MATH 471 Lecture Notes - Lecture 1: Wave Equation, Linear Equation, Polar Coordinate System
20 Jan 2017
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Document Summary
Problems in midterm, and nal similar to homework and prob- lems done in class: attendance helps for nal letter grade. Pde: u = u(x, t) (more independent variables) De nition: a pde (partial di erential equation) is an equation that contains partial derivatives. Ex: ut = uxx, where, u = u(x, t) **heat equation** Ex: utt = uxx + uyy, where, u = u(x, y, t) physical meaning of pde"s u(x, t) = u : temperature x : location t. 5 classi cations: order of p. d. e: order of the highest partial derivative of the equation. Example ut = uxx (second order pde) *heat equation ut = ux (first order pde) ut = uuxxx + sin(x) (third order pde: linearity: 6 general form for second order linear equa- tion in two variables. Auxx + buxy + cuyy + dux + ruy + f u = g. 1: when g = 0, homogeneous equation, when g 6= 0, non-homogeneous equation.
