NAME_
CS412 Introduction to Numerical Methods
Quiz # 6 (Submit to [email protected] dropbox by 8/7, 11AM)
3
1) If f(x) = cos(x), how many panels are needed to evaluate
f(x)dx with a
0
-4
maximum error of 10 using the trapezoidal method?
2) Do one step (using h =
Chapter 21 Objectives
Understanding the application of high-accuracy numerical
differentiation formulas for equispaced data.
Knowing how to evaluate derivatives for unequally spaced
data.
Understanding how Richardson extrapolation is applied for
numeri
Chapter 22 Objectives
Understanding the meaning of local and global truncation
errors and their relationship to step size for one-step
methods for solving ODEs.
Knowing how to implement the following Runge-Kutta (RK)
methods for a single ODE:
Euler
Heun
Chapter 23 Objectives
Understanding how the Runge-Kutta Fehlberg
methods use RK methods of different orders to
provide error estimates that are used to adjust step
size.
Familiarizing yourself with the built-in MATLAB
function for solving ODEs.
Learnin
Chapter 21 Objectives
Understanding the application of high-accuracy numerical
differentiation formulas for equispaced data.
Knowing how to evaluate derivatives for unequally spaced
data.
Understanding how Richardson extrapolation is applied for
numeri
Chapter 19 Objectives
Recognizing that Newton-Cotes integration
formulas are based on the strategy of replacing a
complicated function or tabulated data with a
polynomial that is easy to integrate.
Knowing how to implement the following single
applicati
Chapter 20 Objectives
Understanding how Richardson extrapolation
provides a means to create a more accurate
integral estimate by combining two less accurate
estimates.
Understanding how Gauss quadrature provides
superior integral estimates by picking op
Chapter 14 Objectives
Familiarizing yourself with some basic descriptive
statistics and the normal distribution.
Knowing how to compute the slope and intercept of
a best fit straight line with linear regression.
Knowing how to compute and understand th
Chapter 16 Objectives
Understanding sinusoids and how they can be used for
curve fitting.
Knowing how to use least-squares regression to fit a
sinusoid to data.
Knowing how to fit a Fourier series to a periodic
function.
Understanding the relationship
Chapter 15 Objectives
Knowing how to implement polynomial regression.
Knowing how to implement multiple linear
regression.
Understanding the formulation of the general linear
least-squares model.
Understanding how the general linear least-squares
mode
NAME_
CS412 Introduction to Numerical Methods
Quiz # 5 (Submit to [email protected] dropbox by 8/7, 11AM)
1)
What order of approximation with respect to h does the Composite
(i.e. multiple application) Trapezoidal Rule for integration provide?
2)
If two results us
QUIZ # 4
NAME_
SUBMIT TO [email protected] DROPBOX BY MONDAY, 7/22, 11:00AM
1) A linear least-squares curve fit problem can be solved by the exact
and unique solution of an overdetermined system of equations?
(True/False?, Why?)
2) What is the purpose of the coeff
QUIZ # 3
NAME_
SUBMIT ON MONDAY, 7/8/13, by email before 11:59PM
Given the canonical form Ax=b of a system of linear equations where A is
(n x n), x is (n x 1) and b is (n x 1), please answer the following:
1) What are the requirements for a (n x n) syste
CS412
INTRODUCTION TO NUMERICAL METHODS
HOMEWORK # 5
DUE ON MONDAY 7/29/13, 11:00 AM
Problems:
17.4 Do by hand.
17.11 Do using Matlabs built-in commands. In producing the requested
interpolating polynomials, use the data points that bracket the T = 330 K
CS412
INTRODUCTION TO NUMERICAL METHODS
HOMEWORK # 3
DUE ON THURSDAY, 7/11/12, 11:00 AM
Problems:
1) 10.3 By hand. Carry out check using Matlab.
2) 10.4 By hand.
3) 10.6 Use the naive GE code in the textbook as a model for your
program. Test your code usi
CS 412
Introduction to Numerical Methods
(http:/pages.cs.wisc.edu/~cs412-1/)
Description:
A 3-credit course dealing with basic materials for the
solution of numerical problems using computers. Topics
covered include methods for root finding, interpolation
CS412
INTRODUCTION TO NUMERICAL METHODS
HOMEWORK # 6
DUE ON FRIDAY 8/2/13, 11:59 PM
19.3 Do by hand.
19.6 Do by hand. See Example 19.8
19.14 Plan a suitable solution approach based on textbook discussions in
Chapters 19. You are free to use Matlab built-i
CS412
INTRODUCTION TO NUMERICAL METHODS
HOMEWORK # 4
DUE ON MONDAY 7/22/13, 11:00AM
Problems:
14.5
Do problem by hand by establishing the Normal Equations.
You could use, however, Matlab to do all the computations (i.e.
summations and the solution of the