Exercises
1. Commonly, when we ﬁt a polynomial with n parameters, we choose the lowest order
polynomial that has this number of parameters, namely a polynomial with degree n—I .
Other possibilities exist. ya = a1 x + a2 f + a, x6 + a4 x7 has 4 parameters,
O VDE a u\_)rt.‘_s -
Answers
1 .
I y j
0 2.0000 1.0000
0.2 2.2000 1.0000
0.4 2.4000 1.0000
0.6 2.6000 1.0000
0.8 2.8000 1.0000
1.0 3.0000
The true solution of j) = 1 is a straight line. The method used gets the slope correct at the left
hand side of a seg
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF CIVIL AND ENVIRONMENTAL ENGINEERING
10. A VERY BRIEF INTRODUCTION TO TIME-DEPENDENT SOLUTIONS
OF PARTIAL DIFFERENTIAL EQUATIONS
10.1 TUTORIAL PROBLEMS
1. Solve equation 1 with D=0.25 m/s, t=0.02s, x=0.1m, subjec
~Exercises
1. For the following beam deflection problem, find the deflections
using
(a) h =%
_L
l (.b) h “I
2
E1 = const. A vu- B
Note that the number of unknown deflections can be reduced by taking
account of symmetry.
A get improved eStimates of the m
3.3 TUTORIAL
/ 1) Evaluate In mm xdx us1ng trapezordal or Srmpson's rule to an accuracy of 6 decnnal
places. Your answer is to include evidence that this accuracy has been achieved.
\/ ii) Plot the log error — log panels graphs for the integrals of e" (fr