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### Homework6

Course: AERO 320, Fall 2008
School: Texas A&M
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AERO 320 Spring 2002 Homework #6 Due: Thursday, February 7 Name _______________________ Problems are from Chapter 1 of &lt;a href=&quot;/keyword/applied-numerical-analysis/&quot; &gt;applied numerical analysis&lt;/a&gt; 1. Use Newton iteration to solve for the smallest positive root for each equation (accurate to 0.5%): a) e x = 2 sin(2 x) b) x 4 2 x 1 = 0 2. Use Newton iteration to find...

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AERO 320 Spring 2002 Homework #6 Due: Thursday, February 7 Name _______________________ Problems are from Chapter 1 of <a href="/keyword/applied-numerical-analysis/" >applied numerical analysis</a> 1. Use Newton iteration to solve for the smallest positive root for each equation (accurate to 0.5%): a) e x = 2 sin(2 x) b) x 4 2 x 1 = 0 2. Use Newton iteration to find the cube root of 1,217 (accurate to 4 di...

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Texas A&M - AERO - 320
AERO 320 Spring 2002 Homework #7 Due: Monday, February 11 Some problems are from Chapter 2 of Applied Numerical Analysis Assume we have the following matrices defined for problems 1, 2 and 3: 2 -3 4 2 -1 4 4 1 -2 -5 1 0 [ B ] = 1 3 [C ] = -
Texas A&M - AERO - 320
AERO 320 Spring 2002 Homework #8 Due: Thursday, February 14 Problems are from Chapter 2 of Applied Numerical Analysis 1. Solve the following system of linear algebraic equations by systematic Gaussian elimination as done in class). 2 4 1 3 4 1 2
Texas A&M - AERO - 320
AERO 320 Spring 2002 Homework #9 Due: Wednesday, February 20 Problems are from Chapter 2 of Applied Numerical Analysis1. Problem 18. Use Gauss elimination with systematic reduction factors as done in class. Note that you will be using an augmented
Texas A&M - AERO - 320
AERO 320 Spring 2002 Homework #10 Due: Wednesday, March 6 Problem is from Chapter 2 of Applied Numerical Analysis Problem 60, p. 214. This problem involves solving a set of 3 nonlinear equations for the roots (x,y,z). The equations are nonlinear and
Texas A&M - AERO - 320
AERO 320 Spring 2002 Homework #12 Due: Tuesday, March 19 1. Consider the following data set: x y 0 1.20 1 2.51 1.5 3.14 2.1 3.89 2.9 4.91 3.5 5.64a) Use the Least Squares method to determine the best straight-line curve fit and the best quadratic p
Texas A&M - AERO - 320
AERO 320 Spring 2002 Homework #13Name _Due: Thursday, March 21 1. a) Problem 3-37 (page 303). After getting the natural cubic splines, plot the original function f(x) and your cubic spline representation (ignore the problem part which says to com
Texas A&M - AERO - 320
AERO 320 Spring 2002 Homework #14 Due: Wednesday, March 27 Problems are from Chapter 5 of Applied Numerical Analysis Consider the function f ( x) = x 2e -2 x . Generate values of f(x) at x0 = 0 to x6 = 1.2 in equal increments: x x0 = 0 x1 = 0.2 x2 =
Texas A&M - AERO - 320
AERO 320 Spring 2002 Homework #15 Due: Tuesday, April 2 Problems are from Chapter 5 of Applied Numerical Analysis Consider the function f ( x) = x 2e 2 x . Generate values of f(x) at x0 = 0 to x6 = 1.2 in equal increments: x x0 = 0 x1 = 0.2 x2 = 0.4
Texas A&M - AERO - 320
AERO 320 Spring 2002 Homework #17 Due: Tuesday, April 9 dy = sin( x) + 5 y with y(0)=0 (same as HW 16). dx Obtain y(1) using a step size h=0.5 and: a) 2nd order Runge-Kutta (same as Euler predictor-corrector method but use RungeKutta notation), and b
Texas A&M - AERO - 320
AERO 320 Spring 2002 Homework #18 Due: Thursday, April 18 a) Solve the following boundary value problem for y using finite differences to set up a system of linear algebraic equations (use h=0.2): xy '+ xy '- y = 5, y (0) = 0, y (1) = 1b) Use Maple
Texas A&M - AERO - 320
AERO 320 Spring 2002 Homework #19 Due: Monday, April 22 Same as Homework #18 except boundary condition on right has been changed to a derivative boundary condition. a) Solve the following boundary value problem for y using finite differences to set u
Texas A&M - AERO - 320
AERO 320 Spring 2002 Homework #20 Due: Thursday, April 25 10 -2 0 - 1. Given ([ M ] - [ K ]){u} = {0} where [M] and [K] are given by [ K ] = 2 6 -4 -4 8 0 3 0 0 0 and [ M ] = 2 0 . 0 4 0 a) Determine all the eigenvalues for this eige
Texas A&M - AERO - 320
AERO 320 Spring 2002 Laboratory #1 Due: Tuesday, January 22 Compile and execute the attached Fortran program (exactly as it is written below). Use several values of N to test and validate the program (from 1 to 25). Try some negative values of N (wha
