Please help in any of number
9-12 in differential equations
the questions 9-12 uses the information from the other pictures posted of questions 1-8
Homework Answers
Solution for 10. Following the solution to 3 to obtain fourier sine series. Then I have plotted using desmos for 100 terms. Graph is for - 4pi to 4pi. 4pi=12.56637
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Please help in any of number
9-12 in differential equations
the questions 9-12 uses the information...
please help in any of these in diff eq in Trigonometric Fourier Sine Series and Trigonometric...
please help in any of these in
diff eq in Trigonometric Fourier Sine Series and Trigonometric
Cosine Series
Homework Problems for Handout Sheet 25 In Problems 1 to 4, determine the Fourier Sine Series that converges to the given function at each of its points of continuity 0 when 0x<1/2 1. f(x)=when 1/2<x<1' flx+2)= f(x). 0 when 4<x<-2 2. f(x)={2 when 0<x<1 , f(x+8)= f(x). 1 when 1<x<2 3. f(x) 2-x when 0<x<27, f(x+47)=f(x) 4. f(x) 7-x when 0<x<47, f(x+87)=...
Question: Equations: My attempt (sorry for uneatness) : Tutorial questions - Sine and Cosine trans...
Question:
Equations:
My attempt (sorry for uneatness) :
Tutorial questions - Sine and Cosine transforms 9. U se the Fourier Inversion Theorem to prove for a real-valued odd function f(t) that F.(w) sin wt du at points of continuity. (Hint: first simplify the integral expression for F(w).) Fourier Inversion Theorem. At points where f0) is continuous, is that t at t=( iwt extra te Fo F(w)-マ27: J-0,f(t)e-iwt dt = F(f(t)) w) is called the Fourier cosine transform of f(t). Similarly,...
Im to find the sin and cosine series representations meaning I have to find the coefficients of t...
Im to find the sin and cosine
series representations meaning I have to find the coefficients of
the fourier series when a_n = 0 and when b_n = 0 I believe.
Expand each function into its cosine series and sine series representations of the indicated period T. Determine the values to which each series converges to at x = 0, x = 2 and x =-2 3. a),f(x)-3-x, T=6 b)f(x)=e, T = 2π c)I(x) = sin (x), T=2π 2, 2sr<3...
section is fourier series and first order differential equations 0 Find the Fourier Coefficients a, for...
section is fourier series and first order differential
equations
0 Find the Fourier Coefficients a, for the periodic function f(x) = {: for-2<2<0 O for 0 < x < 2 f(x + 4) = f(x) Find the Fourier Coefficients bn for the periodic function 2 f(x) = -{ for -3 <3 <0 10 for 0 < x <3 f(x+6) = f(x) Determine the half range cosine series of 2 f(x) 0<<< f(x + 2) = f(x) dy Given that =...
4. Let f(x) = 6-2x, 0
4. Let f(x) = 6-2x, 0<x 2 (a) Expand f(x) into a periodic function of period 2, ie. construct the function F(x), such that F(x)-f (x), 0xS 2, and Fx) F(x+2) for all real numbers x. (This process is called the "full-range expansion" of f(x) into a Fourier series.) Find the Fourier series of Fr). Then sketch 3 periods of Fx). (b) Expand fx) into a cosine series of period 4. Find the Fourier series and sketch 3 periods (c)...
There are 3 questions on this assignment. The marks awarded for each part are indi- cated in boxes. 1. Consider the fun...
There are 3 questions on this assignment. The marks awarded for each part are indi- cated in boxes. 1. Consider the function defined by f(x) = 0 and f(x)-f(x +4) 1 (a) Sketch the graph of f(x) on the interval -6,6 (b) Find the Fourier series representation of f(z). You must show how to evaluate any integrals that are needed 2. Consider the function f(x) (a) Sketch the odd and even periodic extension of f(x) for-3< x < 3m (b)...
1. [8] Given x + 2, -2 < x < 0 f(x) = 12 – 2x,...
1. [8] Given x + 2, -2 < x < 0 f(x) = 12 – 2x, 0<x< 2, f(x + 4) = f(x) (a)[3] Sketch the graph of this function over three periods. Examine the convergence at any discontinuities (b)[5] Find the Fourier series of f(x) 2.[10]For the function, f(x), given on the interval 0 < x <L (a)[4] Sketch the graphs of the even extension g(x) and odd extension h(x) of the function of period 2L over three periods...
Could you help me with problem 6? I need precise explanation 1. Write a minimum two...
Could you help me with problem 6? I need precise
explanation
1. Write a minimum two page paper on series. Make sure you cite your work at the end of your paper. history and formulation and process of Fouriern 2.Find the Fourier series of the function f(x)= -I, -T < I <a where f(r+2) f(x). Graph the progression of your terms that approach the function. Something like what we did in class; graph one term of the serics, then the...
could you help me number 6. I thought that it is hardest one. 1. Write a minimum two page paper on series. Make sure...
could you help me number 6. I thought that it is hardest
one.
