×
Log in to StudySoup
Get Full Access to Elementary Differential Equations And Boundary Value Problems - 10 Edition - Chapter 6.2 - Problem 21
Join StudySoup for FREE
Get Full Access to Elementary Differential Equations And Boundary Value Problems - 10 Edition - Chapter 6.2 - Problem 21

Already have an account? Login here
×
Reset your password

See answer: In each of 11 through 23, use the Laplace transform to solve the given

Elementary Differential Equations and Boundary Value Problems | 10th Edition | ISBN: 9780470458310 | Authors: William E. Boyce ISBN: 9780470458310 168

Solution for problem 21 Chapter 6.2

Elementary Differential Equations and Boundary Value Problems | 10th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Elementary Differential Equations and Boundary Value Problems | 10th Edition | ISBN: 9780470458310 | Authors: William E. Boyce

Elementary Differential Equations and Boundary Value Problems | 10th Edition

4 5 1 246 Reviews
31
3
Problem 21

In each of 11 through 23, use the Laplace transform to solve the given initial value problem.y 2y+ 2y = cost; y(0) = 1, y(0) = 0

Step-by-Step Solution:
Step 1 of 3

GPH210GeographyofTerrestrialLife SpringSEMESTER2016 Professor:Dr.ElizabethLarson EliteNotetaker:Phoebe(phoebe@studysoup.com) 1. Interstate Biogeography ○ Human Activities Effects ■ Roads / Highways blocking animals and plants ■ Fire suppression stopping cyclical succession ■ Removal of animal species ■ Bison ■ Wolves ■ Exotic species ■ Increasing range of deserts ○ Endemism ■ A species that thrives within a very restricted geographic range (at a biological hotspot) ■ Migratory birds are most influenced by the loss of two different biomes ■ E.g. Salamander (only in southern Appalachian Mountains) 2. The Geography of Biomes ○ Biomes ■ Communities of similar organisms in a certain climate ■ Defined by the key features of the plants that grow there ■ Determined by atmosphere and climate (temperature/precipitation) ■ The colder it is, the drier the air gets ■ Grouped into three climatic zone ■ Tropical zone— Equator to 25° N/S ■ Temperate zone— 25° N/S to 60° N/S ■ Polar zone— Above 60° N/S 1 ○ Climatography ■ Presenting the climate of biomes ■ Shows the pattern of seasonal changes in precipitation and temperature ■ Moisture availability isn’t directly indicated but can predict ○ Tropical Zone ■ 0°­25° latitude ■ High diversity ■ Warm climate ■ Tropical Rainforest ■ Annual rainfall > 2000mm (80in) ■ Greatest net primary production (NPP) ■ Rapid nutrients cycled ■ Great unique niches and endemic species ■ Tropical Seasonal Rainforest ■ Annual rainfall 1500­2500 (60­98in) ■ Wet and dry season ■ Ranges from tall tree canopy (wet) to scrubby woodlands (dry) ■ Tropical Savanna ■ Climate overlapping with seasonal tropical forest ■ Highly seasonal rainfall ■ Drought persists more than half the year ■ Dominated by grasses ■ Massive herds of grazing animals ○ Temperature Zone ■ 25°­60° latitude ■ Annual rainfall 200­2000mm ■ Annual temperature 5­20℃ ■ 60% of Earth's land mass ■ Dominated by forest ■ Growing season ranges from 4­10 months ■ Temperate Deciduous Forest 2 ■ Broadleaf trees ■ No leaves in winter ■ Moderate summer / Cold winter ■ Growing season: between first and last hard frosts ■ Little remains undisturbed ■ Temperate Evergreen Forest ■ Evergreen conifers (keep leaves) ■ Drier summer / Warmer winter ■ Some can be temperate rainforest ■ Mild temperature all year ■ Less precipitation ■ Seeing Solution— Using Fire To Conserve A Biome ■ Fire suppression ■ Litter accumulating ■ Shade­tolerant trees invades the ecosystem ■ 1960s: ecologists realize stopping the fire = disrupt natural cycles ■ Beneficial Fire ■ Primarily burning litter and woody debris on soil surface ■ Not damaging forest canopy ■ Allows giant sequoias' seeds to germinate ■ Chaparral ■ 30°­40° latitude ■ Mediterranean climate ■ Dominated by summer drought ■ Adapted to fire ■ Evergreen shrubland + low woodlands ■ Stony leafed ■ Water loss resistant ■ Wilting 3 ■ E.g. Sclerophyllous leaves of manzanita ■ Temperate Grasslands ■ 90% are altered by agriculture and cattle grazing ■ Best climate and soil condition for corn, wheat and soybeans ■ Long/Cold winter ■ Hot Summer ■ In between the wetness of forest and the dryness of desert ■ E.g. Konza Prairie of eastern Kansas (undisturbed) ■ Dominated by grasses and herbs (dense sod) ■ Bunch grasses— tussocks of fescue in the arid grasslands of Patagonia (southern Chile) ■ Able to grow back after