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Solve the ODE by integration.

Advanced Engineering Mathematics | 9th Edition | ISBN: 9780471488859 | Authors: Erwin Kreyszig ISBN: 9780471488859 172

Solution for problem 1.1 Chapter CHAPTER 1

Advanced Engineering Mathematics | 9th Edition

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Advanced Engineering Mathematics | 9th Edition | ISBN: 9780471488859 | Authors: Erwin Kreyszig

Advanced Engineering Mathematics | 9th Edition

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Problem 1.1

Solve the ODE by integration.

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What is a TORT • A civil wrong, where the actions/behavior of one unfairly cause harm or injury to another • Not illegal, just injurious • Usually involves (plaintiff must prove): • An act: If the act is intended = intentional tort. If the act is unintentional = negligence, A results and Damages. What is INTENT • Tortfeasor (defendant) actually meant to take the complained-of action • If the tortfeasor intended a specific harm to result from the act, it is specific intent • If the tortfeasor just intended the act itself (not the specific harm), having knowledge that the act would have some consequence, it is general intent • Transferred intent occurs when the tortfeasor intends to act towards/upon one party; however, that intentional act actually injures someone completely different FRAUD • Defendant makes a false statement (or material/important omission); With scienter (knowledge of the falsity); Having intent to induce the plaintiff to do or not do something; and • The plaintiff justifiably relies on the false statement and does/does not do that thing. Resulting in damage to plaintiff Johnson v. GAPVT Motors, 292 Ga. App. 79, 663 S.E.2d 779 (2008) • Dealership (salesman, etc.) tells Johnson car is a Mustang Saleen • Dealership knows it’s a Mustang GT with Saleen “kit” (NOT a Saleen) • Dealership knows Johnson wants a Saleen, so tells Johnson it’s a Saleen to get him to buy • Johnson buys car b/c he thinks it’s a Saleen and he’s always wanted one • Johnson ends up with all kinds of “trouble” as a result of the car not being a Saleen DEFAMATION * • A false, defamatory statement (harm reputation) concerning the plaintif; • Made in an unprivileged (absolute or qualified; “courtroom” v. “self-defense”) communication to a third party (publication); • For which the defendant is at fault (did not care if true/false); Resulting in special harm (damage to property, business, profession); OR Which is defamatory per *e (no need for explanation of damage) • NOTE: slander = spoken, libel = written Smith v. Stewart, 291 Ga. App. 86, 660 S.E.2d 822 (2008) • Plaintiff sues Defendant because book falsely depicted her as a “promiscuous alcoholic . . . who secretly drinks before and during flights while working as a flight attendant, [having] frequent one night stands, secret affairs with married men, brief sexual relationships with younger men, and lewd, outrageous public sexual behavior.” • A false, defamatory statement (see above), in an unprivileged communication to a third party (published fiction book), INVASION OF PRIVACY • Public disclosure of private facts; • Which facts are private, secluded, or secret facts and not public record; • The publication of which would be ofensive and objectionable to a reasonable person of ordinary sensibilities under the circumstances Wilson v. Home Depot, 288 Ga. App. 582, 654 S.E.2d 408 (2007) • Plaintiff goes through divorce and retains custody of child, but custody dispute arises • Both Plaintiff and ex-wife work for Home Depot in different states • Plaintiff terminated by Home Deport after allegedly testing positive for illegal drug use • Plaintiff’s ex-wife telephones Plaintiff’s Home Depot location, identifies self as a manager and gets code indicating why Plaintiff was fired • Plaintiff’s ex-wife then subpoenas Plaintiff’s employment records for use in custody proceedings • Plaintiff claims Defendant disclosed private facts to the public, which a reasonable person would find offensive FALSE IMRISONMENT • A detention, which is unlawful. Taylor v. Super Discount Market, Inc., 212 Ga. App. 155, 441 S.E.2d 433 (1994) • Plaintiff checking out hands cashier $20 bill • Cashier believes bill looks funny b/c missing “In God We Trust” • Cashier hands bill to off-duty police officer working as security guard, telling Plaintiff not to leave • Plaintiff gives cashier another bill and completes transaction • Officer/guard asks Plaintiff to wait (45 or 16 mins.) while he asks another guard/officer to review bill INTENTIONAL INFLICTION OF EMOTIONAL DISTRESS • Intentional or reckless conduct; • Which is extreme and outrageous (create “intense feelings of humiliation, embarrassment, fright or extreme outrage”); and • Causes severe emotional distress Clark v. Arras, 212 Ga. App. 695, 443 S.E.2d 277 (1994) • Plaintiff has 2 miscarriages within 7 months • Because of plaintiff's history and because the second miscarriage appeared unexplained, Defendant performed an autopsy on plaintiff's stillborn fetus. • Plaintiff alleges that Defendant performed the autopsy by mistake and without her permission, causing mental distress, pain and anguish • Court found that Defendant’s actions did “not rise to the necessary level of outrageousness.” CONVERSION • Intentional act of dominion; Over the personal property of another (both