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Solved: In 29–32, use the method of Laplace transforms to

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 29E Chapter 7.5

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 29E

Problem 29E

In Problems 29–32, use the method of Laplace transforms to find a general solution to the given differential equation by assuming y(0) = a and y’(0)=b, where a and b are arbitrary constants. 

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GEOL 1330 EXAM 3 STUDY GUIDE -Relative Dating - Know Stenos 3 laws Steno's Laws -Top Hat Question: - In what orientation are sedimentary layers originally deposited -Answer: Horizontal -Principle of Original Horizontality - layers of sediment are originally deposited horizontally under the action of gravity -Folding or tilting occurs after rocks are deposited -Top Hat Question: -What is the oldest sedimentary layer -Answer: The bottom most layer -Principle of Super Position -Oldest layer is the bottommost layer and the top layer is the youngest -Top Hat Question: -What did the Grand Canyon look like before the Colorado River carved it -Answer: Rocks on one canyon wall were connected to the exact same rocks on the other side -Principle of Lateral Continuity -layers of sediment initially extend laterally in all directions; in other words, they are laterally continuous. -Cross cutting relationships Cross-Cutting Relationships -Principle of Cross-Cutting Relationships -Rocks that do the "cutting" are younger than those being cut -Principle of Inclusion -Inclusions are older than rocks they are included in. -Ex: Rocks in the ceiling of a magma chamber fall into magma, the magma cools. The original rock is older than the cooled magma -Need to know 3 types of unconformities, angular unconformity, disconformity, and non-conformity Unconformities -An erosional surface -Portions of the rock record were eroded away -Usually indicated by a wavy line -period of erosion, called unconformity -Disconformity: Gap in the rock record, represents period of non- deposition and erosion -Nonconformity: Period of uplift and erosion that exposes deep rock at the surface -Angular Unconformity: Horizontal layers are deposited directly on top of tilted layers -There will be at least one diagram where you will need to know what happened first. Refer to your in class assignment. -Absolute dating - what is an isotope (diff number neutrons than protons) -What is half life -Types of rocks that can be dated radioactively Radioactivity and Isotopes -Radioactivity - The spontaneous decay of unstable elements to a stable form -Isotope - Atom with a different number of neutrons -Parent - Unstable radioactive isotope -Daughter - Stable isotope resulting from the decay of the parent -During radioactive decay atoms can lose protons neutrons or electrons, or they can gain electrons -Half-Life - Time it takes for half the unstable (radioactive) parent atoms to decay to stable daughter atoms (non-radioactive) -Collect a rock and what to know its age, you measure: -Number of Parent Atoms present -Number of Daughter Atoms present -You collect 1000 parent atoms and 7000 daughter atoms -(How many Parents were in this rock when it first formed) -8000 original parent atoms -Half-life 1: 4000 parents and 4000 daughters -Half-life 2: 2000 parents and 6000 daughters -Half-life 3: 1000 parents and 7000 daughters -Radiometric dating of minerals provides an age for the moment of crystallization (igneous rocks) or metamorphism (metamorphic rocks) -When used in sediments: Does Not provide an age for deposition of the sediments because depositional age of sediments can only be determined from cross cutting relationships -Wilson Cycle (No need to name stages, just know what the cycle is - opening and closing of an ocean basin /formation or destruction of ocean basin) The Wilson Cycle -The Wilson Cycle: Formation and destruction of Ocean Basins -Formation Stages- -Embryonic Stage: Volcanic and non-marine sediments are deposited in rift valleys -As the crust is pulled apart, large slabs of rock sink, creating a valley. (Divergent plate boundary) -Immature Stage: Continued rifting creates oceanic crust. Cooling and subsidence of rifted margin allows sediments to be deposited -Further spreading creates a narrow sea (I.e. red sea) -Mature Stage: Continental margin continues to grow supplied from erosion of the continent -Eventually, an expansive ocean basin and ridge system are created -Destruction Stages- -Declining Stage: Pacific Ocean, the ocean has reached its maximum size and begins shrinking -Remnant Stage: Mediterranean Sea, The ocean is all but closed and is a fraction of its former size -Suture Stage: Himalayan Mountains, The ocean is no longer there and the plates continue to collide creating a mountain range -Persian Gulf = Remnant portion closed by the convergence between Arabian plate and Asia -Continuous subduction of oceanic lithosphere results in the development of thin continental crust through partial melting -Know different seismic wave (surface wave, s wave, p wave) -Speed, amplitude, mediums traveled through, damage Waves -Seismology is the study of earthquake waves -These waves are recorded by seismographs -Types of seismic waves -Surface waves -Travel along the outer part of Earth -Cause the greatest destruction -slowest speed, highest amplitude, longest period, travels through solids and liquids -P-Waves (primary) -Push-Pull (Compress and expand motion) -Travel through solids, liquids, and gases -fastest speed, lowest amplitude, shortest period -S-Waves (secondary) -Shaking motion at right angles to their direction of travel -Only travels through solids -intermediate speed, amplitude, and period -Surface waves -Have a combination of up and down and side to side movement -P-waves - Particle motion consists of alternating compression and dilation. Particle motion is parallel to the direction of propagation (longitudinal). -S-waves - Particle motion is perpendicular to the direction of propagation (transverse). Transverse particle motion shown here is vertical but can be in any direction -New evidence for plate tectonics -reversing of mag field, how we know that from minerals cooling and align with magnetic field. Like a tape recorder -Tsunamis Tsunami- a series of large waves generated by an abrupt movement on the ocean floor that can result from an earthquake, an underwater landslide, a volcanic eruption or - very rarely - a large meteorite strike. However, powerful undersea earthquakes are responsible for most tsunamis, generally caused by earthquakes in subduction zones -How to monitor earthquakes, how many monitors Measured by seismographs, seismographs measure the force and length of earthquakes. Generally, 3 monitors are used in order to triangulate an area. -Most active earthquakes areas in the world Ring of Fire- an area in the basin of the Pacific Ocean where a large number of earthquakes and volcanic eruptions occur. In a 40,000 km (25,000 mi) horseshoe shape, it is associated with a nearly continuous series of oceanic trenches, volcanic arcs, and volcanic belts and/or plate movements. -Oklahoma earthquakes Fracking is causing the earthquakes in Oklahoma -What generates earthquakes - movement along faults Earthquakes -Earthquakes are vibrations of the Earth caused by the rapid release of energy, often triggered by movement along faults -Hypocenter (focus) - Exact location of the earthquake within the Earth -Epicenter - Location of the surface directly above the hypocenter -Faults move (slip) in two different ways -1. Fault creep - Slow, gradual displacement (motion) -Small Earthquakes -2. Stick-Slip- Fault stays "locked" storing elastic energy, then suddenly slips, releasing the stored energy -Large Earthquakes -How do continents grow in size Continents grow when new crust attaches at subduction zones, locations where a tectonic plate subducts, or sinks back into the mantle. Often, this new crust arrives as small fragments, called micro-continents, or volcanic island chains. -How was continental crust originally created Subduction and partial melting -Earthquakes magnitudes mag 5 = 10 greater than mag 4 -mag 5 = 100 times greater than mag 3 earthquakes

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Chapter 7.5, Problem 29E is Solved
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Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

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Solved: In 29–32, use the method of Laplace transforms to