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14 Across: uxx + ux + uy - 0 is a ______differential equation.

14 Across: uxx + ux + uy - 0 is a ______differential equation.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The following series of questions are regarding the crossword puzzle at the end of Stanley Farlow's Partial Differential Equations for Scientists and Engineers.  (Home-school mom here, who thought it would be "fun" to assign this crossword puzzle, but then realized, I did not have the answer key. Oops.)  So your help is greatly appreciated.

#14 Across: uxx + ux + uy - 0 is a ______differential equation.

6. The author of a famous text on PDE. 7. In order for separation of variables to work, the PDE must be 10. A first-order equation of the form u, + fx = 0 is called a equation. 12. When we solve Laplace's equation in polar coordinates by sepa- ration of variables, the ODE in r is named after this man. 13. The equation un =U is commonly called the equation. differential 14) The equation ux+u+u, - 0 is a equation. = Duxx vu, is by 16. A useful way to solve the equation u, coordinates. 19.) The equation u, = Uxx is commonly called the equation. method. 22. The Crank-Nicolson method is an. 24.) The of a BVP quite often are proportional to the natural frequencies of the problem. 27. When solving Laplace's equation in spherical coordinates by sep- aration of variables, the ODE in is called. equation. Bessel? 28.) The potential due to a point charge is called function. (29) The most basic idea behind the solution to linear problems is 33. A method of minimizing functionals by replacing the functions by polynomials is due to 35) If the dependent variable is found explicitly as a function of the independent variables of the problem, we have an. solution. 38. A famous mathematician/physicist responsible for the discovery of calculus and some differential equations. 40. The quantity that measures the difference between a function at a point and its surrounding points. 41. The basic vibrations of a membrane are called the solutions. -
Transcribed Image Text:6. The author of a famous text on PDE. 7. In order for separation of variables to work, the PDE must be 10. A first-order equation of the form u, + fx = 0 is called a equation. 12. When we solve Laplace's equation in polar coordinates by sepa- ration of variables, the ODE in r is named after this man. 13. The equation un =U is commonly called the equation. differential 14) The equation ux+u+u, - 0 is a equation. = Duxx vu, is by 16. A useful way to solve the equation u, coordinates. 19.) The equation u, = Uxx is commonly called the equation. method. 22. The Crank-Nicolson method is an. 24.) The of a BVP quite often are proportional to the natural frequencies of the problem. 27. When solving Laplace's equation in spherical coordinates by sep- aration of variables, the ODE in is called. equation. Bessel? 28.) The potential due to a point charge is called function. (29) The most basic idea behind the solution to linear problems is 33. A method of minimizing functionals by replacing the functions by polynomials is due to 35) If the dependent variable is found explicitly as a function of the independent variables of the problem, we have an. solution. 38. A famous mathematician/physicist responsible for the discovery of calculus and some differential equations. 40. The quantity that measures the difference between a function at a point and its surrounding points. 41. The basic vibrations of a membrane are called the solutions. -
PDE Crossword Puzzle Fa pery XXXX 0 nservati i NININKAS VAR WAV 13 18 19 20 n + 24 cit ² Be 16 m nge ving 220 23, PL 25 t 22ege dres 29 30 31 37 38 I'Newton |of|u am mental VIXIXINAXINIA 28 26 XA b 8 mogeneous 132 H 34 35 39 aplacian XIXIX 36
Transcribed Image Text:PDE Crossword Puzzle Fa pery XXXX 0 nservati i NININKAS VAR WAV 13 18 19 20 n + 24 cit ² Be 16 m nge ving 220 23, PL 25 t 22ege dres 29 30 31 37 38 I'Newton |of|u am mental VIXIXINAXINIA 28 26 XA b 8 mogeneous 132 H 34 35 39 aplacian XIXIX 36
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