1. Write a minimum two page paper on series. Make sure you cite your work at the end of your paper. history and formulation and process of Fourier 2.Find the Fourier series of the function f(x) =-I, f(x). Graph the progression of your terms that approach the function. Something like what we did in class; graph one term of the serics, then the first two terms, then...
= Problem #2: The function f(x) sin(4x) on [0:1] is expanded in a Fourier series of...
= Problem #2: The function f(x) sin(4x) on [0:1] is expanded in a Fourier series of period Which of the following statement is true about the Fourier series of f? (A) The Fourier series of f has only cosine terms. (B) The Fourier series of f has neither sine nor cosine terms. (C) The Fourier series of f has both sine and cosine terms. (D) The Fourier series of f has only sine terms.
please help in any of these in
diff eq in Trigonometric Fourier Sine Series and Trigonometric
Cosine Series
Homework Problems for Handout Sheet 25 In Problems 1 to 4, determine the Fourier Sine Series that converges to the given function at each of its points of continuity 0 when 0x<1/2 1. f(x)=when 1/2<x<1' flx+2)= f(x). 0 when 4<x<-2 2. f(x)={2 when 0<x<1 , f(x+8)= f(x). 1 when 1<x<2 3. f(x) 2-x when 0<x<27, f(x+47)=f(x) 4. f(x) 7-x when 0<x<47, f(x+87)=...
Question:
Equations:
My attempt (sorry for uneatness) :
Tutorial questions - Sine and Cosine transforms 9. U se the Fourier Inversion Theorem to prove for a real-valued odd function f(t) that F.(w) sin wt du at points of continuity. (Hint: first simplify the integral expression for F(w).) Fourier Inversion Theorem. At points where f0) is continuous, is that t at t=( iwt extra te Fo F(w)-マ27: J-0,f(t)e-iwt dt = F(f(t)) w) is called the Fourier cosine transform of f(t). Similarly,...
Im to find the sin and cosine
series representations meaning I have to find the coefficients of
the fourier series when a_n = 0 and when b_n = 0 I believe.
Expand each function into its cosine series and sine series representations of the indicated period T. Determine the values to which each series converges to at x = 0, x = 2 and x =-2 3. a),f(x)-3-x, T=6 b)f(x)=e, T = 2π c)I(x) = sin (x), T=2π 2, 2sr<3...
section is fourier series and first order differential
equations
0 Find the Fourier Coefficients a, for the periodic function f(x) = {: for-2<2<0 O for 0 < x < 2 f(x + 4) = f(x) Find the Fourier Coefficients bn for the periodic function 2 f(x) = -{ for -3 <3 <0 10 for 0 < x <3 f(x+6) = f(x) Determine the half range cosine series of 2 f(x) 0<<< f(x + 2) = f(x) dy Given that =...
4. Let f(x) = 6-2x, 0<x 2 (a) Expand f(x) into a periodic function of period 2, ie. construct the function F(x), such that F(x)-f (x), 0xS 2, and Fx) F(x+2) for all real numbers x. (This process is called the "full-range expansion" of f(x) into a Fourier series.) Find the Fourier series of Fr). Then sketch 3 periods of Fx). (b) Expand fx) into a cosine series of period 4. Find the Fourier series and sketch 3 periods (c)...
There are 3 questions on this assignment. The marks awarded for each part are indi- cated in boxes. 1. Consider the function defined by f(x) = 0 and f(x)-f(x +4) 1 (a) Sketch the graph of f(x) on the interval -6,6 (b) Find the Fourier series representation of f(z). You must show how to evaluate any integrals that are needed 2. Consider the function f(x) (a) Sketch the odd and even periodic extension of f(x) for-3< x < 3m (b)...
1. [8] Given x + 2, -2 < x < 0 f(x) = 12 – 2x, 0<x< 2, f(x + 4) = f(x) (a)[3] Sketch the graph of this function over three periods. Examine the convergence at any discontinuities (b)[5] Find the Fourier series of f(x) 2.[10]For the function, f(x), given on the interval 0 < x <L (a)[4] Sketch the graphs of the even extension g(x) and odd extension h(x) of the function of period 2L over three periods...
Could you help me with problem 6? I need precise
explanation
1. Write a minimum two page paper on series. Make sure you cite your work at the end of your paper. history and formulation and process of Fouriern 2.Find the Fourier series of the function f(x)= -I, -T < I <a where f(r+2) f(x). Graph the progression of your terms that approach the function. Something like what we did in class; graph one term of the serics, then the...
could you help me number 6. I thought that it is hardest
one.
1. Write a minimum two page paper on series. Make sure you cite your work at the end of your paper. history and formulation and process of Fourier 2.Find the Fourier series of the function f(x) =-I, f(x). Graph the progression of your terms that approach the function. Something like what we did in class; graph one term of the serics, then the first two terms, then...
= Problem #2: The function f(x) sin(4x) on [0:1] is expanded in a Fourier series of period Which of the following statement is true about the Fourier series of f? (A) The Fourier series of f has only cosine terms. (B) The Fourier series of f has neither sine nor cosine terms. (C) The Fourier series of f has both sine and cosine terms. (D) The Fourier series of f has only sine terms.
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