MATH3403 | Assignment 1 This assignment is due at 9am August 9th at the lecture. It is worth 3% of the total assessment. Late penalties are listed in the profile. If you hand it in late, you must hand it to the MATH3403 assignment box (Level 4) AND email your tutor [email protected]saying that you have done so. Clear and consise presentation of mathematics (or any work) is an important skill. Of the 30 marks associated with this assignment, 2 marks will be allocated for clarity and consiseness and 1 mark for neatness (in proportion to number of questions completed). 1. Solve yu x - xu y =1+ u 2 subject to u(x, 0) = 0 (Ans. u(x, y)= -y/x). Write down the pde/fo005.tex general solution for u(x, 0) = f (x). 2. On tutorial sheet one you are asked to solve the equation xu x + yu y = ku with initial conditions pde/fo012.tex u(x, 1 - x)= H (x). Sketch the characteristics of the equation and determine the domain of validity of the solution. 3. Derive new variables to reduce pde/cov005.tex 3y 2 u xx - 4xyu xy + x 2 u yy to one of the three standard forms, and carry out the reduction (One choice is ξ = x 2 +3y 2 , η = x 2 + y 2 .) 1
University of Queensland PDE course Assignment Questions
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MATH3403 | Assignment 1This assignment is due at 9am August 9th
at the lecture. It is worth 3% of the total assessment.
Latepenalties are listed in the profile. If you hand it in late,
you must hand it to the MATH3403 assignmentbox (Level 4) AND email
your tutor [email protected] saying that you have done so.Clear
and consise presentation of mathematics (or any work) is an
important skill. Of the 30 marksassociated with this assignment, 2
marks will be allocated for clarity and consiseness and 1 mark
forneatness (in proportion to number of questions completed).
1. Solve yux xuy = 1 + u2 subject to u(x, 0) = 0 (Ans. u(x, y) =
y/x). Write down the pde/fo005.texgeneral solution for u(x, 0) =
f(x).
2. On tutorial sheet one you are asked to solve the equation
xux+yuy = kuwith initial conditions pde/fo012.texu(x, 1 x) = H(x).
Sketch the characteristics of the equation and determine the domain
ofvalidity of the solution.
3. Derive new variables to reduce pde/cov005.tex
3y2uxx 4xyuxy + x2uyyto one of the three standard forms, and
carry out the reduction (One choice is = x2 + 3y2, = x2 + y2.)
