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# For two- and three-dimensional vectors, the fundamental property of dot products, A B = ISBN: 9780321797056 284

## Solution for problem 2.3.10 Chapter 2.3

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems | 5th Edition

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Problem 2.3.10

For two- and three-dimensional vectors, the fundamental property of dot products, A B = |A||B| cos , implies that |A B||A||B|. (2.3.44) In this exercise, we generalize this to n-dimensional vectors and functions, in which case (2.3.44) is known as Schwarzs inequality. [The names of Cauchy and Buniakovsky are also associated with (2.3.44).] (a) Show that |A B| 2 > 0 implies (2.3.44), where = A B/B B. (b) Express the inequality using both A B = n=1 anbn = n=1 ancn bn cn . *(c) Generalize (2.3.44) to functions. [Hint: Let A B mean the integral L 0 A(x)B(x) dx.]

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Week 1 and 2 of College Pre-algebra Life Saver notes! Order of operations Remember GEMDAS 1.G rouping 2.E xponents 3.M ultiply 4.D ivide 5.A dd 6.S ubtract NOTE: when multiplying, dividing, adding, and subtracting you do it as you are reading a book; you go left to right. Important things to remember!:  When there are parenthesis ( ) inside of brackets [ ] be sure to...

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##### ISBN: 9780321797056

Since the solution to 2.3.10 from 2.3 chapter was answered, more than 235 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 2.3.10 from chapter: 2.3 was answered by , our top Math solution expert on 01/25/18, 04:21PM. This textbook survival guide was created for the textbook: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, edition: 5. The answer to “For two- and three-dimensional vectors, the fundamental property of dot products, A B = |A||B| cos , implies that |A B||A||B|. (2.3.44) In this exercise, we generalize this to n-dimensional vectors and functions, in which case (2.3.44) is known as Schwarzs inequality. [The names of Cauchy and Buniakovsky are also associated with (2.3.44).] (a) Show that |A B| 2 > 0 implies (2.3.44), where = A B/B B. (b) Express the inequality using both A B = n=1 anbn = n=1 ancn bn cn . *(c) Generalize (2.3.44) to functions. [Hint: Let A B mean the integral L 0 A(x)B(x) dx.]” is broken down into a number of easy to follow steps, and 101 words. Applied Partial Differential Equations with Fourier Series and Boundary Value Problems was written by and is associated to the ISBN: 9780321797056. This full solution covers the following key subjects: . This expansive textbook survival guide covers 81 chapters, and 759 solutions.

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