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263ps10

# 263ps10 - Physics 263 Problem Set#10 These problems are due...

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Physics 263: Problem Set #10 These problems are due on Monday June 6. 0. Unassigned homework: go over old homework problems and solutions. Key math tech- niques you’ll want: expansion in Taylor series, Fourier series, various integration tech- niques (parts, parameters), complex numbers and functions thereof, matrices (inverses, de- terminants, eigenvectors). Key physics contexts: basic relativity kinematics, E 2 = p 2 + m 2 collision problems, oscillators (whether damped, driven or coupled). 1. Shankar, BTM problem 6.4.6 pg. 138 (parts A and B only) 2. Shankar, BTM problem 9.7.10 pg. 288. 3. Morin 6.3 (Pendulum with an oscillating support) p. 246. 4. Morin 12.31 (Equal angles) p. 617. 5. (a) Expand the following function about z = 0 through order z 3 (keeping only up to z 3 ) cosh( z ) sin( z ) c 2 - z 2 (b) Given f ( z ) = u ( x, y )+ iv ( x, y ), where u ( x, y ) = x 2 - y 2 +1+2 x , find a v ( x, y ) which makes f ( z ) analytic. What is this f ( z ) (i.e. written explicitly as a function of z )? Is this f ( z ) unique? Explain. 6. (a) Express the complex number - i in both polar and in x + iy format. Same for cosh[1 +

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263ps10 - Physics 263 Problem Set#10 These problems are due...

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