- #1
Karl Karlsson
- 104
- 12
- Homework Statement
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- Relevant Equations
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I want to solve the heat equation below:
I don't understand where the expression for ##2/R\cdot\int_0^R q\cdot sin(k_nr)\cdot r \, dr## came from. The r dependent function is calculated as ##sin(k_nr)/r## not ##sin(k_nr)\cdot r##. I don't even know if ##sin(k_nr)/r## are orthogonal for different ##k_n## values. Why is ##q_n = 2/R\cdot\int_0^R q\cdot sin(k_nr)\cdot r \, dr## ?
I don't understand where the expression for ##2/R\cdot\int_0^R q\cdot sin(k_nr)\cdot r \, dr## came from. The r dependent function is calculated as ##sin(k_nr)/r## not ##sin(k_nr)\cdot r##. I don't even know if ##sin(k_nr)/r## are orthogonal for different ##k_n## values. Why is ##q_n = 2/R\cdot\int_0^R q\cdot sin(k_nr)\cdot r \, dr## ?