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Messages - Yifei Hu

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Chapter 1 / HW1-Problem2
« on: Today at 01:33:08 PM »
Can anyone help me check the answer? Thanks

(11) Second order, linear, homogeneous
(12) Second order, quasilinear
(13) Third order, linear, homogeneous
(14) Third order, quasi linear
(15) Forth order, linear homogeneous
(16) Forth order, linear homogeneous
(17) Forth order, linear inhomogeneous
(18) Forth order, general non-linear

Can we say that, to classify whether an equation is linear, we don't need to move the L.O.T to right hand side, but when classifying non-linear equations , we need to do so?

Chapter 1 / HW1-Problem 1
« on: Today at 01:17:24 PM »
Can anyone help me check the answer? Thanks

(1) linear-homogeneous
(2) Quasi-linear
(3) Semi-linear
(5) Semi-linear
(8) Semi-linear
(10) Quasi-linear

Chapter 2 / Transport Equation Derivation
« on: January 18, 2022, 07:34:32 PM »
Can anyone help explain where does the Ut term in the second last line come from? Thanks

Chapter 1 / Second Order canonical Form
« on: January 13, 2022, 02:37:35 PM »
What is the definition here (when classifying the second order PDEs) for the second order canonical form? what are the Xi and Eta here? Is the operation here defined as taking derivative? e.g: Eta^2 = second derivative of Eta?

Question: let w= 2-i , find w^3 + w
Are we suppose to do multiplications directly or are we suppose to use Euler's formula? Since in this case, \theta = arctan(-1/2), we can't directly come out the sin and cos of n \theta.
Are there any other alternative methods to apply to such complex numbers with a general arguments that can take advantage of Euler's formula's easy computations of power? Can we give the answer to this question as a polynomial of e^iarctan(c)?

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