By Fleisch, Daniel A.; Kinnaman, Laura
"Waves are a major subject within the fields of mechanics, electromagnetism, and quantum concept, yet many scholars fight with the mathematical elements. Written to enrich direction textbooks, this e-book makes a speciality of the themes that scholars locate such a lot tough. protecting the hugely renowned process utilized in Fleisch's different Student's publications, the publication makes use of undeniable language to provide an explanation for primary principles in an easy and transparent approach. workouts and fully-worked examples support readers try out their figuring out of the suggestions, making this an amazing publication for undergraduates in physics and engineering attempting to familiarize yourself with this tough topic. The publication is supported through a collection of on-line assets to be had at www.cambridge.org/9781107643260. those comprise interactive ideas for each workout and challenge within the textual content and a chain of video podcasts during which the authors clarify the $64000 recommendations of each component to the book"-- Read more...
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Extra resources for A student’s guide to waves
Thus a rotating phasor can provide a useful representation of the advancing phase of a wave, and Euler’s relation provides a means of performing mathematical operations using phasors. That’s the subject of the next section. 5 Euler relations While the notation used for z in the previous section is useful when you need separate real and imaginary components, it gets cumbersome very quickly when you start doing algebra or calculus involving z. It would be nice to package all the information you need to define z into an easier-to-use function of θ .
12 Complex numbers on the complex plane, polar form. number of points in the complex plane. That subset is comprised of all the points that form a circle around the origin at a distance of exactly one unit. That circle of points is called the “unit circle” because its radius has unit length. To see the usefulness of the unit circle, consider Fig. 13. Any complex number z lying on the unit circle can be drawn as a vector with length (magnitude) one and angle θ . Using Eqs. 18) so any complex number on the unit circle can be written as z = cos θ + i sin θ.
2 The classical wave equation In the introduction to this chapter, the most common form of the wave equation is described as a linear, second-order, homogeneous partial differential equation. This is often called the “classical” wave equation, and it usually looks something like this: 1 ∂ 2y ∂ 2y = . 5) There are several different ways to derive this equation. Many authors use the approach of applying Newton’s second law to a string under tension, and you can see how that works in Chapter 4. But we think that you can gain a good physical understanding of the wave equation by thinking carefully about the meaning of the partial derivatives that appear on both sides of Eq.
A student’s guide to waves by Fleisch, Daniel A.; Kinnaman, Laura