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.)
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