Mathematics, 10.03.2020 09:00 drobledo9
. The following polynomials are the first five in the sequence known as Chebyshev polynomials of the first kind
T0(x)=1, T1(x)=x, T2(x)=2x2 −1 T3(x)=4x3 −3x, T4(x)=8x4 −8x2 +1.
(a) Show that {T0, T1, T2, T3, T4} is a basis for P4, the space of polynomials of degree ≤ 4.
(b) Check that differentiation defines a linear transformation TD : P4 → P3 and write down the matrix of each linear transformation in the Chebyshev basis. Similarly, check that integration is a linear transformation TS : P3 → P4.
(c) Let D and S be the differentiation and integration matrices, respectively, from part (b). Compute the matrix products DS and SD. Interpret the results using calculus: choose a suitable polynomial in P4, differentiate it, and then integrate it.
(d) Write down bases for the null spaces and column spaces of D and S. Provide the cor- responding polynomials. Can you interpret your results about D and S in light of what you know about differentiation and integration from calculus?
Answers: 3
Mathematics, 21.06.2019 16:20, mattmaddox86
The number of potato chips in a bag is normally distributed with a mean of 71 and a standard deviation of 2. approximately what percent of bags contain between 69 and 73 potato chips? approximately 68% approximately 71% approximately 95% approximately 99.7%
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Mathematics, 21.06.2019 21:00, hartzpeyton136
The description below represents function a and the table represents function b: function a the function is 5 more than 3 times x. function b x y −1 2 0 5 1 8 which statement is correct about the slope and y-intercept of the two functions? (1 point) their slopes are equal but y-intercepts are not equal. their slopes are not equal but y-intercepts are equal. both slopes and y intercepts are equal. neither slopes nor y-intercepts are equal.
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. The following polynomials are the first five in the sequence known as Chebyshev polynomials of the...
Mathematics, 30.10.2019 03:31
Mathematics, 30.10.2019 03:31
Mathematics, 30.10.2019 03:31
Mathematics, 30.10.2019 03:31