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(6) (This question does not relate to the above conditions.) Prove that the following system of...
Please solve this question. Sorry please neglect the bottom picture which says "moreover ...". I am...
Please solve this question.
Sorry please neglect the bottom picture
which says "moreover ...".
I am happy to upbote if you solve (1)-(5).
Problem 1. We denote by the set of all sequences (UK)x=1,2,... = (U1, U2, ...) (ux E C) u= satisfying luxl <00. Moreover, we define k=1 (u, v) = xox(u, v E f). k=1 (1) Prove that is a vector space. (2) Prove that is a inner product space with respect to (5.). (3) Construct the norm...
Problem. We consider the Fourier expansion of the function f(0) = 0 in Lề(–1,1). By the...
Problem. We consider the Fourier expansion of the function f(0) = 0 in Lề(–1,1). By the Fourier expansion of f with respect to the system of trigonometric functions, we have f(0) = 40 + bn cos no + ensin no. n=1 n=1 Moreover, by the Fourier expansion of f with respect to {øn} defined in the slide, we also derive f@) = dneine n=-, n0 Then, please write the value of ao, bn, Cn, dn
5. For any real number L > 0, consider the set of functions fx(x) = cos...
5. For any real number L > 0, consider the set of functions fx(x) = cos ("I") and In(x) = sin (^) se hos e mais a positive in where n is a positive integer. Show that these functions are orthonormal in the sense that (a) 1 L È Lsu(w) m(e)dx = {if m=n. fn (2) fm(x) dx = {. if m En if m =n -L 1 L il fn(x)9m(x)dx = 0 (c) il 9.(X)gm()dx = {{ if m=n...
I need solution as soon as possible thank you Q1 Given, f(x) = { 4,0$*<2...
I need solution as soon as possible thank you
Q1 Given, f(x) = { 4,0$*<2 4x +1,25x<4 (a) Sketch the graph of f(x) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval -12 < x < 12. (6 marks) (b) Determine the Fourier cosine coefficients of Q1(a). (10 marks) (C) Write out f(x) in terms of Fourier coefficients you have found in Q1(b). (4 marks) SOME RELEVANT FORMULA Fourier Series...
Find the temperature function u(x,t)u(x,t) (where xx is the position along the rod in cm and...
Find the temperature function u(x,t)u(x,t) (where xx is the
position along the rod in cm and tt is the time) of a 1818 cm rod
with conducting constant 0.10.1 whose endpoint are insulated such
that no heat is lost, and whose initial temperature distribution is
given by:
u(x,0)={5 if 6≤x≤12
{0 otherwise
To start, we have L=18 0.1 Because the rods are insulated, we will use the cosine Fourier expansion. 22 Ac + =1 A cos(" )e| A cos( u(x,...
do question 3 with the info provided f 0 Question 3 Given the graph above represents...
do question 3 with the info provided
f 0 Question 3 Given the graph above represents a string being plucked at point (g). The wave equation generated when the string is released after being plucked, is given by the wave equation in question 1, and that additionally: 1. u(0, t) 0 u(4, t) 2. u(x, 0) f(x) as in question 2 au 3. atlt-0 Solve wave equation subject to the restrictions above. [10] Question 2 a) In the General Fourier...
Evaluate the following series by applying Parseval's equation to certain of the Fourier expansions in Table...
Evaluate the following series by applying Parseval's equation to
certain of the Fourier expansions in Table 1
10. Evaluate the following series by applying Parseval's equation to certain of the Fourier expansions in Table 1 n2 (n2)2 C. 1 (coth 4 Answer: 7 TABLE 1. FOURIER SERIES 2-1)*! 1. f(0) = 0 (-n <0 < «) sin ne OC 4 cos(2n - 1)e (2n 1)2 2. | f(0) 3D 1Ө| (-п <0 < п) 2 T sin ne (0 0...
Express the general solution of the given system of equations in terms of real-valued functions sin...
