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Get Full Access to Fundamentals Of Differential Equations - 8 Edition - Chapter 9.8 - Problem 7e
Get Full Access to Fundamentals Of Differential Equations - 8 Edition - Chapter 9.8 - Problem 7e

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# In 7–10, determine e At by first finding a fundamental

ISBN: 9780321747730 43

## Solution for problem 7E Chapter 9.8

Fundamentals of Differential Equations | 8th Edition

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Problem 7E

Problem 7E

In Problems 7–10, determine e At by first finding a fundamental matrix  and then using formula (3).

Step-by-Step Solution:
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PHYS 1010 Notes Week 10 ­ March 14­18 Sound waves ­ The Doppler Effect ­ Change in frequency as a sound­emitting object moves with respect to an observer ­ As wave are emitted they are catching up to the wave in front of them ­­> smaller wavelengths in front of source, bigger waves behind the source ­­> higher frequency (higher pitch) ­ Source of sound travelling at speed of sound ­­> overlapping waves with huge amplitude ("sonic boom") and change in pressure ("shock waves") ­ Thunder is a sonic boom: lightning heats air, which creates expansion and a pressure/sound wave ­ Measuring weather ­ Satellites give off waves, which travel until they hit something dense that reflects it (like a cloud); reflected waves have a higher frequency the faster the clouds are moving toward them/lower frequency if clouds are moving away ­ Big bang theory ­ Hubble noticed the farther away a star is from earth, the redder it looks (lower frequency because stars are moving away) ­ Everything is moving away from everything else in the universe ­ Means that everything in the universe had to start in one place Electromagnetic spectrum ­ Light behaves as a traveling wave of electric and magnetic fields ­ Different frequencies are different colors, most of which are invisible to humans ­ Spectrum has no upper or lower bound, and is continuous ­ All electromagnetic waves in a vacuum travel at the same speed ­ Long waves ­­> radio waves ­­> infrared ­­> visible light spectrum ­­> ultraviolet ­­> x­rays ­­> gamma rays ­ Everything below visible light spectrum can't cause chemical change Reflection and Refraction ­ Reflection: light bounces off the surface in a slightly different direction ­ Refraction: light moves through the surface, and speed changes based on the densities of the new medium; the direction then changes to compensate for the new speed ­ Light travels more slowly in denser material ­ Light has to always be the fastest thing in the room, and it takes the fastest path, not the shortest path ­ If light has to travel through air and water, it will spend longer in the air and shorter in the water because it moves faster through air ­ Chromatic dispersion: light spreads out by color when moving through glass/water, because the amount light bends depends on the frequency of light and the density of the mediums (rainbows) ­ Higher frequencies bend more than lower frequencies ­ Reason why the sky is blue: sun is white light, which refracts when it hits the atmosphere. Light from sun travels at an angle, which then refracts at us. We see blue because blue bends more than any other color. The sun is red at sunset because it has to travel through a lot more atmosphere to get to us. The red light gets through because it doesn't have to bend very much. Polarization ­ Polarization: the direction in which the electric field is oscillating ­ Sun's light/light from most common sources is un­polarized because it comes from all different directions ­ Using a filter that blocks one specific direction of polarization can polarize un­polarized light ­ Filters in both directions block all light ­ Polarized sunglasses prevent glare Diffraction ­ Occurs when waves encounter a barrier that has a small opening ­ After the wave passes through, it spreads out ­ Lower frequencies bend more than high frequencies, so putting a barrier up to block sound will result in us only hearing low pitches ­ Diffraction causing interference ­ Thomas Young's Interference experiment ­ Shining light through two openings creates overlap of waves, creates bright spots and dark spots ­ Proves light is a wave because it interferes and diffracts ­ Problem with light as a wave ­ Shining light onto a piece of metal makes electrons pop off the metal, but the energy and speed of those electrons did not depend on the intensity of the light, just the color. But, the brighter light is, the more it should be moving the electrons ­ Einstein said we can explain this experiment if light is a particle ­ Light is a wave AND a particle ­ Wave/particle duality ­ Perform Interference Experiment and see particles behave like waves Issues with light ­ Light moves at a constant speed, always ­ Light behaves like a wave sometimes and like a particle sometimes Relativity: trying to describe when/where something happened ­ Reference frames: different perspectives of viewing an event ­ Space­time coordinates: 4 assigned values: N/S, E/W, up/down (space), and time ­ Different depending on reference frame ­ Idea that stationary viewer is more correct about direction of movement ­ But, there is no "correct" reference frame ­ Special relativity ­ Because of reference frames, there's no such thing as simultaneous events (depends on motion of observer) ­ The "special theory of relativity" ­ Postulate 1: laws of physics are the same in any inertial (non­ accelerating) reference frame ­ Postulate 2: speed of light in a vacuum has the same value in all directions and all inertial reference frames ­ Relativity of time ­ Light moves the same speed, but shorter/farther distance and longer/shorter time depending on different reference frames ­­> Time is not absolute/different depending on reference frames ­ If you're moving, time slows down ­ Grows exponentially as speed increases ­ When travelling at the speed of light, time is infinite ­ Therefore, we can never reach the speed of light (it would take an infinite amount of time)

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##### ISBN: 9780321747730

The answer to “In 7–10, determine e At by first finding a fundamental matrix and then using formula (3).” is broken down into a number of easy to follow steps, and 16 words. Since the solution to 7E from 9.8 chapter was answered, more than 281 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. The full step-by-step solution to problem: 7E from chapter: 9.8 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM. This full solution covers the following key subjects: determine, finding, formula, Fundamental, Matrix. This expansive textbook survival guide covers 67 chapters, and 2118 solutions.

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