grazed ■ Individual clumps can survive centuries ○ Polar Biomes ■ 60° and above latitude ■ Less than 5℃ ■ Short growing seasons ■ Limited abundance and diversity ■ E.g. Northern Hemisphere / Antarctica ■ Global warming impacts ■ Increasing depths to permafrost ■ Increasing infestation of bark beetles ■ Boreal Forest ■ Cold and wet ■ Less than 4 months of growing season ■ Long/dry/bitterly cold winters ■ Forests are dominated by conifers ■ Permafrost ■ Permanently frozen soil ■ 30­100 cm below surface ■ E.g. Siberia Taiga ■ Tundra 4 ■ Annual rainfall 100­500mm ■ Less than 3 months of growing season ■ Cold and dry (harsh winter) ■ Permafrost ■ E.g. Alaska Range ■ Supports a diverse array of shrubs and herbs ■ Alaska Pipeline disturbs the tundra ○ Deserts ■ Occur worldwide ■ 25% of Earth’s surface ■ Extremely arid ■ Annual rainfall < 250mm ■ Daily temperature vary extremely (cold to hot) ■ Animals and plants adapted for litter water (succulents) ■ Kangaroo rat of North America (never drinks) ■ Being nocturnal (active at night) ■ E.g. Dry valleys of Antarctica / Asian Gobi / North American Sonoran 3. Mountains and Coastlines ○ Facts ■ Not Biomes ■ Including all climatic zones ■ Affected by environmental change ■ Changes in elevation produce different climates ■ Vulnerable to human activities and global warming ■ Elevation of treeline is lower at higher latitudes ○ Mountains ■ Climate changes ■ Temperature decreases as altitude increases ■ Same biome transitions in altitude as continent in latitude ■ Rain shadow (orographic rainfall) ■ Rain falls on the side of the mountain where air climbs (windward) 5 ■ Rain doesn’t fall on the side of the mountain where air slides (leeward) ○ Coastlines ■ Narrow transition of terrestrial biomes and ocean ■ Vegetation ■ Saltwater / Wave action = harsh environment ■ Plants / animals are adapted to high salt / less fresh water ■ Human actions damage coastal areas ■ E.g. Sea Rocket ■ Dune pioneer ■ Stabilize 6 GPH210BiodiversityConsevation SpringSEMESTER2016 Professor:Dr.ElizabethLarson EliteNotetaker:Phoebe(phoebe@studysoup.com) 1. Requiem for the Po'ouli ○ Human Activities Effects ■ 1973, in Hawaii ■ 2004, extinct due to: ■ Overhunting ■ Exotic species ■ Indian mongoose­ to control rats ■ Affected akiapola’au (honeycreeper) ■ Destructed habitat ○ Captive Breeding ■ Puaiohi (small thrush­like bird) ■ In Kauai, Hawaii ■ San Diego Zoo hatched over 200 of them out of 20 ■ Over 150 have been reintroduced into wild ■ Population growing still 2. Biodiversity ○ Definition ■ Variety of life in all forms, combinations and organization ○ Types of biodiversity ■ Landscape biodiversity ■ Variety and abundance of species from place to place ■ Two factors ■ Gradual change in environmental factors ■ E.g. temperature / growing seasons / water availability ■ History of local ■ E.g. Fire / food cycles ■ Community biodiversity ■ Definition ■ The number of different species (richness) ■ The relative abundance of different species (evenness) ■ The spatial distribution of different species (3­D) ■ Structural complexity ■ Complexity = Diversity 1 ■ Marine complexity ■ Coral reefs supports many more species comparing to sandy ocean bottoms ■ The higher the latitudes, the less species we should see ■ Population biodiversity ■ Definition ■ Genetic diversity (genetic variation) ■ Outbreeding (mating with nonrelated individual) ■ Inbreeding (mating with closely related individuals) ■ Impacts ■ Improves survival ■ Maximize diversity ■ Increases genetic disease and reproductive failure ○ Importance Of Biodiversity ■ Impacts on human ■ Provide humans with a lot more ecosystem services ■ Depending on individual species and interactions ■ Producers are more abundant ■ Increases productivity ■ Complementarity effect ■ Resources used by various species in a complementary way are more efficient ■ Ecosystem​ stability ■ Help ecosystem to change/adjust/recover/resist to disturbances ■ Enhance survival rates (increase tolerance) ■ Economic value ■ Improve production of good ■ E.g. food, fuel, fiber, medicine ■ Ecotourism ■ Interested in exploring natural exploring natural environments ■ Existence value ■ Intrinsic value of plants and animals ■ Religious beliefs ■ Ethics (UN Charter for Nature) 3. Global Patterns of Biodiversity ○ Facts ■ Earth supports 7­15 million species of eukaryotes ■ 10­20% are described by human ■ Land: 80% are insects ■ Marine: 50% are algae ■ Specie richness ■ Number of species decreases when moving away