Express the general solution of the given system of equations in terms of real-valued functions sin 4t - cos 4t - sir 4t cos 4t sin 4t -cos 4t 4 sin 5t -cos 5 4 sin 4t cos 4t Find the solution of the given initial value problem. Describe the behavior of the solution as t 00 x, x (0) 2 -3 Enclose arguments of functions in parentheses. For example, sin (2) Do not simplify trigonometric functions of nt, where...
Please solve this question.
Sorry please neglect the bottom picture
which says "moreover ...".
I am happy to upbote if you solve (1)-(5).
Problem 1. We denote by the set of all sequences (UK)x=1,2,... = (U1, U2, ...) (ux E C) u= satisfying luxl <00. Moreover, we define k=1 (u, v) = xox(u, v E f). k=1 (1) Prove that is a vector space. (2) Prove that is a inner product space with respect to (5.). (3) Construct the norm...
Problem. We consider the Fourier expansion of the function f(0) = 0 in Lề(–1,1). By the Fourier expansion of f with respect to the system of trigonometric functions, we have f(0) = 40 + bn cos no + ensin no. n=1 n=1 Moreover, by the Fourier expansion of f with respect to {øn} defined in the slide, we also derive f@) = dneine n=-, n0 Then, please write the value of ao, bn, Cn, dn
5. For any real number L > 0, consider the set of functions fx(x) = cos ("I") and In(x) = sin (^) se hos e mais a positive in where n is a positive integer. Show that these functions are orthonormal in the sense that (a) 1 L È Lsu(w) m(e)dx = {if m=n. fn (2) fm(x) dx = {. if m En if m =n -L 1 L il fn(x)9m(x)dx = 0 (c) il 9.(X)gm()dx = {{ if m=n...
I need solution as soon as possible thank you
Q1 Given, f(x) = { 4,0$*<2 4x +1,25x<4 (a) Sketch the graph of f(x) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval -12 < x < 12. (6 marks) (b) Determine the Fourier cosine coefficients of Q1(a). (10 marks) (C) Write out f(x) in terms of Fourier coefficients you have found in Q1(b). (4 marks) SOME RELEVANT FORMULA Fourier Series...
Find the temperature function u(x,t)u(x,t) (where xx is the
position along the rod in cm and tt is the time) of a 1818 cm rod
with conducting constant 0.10.1 whose endpoint are insulated such
that no heat is lost, and whose initial temperature distribution is
given by:
u(x,0)={5 if 6≤x≤12
{0 otherwise
To start, we have L=18 0.1 Because the rods are insulated, we will use the cosine Fourier expansion. 22 Ac + =1 A cos(" )e| A cos( u(x,...
do question 3 with the info provided
f 0 Question 3 Given the graph above represents a string being plucked at point (g). The wave equation generated when the string is released after being plucked, is given by the wave equation in question 1, and that additionally: 1. u(0, t) 0 u(4, t) 2. u(x, 0) f(x) as in question 2 au 3. atlt-0 Solve wave equation subject to the restrictions above. [10] Question 2 a) In the General Fourier...
Evaluate the following series by applying Parseval's equation to
certain of the Fourier expansions in Table 1
10. Evaluate the following series by applying Parseval's equation to certain of the Fourier expansions in Table 1 n2 (n2)2 C. 1 (coth 4 Answer: 7 TABLE 1. FOURIER SERIES 2-1)*! 1. f(0) = 0 (-n <0 < «) sin ne OC 4 cos(2n - 1)e (2n 1)2 2. | f(0) 3D 1Ө| (-п <0 < п) 2 T sin ne (0 0...
Express the general solution of the given system of equations in terms of real-valued functions sin 4t - cos 4t - sir 4t cos 4t sin 4t -cos 4t 4 sin 5t -cos 5 4 sin 4t cos 4t Find the solution of the given initial value problem. Describe the behavior of the solution as t 00 x, x (0) 2 -3 Enclose arguments of functions in parentheses. For example, sin (2) Do not simplify trigonometric functions of nt, where...
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