Applied Mathematical Models Mid term test 17-2-2009 Each subproblem is worth ten points 1 Consider a continuous medium occupying a cylindrical domain with constant cross section. The Eulerian and Lagrangian velocity and density functions are denoted by v(
THE UNIVERSITY OF SUSSEX
G1110
BSc/MMath EXAMINATIONS 2012
MATHEMATICS: NUMERICAL LINEAR ALGEBRA (LEVEL 3)
Tuesday, 22nd May 2012
9.30 am11.30 am
You may attempt as many questions as you wish, but marks will be given for
the best THREE answers only.
Time
THE UNIVERSITY OF SUSSEX
G1110
BSc/MMath EXAMINATIONS 2011
MATHEMATICS: NUMERICAL LINEAR ALGEBRA (LEVEL 3)
Tuesday, 24th May 2011
2.00 pm4.00pm
ATTEMPT ALL QUESTIONS.
Time allowed: TWO hours.
Each question carries THIRTY marks. The numbers beside the ques
THE UNIVERSITY OF SUSSEX
G1110/852G1
BSc/MMath EXAMINATIONS 2009
MATHEMATICS: NUMERICAL LINEAR ALGEBRA
Tuesday, 19th May 2009
9.30 am11.30 am
You may attempt as many questions as you wish, but marks will be given for
the best THREE answers only.
Time allo
Methods of Applied Mathematics
Sheet 4. Singular Perturbations
1. Consider the cubic equation
x3 + x 2 = 0,
0<
1.
Use the direct method of perturbation to nd the root close to 2, working
as far as the rst-order correction.
Use a balancing argument in orde
Methods of Applied Mathematics
Sheet 3. Regular Perturbation
1. Consider the initial-value problem:x + (1 + )x = 0,
t (0, ), 0 < < 1, x(0) = 1, x(0) = 0.
(a) Show that if a solution is sought by the direct method of perturbation using x = x0 + x1 +
2 x2 +
Methods of Applied Mathematics
Sheet 2. Scaling
1. In Example 1.15 of lectures three dierent ways of obtaining a dimensionless version of the projectile problem were given (Versions A, B and C).
Verify that in each case the characteristic values used for
Models of Continuous Media
Questions
1 (a)A continuous medium in R3 undergoes a deformation with displacement function at time t > 0 given by U(X, t) := x(X, t) - X = (X2 t2 , X3 t2 , X3 t). Find (i)The acceleration in both Lagrangian and Eulerian forms a
Models of Continuous Media
Questions M304A
A1 Consider a continuous medium occupying a cylindrical domain with constant cross section. The Eulerian and Lagrangian velocity and density functions are denoted by v(x, t) and V (X, t) and by (x, t) and (X, t)
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The University of Sussex Department of Mathematics
G1110 & 852G1 Numerical Linear Algebra
Lecture Notes Autumn Term 2011
Gabriel Koch
(w a) w
Sw
a
w
w
(w a) w
H (w) a = (w a) w + w
Figure 1: Geometric explanation of the Householder matrix H (w).
Lecture n