from equator ○ 4 Factors For Global Pattern ■ Net primary production 2 ■ Past disturbance ■ Habitat gradients ■ Ecosystem complexity ○ Biodiversity Hotspots ■ Large number of endemic species ■ Human actions are threatening habitats ■ 1.5k endemic species have at least 70% of original area disturbed ■ Conservation internationally to prioritize hotspot areas (25 of them in the world ○ Ecological Communities Biodiversity ■ Immigration / Extinction ■ Mostly due to human activities ■ Affects species on island the most ■ Habitat diversity ■ More niches and species supported ■ Different topography = different habitat ■ E.g. mountains, rivers, valleys ■ Species interaction ■ Competition ■ Predation ■ Predators (no single prey can dominate) ■ Herbivores (drive adaptation/diversity of plants) ■ Disturbance ■ Peaks at intermediate level of disturbance ■ Acts like an herbivore ■ Prevent one species dominating ■ Fire / Flood / Hurricanes 4. Threats to Biodiversity ○ Habitat Loss ■ Greatest treat ■ 82% of endangered bird lost their habitat ○ Logging / Agriculture / Development ■ 95% of North American deciduous forest are gone or altered ■ 3% of U.S. mixed and tallgrass prairie remain ○ Endangered Species ■ Gopher tortoise ■ Red­cockaded Woodpecker ■ Dugong ○ Habitat Fragmentation ■ Habitat divided into small disconnected habitats due to roads, dams, developments ■ Behave as islands ■ Reduces/Eliminates movement or dispersal ■ Reduces gene flow 3 ■ E.g. Forest songbirds, shad and salmon declining ○ Overharvesting ■ Human consumption (food, industry, pet) ■ Reproduction rate cannot keep up with the harvest rate ■ Certain vulnerable species ■ Slow population growth rates ■ Flocking/schooling behavior ■ Large bodied ○ Non­Native Invasive Species ■ Population explodes and displaces natives ■ Lacking predators / pathogens ■ Lacking competitors ■ Own adaptations ■ Disrupt food web or species composition ○ Pollution ■ Air / water pollution kill species ■ Pollutants build up through food web ○ Altered Patterns of Disturbance ■ Change in frequency and intensity ■ E.g. Floods / Fire ■ Change in species composition ○ Climate Change ■ Alter or eliminate habitat ■ Example ■ Sea ice melting (polar bear habitat) ■ Coral bleaching 5. Strategies For Conserving Biodiversity ○ Preserves and Protected Areas ■ Health of individual species population ■ Management of habitat ■ Maximizing migration ■ Maintaining cycles ■ Minimizing human influence (buffers) ■ Behave as islands (distance from other preserves) ■ Depend on principles of island biogeography ■ Larger preserves support more species ■ Migration corridors increases connectivity ■ Using abandoned railway or streams to connect the preserves ○ Managing Populations of Individual Species ■ Restoration / Maintenance of healthy population ■ Population viability ■ Probability of extinction in given number of years 4 ■ Affecting factors ■ Availability/quantity of habitat ■ Size of population ■ Disease ■ Predators ■ Umbrella species ■ Species whose protection protects other species that require similar habitat ○ National Parks and Wilderness Areas ■ Park system setting high standards ■ Establish protection of habitat and preservation for human use ■ Protect sensitive habitat ■ Some suffer from overuse or visitation 6. U.S. Policies for Conserving Biodiversity ○ Legislation to protect species ■ Limit commerce and injury to threatened and endangered species ■ E.g. 1900 Lacey Act (prevent illegal killing or sale) / U.S. Fish and Wildlife Service ■ Endangered Species Act ■ Species whose population is reduced to near critical levels are threatened ■ Prohibits taking endangered or threatened species regardless of landownership 7. International Policies for Conserving Biodiversity ○ Convention on International Trade in Endangered Species of Wild Fauna and Flora ■ aka CITES ■ Slowing down overhunting and collection of plants and animals ■ Created black market ■ E.g. regulation of whaling (more effective than rhinos since it’s easier to kill rhinos) ○ Economic Incentives ■ Hotspots are in poor developing countries ■ Ecotourism ■ Debt­for­nature swags (debts forgiven if create preserves and parks) 5

Step 2 of 3

Chapter 6.2, Problem 21 is Solved
Step 3 of 3

Textbook: Elementary Differential Equations and Boundary Value Problems
Edition: 10
Author: William E. Boyce
ISBN: 9780470458310

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

See answer: In each of 11 through 23, use the Laplace transform to solve the given