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Unformatted text preview: The energy of an electron at speed v in special relativity theory is E = mc 2 (1v 2 /c 2 )1 / 2 , where m is the electron mass, and c is the speed of light. The factor mc 2 is called the rest mass energy (the energy when v = 0). Find the ﬁrst three terms of the series expansion of E in v . What is the second term in the series? 6. (Problem 1.16.33, p. 43) If you are at the top of a tower of height h above the surface of the earth, show that the distance you can see along the surface of the earth is approximately s = √ 2 Rh , where R is the radius of the earth. (See the ﬁgure and the hints in the book.) Mathematical Physics, Fall, 2010 Problem Set I, Page 2 7. (Problem 4.12.16, p. 237) In kinetic theory, we have to evaluate integrals of the form I ( n ) = Z ∞ t n eat 2 d t. Given that I (0) = p π/ 4 a , evaluate I for all integers n ....
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 Fall '10
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 Maclaurin Series, Power Series, Taylor Series, Special Relativity, Maclaurin

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