4.2.8 A function of the form n ...
4.2.8 A function of the form
n m
f(θ) = ∑ ak sin(kθ) + b0 + ∑ bl cos(lθ) for a1, ... , an, b0, ... , bm ∈ R is called a trigonometric polynomial.
k=1 l = 1
2π
If we put the inner product 〈 f, g 〉= ∫ f(Ө)g (Ө) dӨ on the space of trigonometric polynomials,
0
express II f II in terms of the ak and bl without computing any integrals.
Homework Answers
3. Give P an inner product structure by defining (f,9)-of(ag(x)e"da (you do not have to show that...
3. Give P an inner product structure by defining (f,9)-of(ag(x)e"da (you do not have to show that this is an inner product). Apply the Gram-Schmidt process to (1, , ) with this inner product. Show your work. Hint: You may want to use the fact that Jooz"e-xdz = nl, which follows from n application of integration by parts. (You do not have to show this.) Fun Fact: The polynomials you find here are the first three Laguerre Polynomials, and are...
11. In an introductory calculus course, you may have seen of the form approximation formulas for...
11. In an introductory calculus course, you may have seen of the form approximation formulas for integrals f(t)dt wf(a,), 2 where the a, are equally spaced points on the interval (a,b) and the u, are certain "weights (giving Riemann sums, trapezoidal sums, or showed that, with the same computational effort (same type of formula) we can get better approximations if we don't require the a, to be equally spaced. Simpson's rule depending on their values). Gauss Consider the space P,...
1. Taylor series are special power series that are defined from a function f(z) atz = a by fittin...
1. Taylor series are special power series that are defined from a function f(z) atz = a by fitting higher and higher degree polynomials T, a(x) to the curve at the point (a, f(a)), with the goal of getting a better and better fit as we not only let the degree grow larger, but take a series whose partial sums are these so-called Taylor polynomials Tm,a(x) We will explore how this is done by determine the Taylor series of f(z)...
MA330 Homework #4 1. This exercise concerns the function its gradient vector field F-vo See the p...
the excercise concerns the function (x^2 + y^2)* e^(1-x^2 -
y^2)
please do all parts
MA330 Homework #4 1. This exercise concerns the function its gradient vector field F-vo See the plots of each below. a) Compute the partial derivatives os and ty to find the gradient field vo. (b) In MA231, learned 1, you learned that mixed second-order partial derivatives of reasonable functions Verity that here by computing day and dys and checking that they are the same. should...
mperial Valley College PROJECT #3 You may work in groups of up to 4 students. Each group turns in one homework, w...
mperial Valley College PROJECT #3 You may work in groups of up to 4 students. Each group turns in one homework, wnitten on separate paper e,aat in tiny writing on this sheetl with llwri and all stens shoan doack All students in each group recee the same grade This assignment is due ot the begrring 덱 dass on"huidey July 27 (day of Find Exon This project is worth o total f 40points Homework will be graded not only on correctness,...
please answer all prelab questions, 1-4. This is the prelab manual, just in case you need...
please answer all prelab questions, 1-4.
This is the prelab manual, just in case you need background
information to answer the questions. The prelab questions are in
the 3rd photo.
this where we put in the answers, just to give you an
idea.
Lab Manual Lab 9: Simple Harmonic Oscillation Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and...
3. Give P an inner product structure by defining (f,9)-of(ag(x)e"da (you do not have to show that this is an inner product). Apply the Gram-Schmidt process to (1, , ) with this inner product. Show your work. Hint: You may want to use the fact that Jooz"e-xdz = nl, which follows from n application of integration by parts. (You do not have to show this.) Fun Fact: The polynomials you find here are the first three Laguerre Polynomials, and are...
11. In an introductory calculus course, you may have seen of the form approximation formulas for integrals f(t)dt wf(a,), 2 where the a, are equally spaced points on the interval (a,b) and the u, are certain "weights (giving Riemann sums, trapezoidal sums, or showed that, with the same computational effort (same type of formula) we can get better approximations if we don't require the a, to be equally spaced. Simpson's rule depending on their values). Gauss Consider the space P,...
1. Taylor series are special power series that are defined from a function f(z) atz = a by fitting higher and higher degree polynomials T, a(x) to the curve at the point (a, f(a)), with the goal of getting a better and better fit as we not only let the degree grow larger, but take a series whose partial sums are these so-called Taylor polynomials Tm,a(x) We will explore how this is done by determine the Taylor series of f(z)...
the excercise concerns the function (x^2 + y^2)* e^(1-x^2 -
y^2)
please do all parts
MA330 Homework #4 1. This exercise concerns the function its gradient vector field F-vo See the plots of each below. a) Compute the partial derivatives os and ty to find the gradient field vo. (b) In MA231, learned 1, you learned that mixed second-order partial derivatives of reasonable functions Verity that here by computing day and dys and checking that they are the same. should...
mperial Valley College PROJECT #3 You may work in groups of up to 4 students. Each group turns in one homework, wnitten on separate paper e,aat in tiny writing on this sheetl with llwri and all stens shoan doack All students in each group recee the same grade This assignment is due ot the begrring 덱 dass on"huidey July 27 (day of Find Exon This project is worth o total f 40points Homework will be graded not only on correctness,...
please answer all prelab questions, 1-4.
This is the prelab manual, just in case you need background
information to answer the questions. The prelab questions are in
the 3rd photo.
this where we put in the answers, just to give you an
idea.
Lab Manual Lab 9: Simple Harmonic Oscillation Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and...
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