Math 400
Assignment #3 - Numerical Integration and Differentiation
Due: April 20, 2010
1.
Find the exact values of the Gauss points 1 < x1 < x2 < x3 < 1 and weights for n = 3.
2.
Estimate each of the following integrals to seven decimal place accuracy (ab
Math 400
Assignment #2 - Interpolation
1.
Due: April 6, 2010
For Lagrange interpolation on the nodes x1 < x2 < < xn 1 < xn of the data
cfw_( x , f ( x ) )
i
i
n
n
i =1
the interpolating polynomial is p ( x ) = f ( xi )L n , i ( x ) , where
i =1
L n,i ( x
Math 400
Numerical Analysis
Spring 2011
Handout
Review Final
The nal exam is on Friday, May 20, 10:45 am - 1:15 pm. It is a closed book, closed notes exam. You must
bring your calculator. On the exam sheet, there will be enough space for your answers, but
Math 400 - Numerical Analysis
Instructor:
David Sklar
[email protected]
Time:
TTH 3:35 4:50
Location:
Humanities 579
Office: SCI 229
Phone: 338-2251
Hours: TTH 11:00 11:30 and
2:15 2:45, with other
times by appointment
Prerequisites:
Math 228, Math 325, and
Exercises : 85page
11.3 Take m=50, n=12. Using MATLABs linspace, define t to be the m-vector
corresponding to linearly spaced grid points from 0 to 1. Using MATLABs vander and
fliplr, define A to be the m n matrix associated with least squares fitting on
A Presentation on Interpolation
Using Piecewise Linear and Cubic Spline Functions for
Math 400 - Spring 2016
David Sklar
[email protected]
Connecting the Dots
Write a formula for a piecewise linear function
that interpolates five given data points
3,2.5
Math 400
Assignment #4
1.
Due: April 30, 2016
Find approximate numerical solutions on the interval 0, 2 for the differential equation
dx
t - 2 x , with initial condition t0 0, x0 1
dt
Use Euler's method, the modified Euler method, and a fourth order Rung
Math 400
Assignment #4
1.
Due: April 30, 2016
Find approximate numerical solutions on the interval 0, 2 for the differential equation
dx
t - 2 x , with initial condition t0 0, x0 1
dt
Use Euler's method, the modified Euler method, and a fourth order Rung
A Short Introduction to Romberg Trapezoidal Integration and
Gaussian Quadrature
David Sklar
San Francisco State University
[email protected]
Bruce Cohen
Lowell High School, SFUSD
[email protected]
http:/www.cgl.ucsf.edu/home/bic
March 2016
Ver. 6.00
Trapezoi
Math 400
Assignment #1 - Systems of Linear Equations
Due March 3, 2016
1. A widely used method for computing the inverse of an n by n matrix is to row reduce an n by
2n augmented matrix to reduced row echelon form. In this computation the initial augmente
Math 400
Assignment #3 - Numerical Integration and Differentiation
1. For the function g x e x
2
2
Due: 6am April 09, 2016
use the centered difference formula with h 101 , 102 ,
, 1020
to create a table of estimates of g 1.4 . Include a column for the rel
Math 400
Assignment #2 - Interpolation
1.
Due: March 18, 2016
For Lagrange interpolation on the nodes x0 x1
xn 1 xn of the data
x , f x
i
i
n
n
i 0
the interpolating polynomial is p x f xi L i x , where
i 0
x x0
xi x0
x xi 1 x xi 1
xi xi 1 xi x
Math 400
Assignment #5 Approximation Theory
1.
Due: May 17, 2016
Find the least squares polynomials of degrees 1, 2, 3, and 4 for the data:
x i 0.0
y i 2.56
0.2
13.18
0.5
30.11
0.7
42.05
1.1
67.53
1.5
1.9
2.3
2.8
3.1
95.14 124.87 156.73 199.50 226.72
In e
Math 400
Assignment #0 (Programming Exercise Set 1)
Due Tuesday 2/9/16 by 3pm
The assignment is to write the needed python code for the three vector functions and nine matrix
functions in the files we obtained from Bruce Cohens website tetrahedra.net. You
Math 400
Assignment #1 - Systems of Linear Equations
1.
Find an approximate numerical solution to the system Ax = b with
10 10
10
3
1 10
103
A=
1 1
103
1
1 1
1017
103
and
103
103
1017
1
b=
2
3
a) using basic Gaussian elimination
b) using Gaussian el
Math 400
Assignment #4
1.
Due: May 11, 2010
Find approximate numerical solutions on the interval [ 0, 2] for the differential equation
dx
= t - 2 x , with initial condition t0 = 0, x0 = 1
dt
Use Euler's method, the modified Euler method, and a fourth orde
Math 400
Assignment #4 (corrected)
1.
Due: May 11, 2010
Find approximate numerical solutions on the interval [ 0, 2] for the differential equation
dx
= t - 2 x , with initial condition t0 = 0, x0 = 1
dt
Use Euler's method, the modified Euler method, and a
Math 400
Assignment #5 Approximation Theory
1.
Due: May 20, 2010
Find the least squares polynomials of degrees 1, 2, 3, and 4 for the data:
x i 0.0
0.2
0.5
0.7
1.1
1.5
1.9
2.3
2.8
3.1
y i 102.56 113.18 130.11 142.05 167.53 195.14 224.87 256.73 299.50 326.
A First Look at R:
Exploring Gaussian Elimination
Bruce Cohen and David Sklar
January 24, 2008 v0.2
1
2
Introduction
The purpose of this handout is to introduce
you to the R-Project [2]. We assume you also
have a handout on Gaussian elimination taken
from
Revisiting Numerical
Integration:
Getting More from Fewer Points
Part II
David Sklar
San Francisco State University
[email protected]
Bruce Cohen
Lowell High School, SFUSD
[email protected]
http:/www.cgl.ucsf.edu/home/bic
March 2010
Ver. 5.00
Plan
Romberg in
A Short Introduction to Romberg
Integration and Gaussian
Quadrature:
Getting More from Fewer Points
David Sklar
San Francisco State University
[email protected]
April 2010
Ver. 1.00
Romberg Integration
The method arises from a technique called Richardson ex
A Presentation on Interpolation
Using Piecewise Linear and Cubic Spline Functions for
Math 400 - Spring 2010
Bruce Cohen
[email protected]
http:/www.cgl.ucsf.edu/home/bic
David Sklar
[email protected]
Connecting the Dots
Write a formula for a piecewise li
A Presentation on Interpolation
Using Piecewise Linear and Cubic Spline Functions for
Math 400 - Spring 2010
Bruce Cohen
[email protected]
http:/www.cgl.ucsf.edu/home/bic
David Sklar
[email protected]
Connecting the Dots
Write a formula for a piecewise li
Math 400 - Numerical Analysis
Instructor:
David Sklar
[email protected]
Time:
TTH 9:35 10:50
Location:
Thornton 325
Prerequisites:
Math 228 and Math 325 (The real prerequisite is a solid working knowledge of
calculus and basic linear algebra.)
Textbook:
The
Chen, Chenghui(Calvin)
Homework V
05/08/2017
1.) This exercise is about solving the following system of two equations via the Newtons method:
x2 y + sin(x y) = 2 and y 2 x = 3.
a) Develop a simple MATLAB code that implements the Newtons method for solving