tangibles and intangibles reduced to physical form); So inconsistent with the owner’s rights; • As to warrant payment of the full value of the property (damages) Examples • Wrongful acquisition (theft), Wrongful transfer (selling), Wrongful detention (refusing to return), Substantially changing, and Severely damaging or destroying TRESPASS To Chattels (personal property): • Intentional act by Defendant; Interfering with Plaintiff’s right of possession in personal property; Resulting in damages • Interference can be: (1) an intermeddling – directly damaging the property (dent the car); or (2) a dispossession – depriving lawful right of possession (“joyride” in the car) • Actual damages required, although not necessarily to the property itself (missed work, gas used) • Not as serious an interference as conversion (joyride with a scratch v. wrapped around a tree) To Land: • Intentional, physical invasion of Plaintiff’s real property; Which causes injury/damage. Physical invasion can be by person or object (baseball) and, possibly, intangible objects (vibrations, odor) • Real property includes airspace and subterranean space • “Intent” only requires intent to enter land, not intent to enter a specific owner’s land BATTERY & ASSAULT Battery: • Harmful or offensive act/contact; To Plaintiffs person; With intent to commit the act (not necessarily the harm); Which causes injury. Harmfulness/offensiveness judged by reasonable person standard • Contact must NOT be consented to and consent can be implied • Contact can be direct (hitting Plaintiff) or indirect (setting trap for Plaintiff) NEGLIGENCE • People (and companies) owe those around them a DUTY to act a certain way. If they BREACH that duty, and that breach CAUSES some level of injury, or DAMAGES, they are liable for Negligence. Duty • Legal obligation to act with a certain level of care • Generally, everyone is expected to act as a reasonable, ordinarily prudent person, and avoid unreasonable risks which may injure others, i.e., Duty of Reasonable Care • People owe a Duty of Reasonable Care to who could “foreseeably” get hurt if you don’t act with reasonable care • But, who is foreseeable (to whom is the duty owed) • What if D breaches a duty owed to P1, but the same breaching act also injures P2 • Majority View – P2 recovers only if a reasonable person would have foreseen a risk of injury to another person under the circumstances (“zone of danger”) • Minority View – If D breached duty owed to P1, duty extended to everyone injured by that breaching action • Under the Duty of Reasonable Care, conduct is measured against what an average person (similarly situated, with same circumstances and limitations) would do • What is “Reasonable” can differ based on the person • Professionals (not just a reasonable person, but a member in good standing in similar community) • Children (not just any child, but one of like age, education, intelligence, experience) • Common Carriers/Innkeepers (not just like any reasonable business, but have a heightened duty) • Owners/Occupiers of Land (owe certain people more than just reasonableness; licensees/warn v. invitees/warn + inspect) Duty typically does NOT require you to act, unless: • You start helping someone, then you must do so with reasonable care; Good Samaritan statutes exempt doctors, nurses, etc. from liability for ordinary (NOT gross) negligence • You negligently or innocently placed someone in danger • There is a special relationship (parent-child) can create duty to act; • You are a common carriers, innkeepers, shopkeepers (gather public for profit), then you owe duties to aid/assist patrons Generally, no duty to prevent third person from injuring another, unless: • You have the actual ability or authority to control the third person’s actions, AND • You know or should know the person is likely to commit acts requiring exercise of that control Duty to Visitors (when you own/occupy of land) • Always have a duty of reasonable care, PLUS • Duty to Licensees • Enter land with owner’s permission for their own purpose or business, rather than owner’s benefit • Owner/Occupier has an affirmative duty to warn of, or make safe, known conditions, if non-obvious and dangerous • Duty to Invitees • Enter land upon invite from owner/occupier for purpose connected with the business (business visitor) • Owner/Occupier has an affirmative duty to make reasonable inspections to discover non-obvious dangerous conditions and warn of or make safe Breach • Conduct falls short of the required duty • Using less care than expected • Conduct creates more risk than the law allows • Can be established by: • Custom • Violation of Statute (Duty & Breach established by Negligence Per Se) • Res Ipsa Loquitor (Duty & Breach established by an inference of negligence) • Accident the type usually resulting from someone not meeting the standard of care • D had exclusive control of instrumentality of harm at time the negligence would have occurred • P did nothing to cause the harm Causation • Factual Causation (“But-For” Causation) • What D did actually caused the harm. Injury would not have occurred but for Defendant’s actions. Train station example . . . at least the first part. • Legal Causation (Proximate Causation) • Limitation on Factual Causation because something else happens between the allegedly negligent act and the actual injury • Even if we have a causal connection (“but for . . .”), perhaps