PROBLEM 21E
Suppose y satisfies the equation y” + 10y’ + 25y = subject to y(0) = 1 and y’ (0) = -5. Estimate y(0.2) to within ±0.0001 by numerically approximating the integrals in the variation of parameters formula.
Chapter 11 Alcohol Abuse and Dependence Prevalence take developmental factors into account abuse – overdoing it dependence – built up tolerance enough to always need more; withdrawal symptoms if stopped 12 years shorter of life expectancy for someone who is alcohol dependent 37% of those that use alcohol have another disorder (depression) strong genetic heritability of developing alcohol problems lack of supervision from parents as an adolescent learning behaviors from stress/attention Clinical Picture Biological Factors Psychosocial cause factors Sociocultural Treatment medications to reduce desires to drink drugs that block how alcohol feels drugs to treat alcohol withdrawal group therapy environmental interventions: get you away from alcohol Behavioral & CBT: treat thought processes control drinking: learn how to drink under control and effectively hard for people that abuse alcohol AA/NA groups free sponsor that you can always contact Drug Abuse and Dependence Base Rates hard to get base rates drug screenings found ~10% of the population abuse drugs Opium and its derivatives opium: smoke/take; pain relieving effects morphine heroin: preferred abused drug; injected into bloodstream, very water soluble; most euphoric effects prescribed frequently to help with pain effects of abuse poor nutrition, not sleep well, fluctuating withdrawal symptoms withdrawal impacts immune system affordable treatments: drugs that prevent withdrawal symptoms quitting cold turkey drugs that act as antagonists and block effects of opiates popular in younger people Cocaine and amphetamines stimulant; snorted; smoke it impacts dopamine; floods brain with dopamine feels good joy/happy feelings; euphoria meth amphetamine: high power stimulant supplies easily accessible most harmful for your body kills body tissue comprises values brain impairment Sedatives barbiturates not around anymore very small lethal dose; rarely prescribed Xanax dependent; builds up tolerance LSD and related drugs powerful drug 10,000 hits in one gram hallucinating impact volatile emotions low lethal dose rate shrooms Ecstasy Marijuana THC hard to test amount of THC low lethal dose rate seen as the safer drug used as medication used to help ease suffering blood flow nausea problematic: not entirely safe to use edibles can ingest too much