Exercise 17 Show that the above results can be written independently for the sine and cosine functions to give X+ °x√ To •Hotd Xo cos(kmx) cos(knx) dx = Czo+λ { sin(kmx) sin(knx) dx = { cos(kmx) sin(knx) dx = 0, X mn 8mn 0 m, n‡0 m=n=0 m, n‡0 m=n=0 " (19) (20) (21) where kn = 2nT/λ. [In the last case, one has to deal with a degeneracy of eigenvalues when m = n. Both the cosine and sine functions have the same eigenvalue, although they are linearly independent.]
Exercise 17 Show that the above results can be written independently for the sine and cosine functions to give X+ °x√ To •Hotd Xo cos(kmx) cos(knx) dx = Czo+λ { sin(kmx) sin(knx) dx = { cos(kmx) sin(knx) dx = 0, X mn 8mn 0 m, n‡0 m=n=0 m, n‡0 m=n=0 " (19) (20) (21) where kn = 2nT/λ. [In the last case, one has to deal with a degeneracy of eigenvalues when m = n. Both the cosine and sine functions have the same eigenvalue, although they are linearly independent.]
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 80E
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