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@jemoka / Jemoka Knowledge Base / raw/course/math53_problem/kbhsu_math53_problem_session.md
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--- title: "SU-MATH53 Problem Session" source: https://www.jemoka.com/posts/kbhsu_math53_problem_session/ --- L-Periodic Functions So, we have: \begin{equation} f(x+L) = f(x) \end{equation} The integral is equivalent for any: \begin{equation} \int_{a}^{a+L} f(x) \end{equation} for any \(a\). Heat Equation Recipe are we on a finite interval? then, decompose into product-type solution \(A(t)B(x)\) and solve. are we not? Fourier transform on the space variable and solve. What if \(\lambda \in \mathbb{C} \backslash \mathbb{R}\) Shush. Why can we guess \(A(t)B(x)\) Because we were able to find solutions. Believe that the solution set spans. Fourier Transform on Three-Variable Expressions We have better Fourier transforms on n-space rather than on a line. Use those. Existence and Uniqueness + Superposition