1
Math 128b, Spring 2015: Problem Set 10
Exercise 1 Write an integral equation solver for two-point boundary value
problems, following the scheme of the handout. Use an equidistant mesh of
N intervals covering [a, b]. Use the 10-point Gaussian integration
Second-order boundary-value problems
Chapter 11
Boundary-Value Problems for
Ordinary Dierential Equations
Theorem
Support f in the boundary-value problem
for a x b, with y(a) = and y(b) =
y = f (x, y, y ),
is continuous on the set
D = cfw_(x, y, y ) | fo
M ATH 128 B : W ORKSHEET 1
This worksheet is intended to give you a chance to think about and talk about (I) some basic Matlab tools and
(II) some ideas in approximation theory. It will not be collected or graded.
Part I: Make Friends with Matlab
You dont
Gergorin Circle
s
Chapter 9
Approximating Eigenvalues
Per-Olof Persson
Theorem (Gergorin Circle)
s
Let A be an n n matrix, C the complex plane, and
n
|aij |
Ri = z C |z aii |
j=1,j=i
[email protected]
Then
Department of Mathematics
University of Calif
Prof. Ming Gu, 861 Evans, tel: 2-3145
Email: [email protected]
Math128B: Numerical Analysis Sample Final
Exam
This is a closed book, closed notes exam. You need to justify every one of your
answers. Completely correct answers given without justication
UCB Math 128B, Spring 2013: Midterm Exam
Prof. Persson, March 12, 2013
Grading
1
/5
/5
4
/4
5
SID:
2
3
Name:
/8
/4
/26
Instructions:
No notes, no books, no calculators.
Exam time 80 minutes, do all of the problems.
You must justify your answers for ful
UCB Math 128B, Spring 2013: Midterm Exam
Prof. Persson, March 12, 2013 I
Grading
1 / 8
_ Name; 30 (wflcms 2 /5
3 / 5
SID: 4 /4
5 /4
/26
Instructions: I
o No notes, no books, no calculators.
«- Exam time 80 minutes, do all of the problems.
0 You must justi
Prof. Ming Gu, 861 Evans, tel: 2-3145
Email: [email protected]
Math128B: Numerical Analysis Sample Midterm
This is a closed book, closed notes exam. You need to justify every one of your
answers. Completely correct answers given without justication wi
Mock final exam, Math 128B
1. Find the limit limn An v where
2/3 6
10
A = 0 1/2 1/2 ,
0 1/3 1/2
1
v = 1 .
1
2. Convert the equation y = x2 y xy + y into a system of linear ODEs, and perform
one step of Heuns method with step site h = 0.5 using initial val
09/27/2000 WED 11:06 FAX 6434330 MOFFITT LIBRARY 001
Math 128-B: Spring 1999, J. Strain.
Final Exam, 19 May 1999, 12301530.
The following problems are worth 30 points each. Please solve enough to get 90 points.
1. Assume a fundamental matrix Y(t) for y =
Fall 2015 Concurrent Enrollment Orientation
WHEN: Friday, August 21, 2015 10:00 am
-Please plan to arrive up to 10 minutes before. Presentations are scheduled to begin at 10 am.
WHERE: 1
Pimentel Hall (see campus and building map)
PLEASE BRING: Passport a
2015/8/25
25-AUG-15, Fall 2015
STATISTICS
Control Course
Number Number
87303 P 2
87306 S 2
87309 S 2
87312 S 2
87315 S 2
87318 S 2
87321 S 2
87324 S 2
87327 S 2
87330 S 2
87333 S 2
87336 S 2
87339 S 2
87342 S 2
87345 S 2
87348 S 2
87351 S 2
87363 P 20
873
2015/8/25
25-AUG-15, Fall 2015
MATHEMATICS
Control Course
Number Number
53303 P 1A
53306 8 1A
53312 S 1A
53318 8 1A
53324 S 1A
53330 S 1A
53333 8 IA
53339 S 1A
53345 S 1A
53348 8 1A
53351 S 1A
53354 P 1A
53357 8 1A
53360 S 1A
53363 8 1A
53366 S 1A
53369 8
Least Squares Approximation
Consider the approximation of the data cfw_(xi , yi ) for i = 1, . . . , m
by a polynomial
Chapter 8
Approximation Theory
Pn (x) = an xn + xn1 xn1 + + a1 x + a0 .
The coecients a = (a0 , . . . , an ) are given by the solution t
Vector Norms
Denition
A vector norm on Rn is a function,
properties:
Chapter 7
Iterative Techniques in Matrix Algebra
, from Rn into R with the
(i) x 0 for all x Rn
(ii) x = 0 if and only if x = 0
(iii) x = | x for all R and x Rn
Per-Olof Persson
(iv) x
Exercise 1 Prove that the error en = un y(tn ) in the numerical solution
of any dissipative initial value problem y = f (y) by the implicit midpoint
rule
un + un+1
un+1 = un + hf
2
satises
en T
for all nh T , where = O(h2 ) is a bound for the local trunc
1
Convergence of Eulers method
Convergence is the rst basic requirement that a reasonable numerical method
must satisfy. It requires that we get arbitrarily accurate solutions if we put
sucient eort into solving the problem, by taking h suciently small.
D