we should limit Defendant’s liability • Must ask whether Defendant’s act actually increased the risk of harm • Typically, we don’t like to hold people liable when someone else commits and intentional or criminal act • Oil tanker example Damage • Damages NOT presumed and must be proven • If personal injury, P to be compensated for ALL damages (past, present, prospective), BOTH economic (med. bills, wages) and non-economic (pain, suffering) • Foreseeability of the extent of the harm is irrelevant, so take P as D finds him/her (eggshell skull P) • If property damage, reasonable cost of repair, unless property (nearly) destroyed, then fair market value at time of accident • Punitive Damages awarded if D’s conduct “wonton and willful,” reckless, or malicious • Typically, cannot recover: (1) Interest from the date of damage in personal injury; and (2) Attorneys’ fees • Duty to Mitigate still exists • Collateral Source Rule prevents D from reducing damages by presenting evidence that P received benefits from other source (e.g., health insurance) Defenses • Contributory Negligence: • P’s own negligence contributes to the injury. Complete bar to recovery, unless act was reckless. Rebuttal is “last clear chance” – whoever has last clear chance to avoid injury is liable (car/train). Minority view • Assumption of Risk: • P knew of the risk of injury and voluntarily proceeded. Complete bar to recovery, unless act was reckless. Rebuttal is “no available alternative” (machine repair) • Comparative Negligence: • PURE (minority view) - P’s negligence contributed to injury, so P’s damages reduced by % of fault assigned to P • PARTIAL (majority view) - P’s negligence contributed to injury, so P can only recover if fault assigned to P is less than or equal to % assigned to D Product Liability Claims OR Warranty Claims When products are defective or don’t work as expected, Product Liability Claims OR Warranty Claims can result: • Product Liability claims usually come when the something is wrong with a product (defect) which causes some injury to the consumer • Warranty claims usually come when the product just doesn’t work the way it should (as warranted) and the consumer didn’t get what he/she expected Product Liability Three (3) Types of Defects in Products, which can cause injury: 1. Manufacturing Defect • Occur during the manufacturing process • Involve poor materials or workmanship 2. Design Defect • Product design itself is inherently dangerous/defective • Defective no matter how manufactured Product fails to satisfy ordinary consumer expectations of what constitutes a safe product • Risks of product as designed outweigh its benefits (any safer alternative designs) 3. Marketing Defect (a.k.a., Failure to Warn) • Product carries inherent, nonobvious dangers which could be mitigated through adequate warnings • Dangers are present regardless of manufacture or design Claims are based on one (or both) of the following theories: 1. Negligence • Defendant was negligent in design, manufacture, or marketing of the product (had a duty to make safe products and breached), resulting in a defect • The defect causes injury • Manufacturers, distributors, and retailers can be liable • Still, can be tough to establish breach if an entire industry operates under lax standards 2. Strict Liability • Irrelevant whether negligence involved in making/designing/marketing the product (avoids issues with industry custom) • If a product is defective and that defect causes injury • Manufacturers, distributors, and retailers are liable • In GA, only manufacturers can be strictly liable NOTE: In all cases, the product must be new property when first sold AND not substantially altered/modified Product Warranties NOTE: To sue on a product warranty claim, you must have PRIVITY of CONTRACT (you bought it from THEM) with the person/company you sue 1. Express warranty • Oral or written agreement • Subject to contract rules, such as conditions precedent 2. Implied warranty of merchantability • In all sales of goods, it is implied that the seller of goods (“merchant”) warrants (promises) that the goods are fit for their intended purpose, i.e., they are what seller claims them to be and will do what buyer expects • Can be expressly disclaimed or if sale is “as is" or "with all faults" 3. Implied warranty of fitness for a particular purpose • Buyer must rely upon expertise of seller to recommend particular product to be used for particular purpose • Seller must know buyer is relying upon seller’s expertise • Can also be expressly disclaimed

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Chapter CHAPTER 1, Problem 1.1 is Solved
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Textbook: Advanced Engineering Mathematics
Edition: 9
Author: Erwin Kreyszig
ISBN: 9780471488859

Since the solution to 1.1 from CHAPTER 1 chapter was answered, more than 273 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 220 chapters, and 9259 solutions. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics, edition: 9. The full step-by-step solution to problem: 1.1 from chapter: CHAPTER 1 was answered by , our top Math solution expert on 12/23/17, 04:46PM. The answer to “Solve the ODE by integration.” is broken down into a number of easy to follow steps, and 5 words. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9780471488859.

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Solve the ODE by integration.