Texas A&M - AERO - 320
AERO 320 Spring 2002 Laboratory #2 Due: Tuesday, January 29 Suppose we are given a set of positive real numbers (grades for a course) in the range 0 to 100 in a data file (Windows .txt file). Write a Fortran program to determine the minimum value, th
Texas A&M - AERO - 320
AERO 320 Spring 2002 Laboratory #6 - Gauss Elimination, Matrix Operations and Subroutines Due: Wednesday, March 20 Write a Fortran main program with subprograms that performs various input, matrix operations, and output as described below. Use your m
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Cours MGP71112 mergence et articulation de la gestion de projet dans l'volution de la pense managrialeGilles Corriveau Matrise en Gestion de Projet UQTRAutomne 1998MGP7111 par Gilles Corriveau, UQTR, ao t 1998.Sommaire de la priodesL
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CS 530: Theory of ComputationFall 2008Lecture 1 - Auguest 21Lecturer: Xiang-Yang Li Scribe: Te-han Chen1.1Basic Mathematical NotionsSet: a group of elements. ex. {a, b, c} Subset: every element of subset A is a member of the set B. ex. A
Illinois Tech - CS - 530
CS 530: Theory of ComputationFall 2008Lecture 2 - Auguest 26Lecturer: Xiang-Yang Li Scribe: Te-han Chen2.1Proof Technique continue.Proof By Induction ex.n 2 i=1 i=n(n + 1)(2n + 1) 6(1) base case: when n=1, when n=2, 1x2x3 6 2x3x5 6
Illinois Tech - CS - 530
Lecture Notes Class 3viggnesh kandasamy cwid : 10458478 September 16, 2008Topics covered in this class: Finite Automata Deterministic Finite automata Regular expressions Deterministic Finite automata Non-Deterministic Finite Automata Probabi
Illinois Tech - CS - 530
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Previously we tried to write a grammar for {an bn cn | n 1} and we conjectured that it could not be done. How can we prove this rigorously that no CFG can generate this language? Recall that to prove a language is not regular, we need to show that fo
Illinois Tech - CS - 530
At this point in the course we are studying the subject of context-free grammars (CFG's) and the important problem of, when given a grammar G, how to characterize the language accepted by G. Up to this point we have discussed the relationship between
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Sep 11 For regular language L and L , we know that L L is still regular, the same that L is regular. Things are dierent if they are CFL. Start from the example {an bn cn |n 1}, how can we prove it is not CFL? We just can not nd a Grammar for this l
Illinois Tech - CS - 530
Sep 16 PDA:push down Automata with a stack PDA M=(Q, , , , q0 , z0 , F ) Q: a set of states :input alphabet :stack alphabet :transition function q 0 :initial state Z0 :the start symbol in statck F: the set of nal states { PDA Here means that elemen
Illinois Tech - CS - 530
CS 530 - Lecture 10 - September 23September 30, 2008Lecturer: Xiang-Yang Li1Review of Last LessonWhat is the main dierence between PDA and DFA/NFA?PDA has a stack. The size of the stack is innite. Transition functions of the PDA are non-d
Illinois Tech - CS - 530
1.5emL ECTURE -N OTES DATE : S EP 18, 2008 AUTHOR : B HUPENDRA M ISHRAContext Free Grammar: Context Free Grammar is a way of describing language by recursive rules called productions. A CFG consists of a set of variables, a set of terminal symbols
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1.5emL ECTURE -N OTES DATE : S EP 23, 2008 AUTHOR : B HUPENDRA M ISHRAPoints to Remember: Context Free Languages and Push Down Automaton are equivalent. PDAs are non-deterministic. Deterministic Finite Automaton, Non-deterministic Finite Automat
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Lecture Notes - Lecture Dated 10/02/08 Lecture Number 13Vignesh Pandurengan CWID : 10428060 October 28, 2008Turing MachineWhat is turing machine? So far most powerful computing model.Its just as powerful as a computer.Turing machine is indeed as
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Lecture Notes - Lecture Dated 10/07/08 Lecture Number 14Vignesh Pandurengan CWID : 10428060 October 29, 2008Turing MachineIts a acceptor that is it basically accepts the language Its a function computator Its a generator ( enumerator ) , the stri
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Lecture 2 NotesZhang Jing September 3, 2008Contents 1 Preview1. Basic mathematical objects. 2. Proof Techniques: (1)controdiction; (2)construction.22.1Proof Techniques Cont.Example 1: Proof the formulan i=1i2 =n(n + 1)(2n + 1) 6(1)
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