects on target organs. Chapter 37  Endocrine System o Consists of all hormone-secreting cells o Works with the nervous system in regulating body activities  Work in conjunction with each other to regulate bodily responses o Compared to the nervous system the response of the endocrine system is slower but longer lasting  Chemical messengers (signaling molecules) o Hormones—endocrine glands and some neurons  Produces and releases neurons o Neurotransmitters—function at ends of axon o Local signaling molecules—released by a variety of cells o Pheromones—secretions of exocrine glands (ex. sweat & body odor); released by animal to outside o Exert their effects on specific cells called o Target cells/tissues  Chemistry of Hormones o Hormones use two signaling mechanisms to affect target tissues o Can this molecule transverse the cell membrane or does it have to remain outside the cell because it can’t pass through o Hormone signaling involves three stages:  Reception—receptor protein on or in the target cell  If it stays on the surface, the receptor on the cell starts signaling (surface receptors)  If it enters the cell, the receptor in the cell starts signaling (internal receptors)  Very specific  Signal transduction—converts signal through a series of relay molecules  Response—a change in the cell’s behavior  How does the cell respond to the hormone  Maybe creates an enzyme o Two groups of hormones  Water-soluble—includes proteins, short polypeptides and some modified amino acids; most hormones  Most hormones are protein molecules or derivatives of them  Cannot pass through the cell membrane (phospholipid bilayer); therefore, they function on the surface of the membrane  Can bring about cellular changes without entering their target cells  Lipid soluble—includes the steroid hormones, small molecules made from cholesterol  Can pass through the phospholipid bilayer & bind to receptors inside the cell  Enters nucleus and binds to DNA which triggers gene transcription and translation  Ex. testosterone & estrogen  Vertebrate Endocrine System o Endocrine glands—secrete hormones into blood system (ductless glands) o Endocrine and nonendocrine functions—pancreas  Large role in digestion o Stomach and heart have some cells that secrete hormones o Hormones are produced in a lot of different places  Hypothalamus/Pituitary Interaction o The hypothalamus-blurs distinction between endocrine and nervous systems  Master gland; hypothalamus cannot function without the pituitary gland and vice versa o Receives input from the nerves about internal conditions of the body and external environment o Responds by sending out appropriate nervous and endocrine signals o Uses the pituitary gland to exert master control over the endocrine system  Hypothalamus controls pituitary o Pituitary gland consist of 2 parts  Posterior pituitary  Composed of nervous tissue  Is an extension of the hypothalamus  Stores and secretes oxytocin (works on mammary glands and uterus) and ADH (antidiuretic hormoneregulates urine flow) which are made in the hypothalamus o Does not manufacture!!  Does not produce hormones  Anterior pituitary  Synthesizes and secretes hormones that control other glands  Is controlled by two types of hormones released from the hypothalamus o Releasing hormones—stimulate the anterior pituitary o Inhibiting hormone—inhibit the anterior pituitary  Portal—localized circulatory system  Regulation of Blood Glucose o Pancreas secretes two hormones that control blood glucose— antagonistic hormones  Insulin—signal cells to use and store glucose  Removes excess glucose  Glucagon—causes cells to release stores glucose into the blood  Adds more glucose  These two have opposite effects  antagonistic o Blood glucose rises  pancreas releases insulin  in response to insulin, target cells take up glucose and the liver converts glucose to glycogen  blood glucose level falls pancreas releases glucagon  in response to glycogen, the liver breaks down glycogen and releases glucose into the blood  Insect Metamorphosis o Hormones regulate insect life cycle o Metamorphosis—change of body form o Eggs  several larval molts  pupa  adult  eggs  etc o Larval stage—feeding stage o Metamorphosis is controlled by the presence and amount of juvenile hormone and ecdysone  Optimal levels of ecdysone are needed for larva-to-larva and pupa-to-adult molts  Optimal levels of juvenile hormone and ecdysone assures larva-to-larva molts

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Chapter 14, Problem 14.2 is Solved
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Textbook: Advanced Engineering Mathematics
Edition: 7
Author: Peter V. O'Neill
ISBN: 9781111427412

Since the solution to 14.2 from 14 chapter was answered, more than 258 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics, edition: 7. This full solution covers the following key subjects: . This expansive textbook survival guide covers 23 chapters, and 1643 solutions. The full step-by-step solution to problem: 14.2 from chapter: 14 was answered by , our top Math solution expert on 12/23/17, 04:48PM. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781111427412. The answer to “In each of 1 through 10, write the Fourier integral representation (14.1) of the function and determine what this integral converges to.f (x) = k for 10 x 10 0 for |x| > 10” is broken down into a number of easy to follow steps, and 34 words.

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In each of 1 through 10, write the Fourier integral representation (14.1) of the