Lectures on Numerical Analysis
Dennis Deturck and Herbert S. Wilf Department of Mathematics University of Pennsylvania Philadelphia, PA 19104-6395
Copyright 2002, Dennis Deturck and Herbert Wilf April 30, 2002
2
Contents
1 Dierential and Dierence Equation
ChBE 2120 Homework 2 Due: Friday, September 3 at 8:05 AM In this homework assignment you will modify the Gauss elimination code we wrote in class to detect zero pivots and then use your code to solve a chemical engineering mass balance problem. Part 1: Mo
ChBE 2120 Homework 3 Due: Friday, September 10 at 8:05 AM Part 1: Modify your Gauss elimination function from Homework 2 to include partial pivoting. Rename this function mygehw3_yourGtAccountId in the first line of the function and in the file name. Inst
Lessons we have taken away from our time doing HYSYS together: To return to the basis manager (the initial windows that HYSYS starts on before you go to the simulation environment), either: a) Click the picture of a flask in the toolbar, or b) Go to Simul
Chapter 08.05 On Solving Higher Order Equations for Ordinary Differential Equations
After reading this chapter, you should be able to: 1. solve higher order and coupled differential equations, We have learned Eulers and Runge-Kutta methods to solve first
Math 233
Hessians and Unconstrained Optimization
Fall 2001
The Big Picture: Second derivatives, whether in single or multi variable calculus, measurethe rate of changein slopes (i.e. the curvature of the function f ). What makesproblemsharder in multivari
Numerical Methods Natural Sciences Tripos 1B Lent Term 1999
Problem Sheet 1 1. ROOT FINDING
1.1 Roots of a cubic Consider the solution to f(x) = 0.5 where f(x) = x3. Choosing initial guesses of xa = 0 and xb = 1, (a) (b) (c) (d) Write down an expression t
Chapter 04.06 Gaussian Elimination
After reading this chapter, you should be able to: 1. solve a set of simultaneous linear equations using Nave Gauss elimination, 2. learn the pitfalls of the Nave Gauss elimination method, 3. understand the effect of rou
OUTLINE: Announcements: No office hours today, will announce replacements when possible CIOS: 61.4%. Target = 70% Keep an eye out for an email to try to set up a review session. This weekend? Early next week? Design of Experiments: Overview/explanation 2-
Chapter 04.06 Gaussian Elimination More Examples Chemical Engineering
Example 1 A liquid-liquid extraction process conducted in the Electrochemical Materials Laboratory involved the extraction of nickel from the aqueous phase into an organic phase. A typi
CHBE 2120 Sample Final Exam
This exam was given as the final exam in this course in a past semester.
We will discuss this exam (and any other questions) in the final class of the semester (Friday
December 9)
Please take a few minutes to complete the onlin
2b) the inverse Fast Fourier transforms got the plot to be the box function again. Taking off the
higher spatial frequency makes the box function act like a sine wave. The more I took off, the
bigger the amplitude of the sign wave until it becomes a strai
CHBE 2120 Optional Homework/Sample Exam
All of the problems below have been used on previous exams in this course. We will discuss
these problems in class on Friday 11/11. The maximize the benefit from this discussion, you
should complete the problems bef
CHBE 2120 Sample Exam 1, Fall 2011
This exam was given in 2120 in a previous semester. The class had 80 minutes to complete the
exam.
You will be asked to sign this statement when taking exams in this course:
By signing below, I am agreeing to abide by th
ChBE 2120, Fall 2009, Quiz 4
NAME:_
On this sheet, give only the final answers for each question in the box provided no partial credit.
1. What is the term we used for a uniform amount of payment made at the end of every period? (Hint:
we represented the
ChBE 2120, Fall 2009, Quiz 1
NAME:_
On this sheet, give only the final answers for each question in the box provided no partial credit.
1. Consider the following system of equations:
3
8
2
2
5
8
27
11
a. Can this system be solved using Gauss elimination?
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ChBE 2120, Fall 2009, Quiz 2
NAME:_
On this sheet, give only the final answers for each question in the box provided no partial credit.
1. Write the equation for the Newton-Raphson method of root finding in terms of xi, xi+1, f(xi), f(xi+1),
f(xi), and f(
Name: _
CHE 2120 Numerical Methods in Chemical Engineering
Professor C.L. Henderson
Test #1 (2 hours)
1. (20 pts)
Please answer the questions below by selecting either (a) one of the answers provided.
i.
The following orders can be included in a Taylor Se
ChBE 2120-Spring 2007
Test #2
Name: _
Section 1: Please answer the following multiple choice questions by selecting one
of the answers provided. Each problem is worth 5pts.
1. The presence of a double root in an equation means that which of the
following
CHE 2120 Fall 2013
Homework #1, Due Monday, August 26th by 5 p.m.
Complete the following assignments:
1. Using Figure 3.11 as a guide, write a function in MATLAB that calculates the smallest number that
MATLAB can add to 1,2,4,8,1024, and 10. Compare the
function [ f ] = ColebrookDirectSubstitutionSolution( initialfGuess, density,
velocity, diameter, viscosity, roughness, errorTolerance )
%input: initial guess for f
%output: calculated f, obtained via the Direct Substitution root finding
%method described
function [ detM ] = CalculateDeterminant( M )
%in: M is a square matrix
%out: The determinance of M.
dimM = size(M);
if (dimM(1) = 1)
detM = M(1, 1);
else
detM = 0;
for i = 1:dimM(2)
detM = detM + (-1)^(i+1) * M(1, i) *
CalculateDeterminant(MatrixMinor(M,