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Homework_1_Spring_2010(2)

# Homework_1_Spring_2010(2) - (A Write down the values of(i...

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1 MAE 105: Introduction to Mathematical Physics Homework 1 Posted: April 2, 2010 , DUE: April 9, 2010 (Friday, 1 pm), 1. In class, we derived the heat equation for a one-dimensional rod of constant cross-sectional area, A. If the rod has a variable cross-sectional area, say A(x) , derive the modified form of the heat equation. Assume no internal heat sources. Hint: Use similar rationale as the class derivation. The area A(x + x) can be approximated as A(x) + x etc. 2. A brief review of basic math. and Math 20D
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Unformatted text preview: (A) Write down the values of (i) sin 0 o , (ii) cos 180 o , (iii) tan 30 o , (iv) cos 90 o , (v) sinh 1, (vi) cosh 1 (B) Solve the following integrals, by using the method of “integration by parts”: (a) , (b) , for (i) a = b , and (ii) a ≠ b, (c) , for (i) a = b , and (ii) a ≠ b (C) Solve the following ordinary differential equations (ODEs) for y(x) : (a) , (b) , (c) , (d) , (e) = 9 y , (f) = - 9 y (g) (h) = 3 x 2 ,...
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