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Course: REDER 625, Fall 2009School: Wisc Stevens Point
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Wisc Stevens Point - REDER - 625
Galaxy a giant flat structure that contain hundreds of billions of starsSupergiant/ Giant Stars very large starsUniverse all of space and everything in itApparent Magnitude a star's brightness as seen from EarthLight Year the distance th
Wisc Stevens Point - REDER - 625
Wisc Stevens Point - REDER - 625
Becca Ederer Reading Lesson - Holes Readers TheaterObjective: Students will participate in a class discussion about what they have read so far in their reading book, Holes. They will discuss their attitudes and/or feelings about different character
Neumont - MAT - 6470
Retour a l'exemple de motivation 1, cette fois-ci avec Taylor2.=1. Taylor 2 specialise-type taylor2_ex1.mfunction [t,y]=taylor2_ex1(intervalledetemps,y0,n);t0=intervalledetemps(1);tf=intervalledetemps(2);h=(tf-t0)/n;t=t0:h:tf;y=zeros(n+1,1
Neumont - MAT - 6470
Conditions pour ordre 2, methode Runge-KuttaIn[1]:= y'[t_]:=f[t,y[t];In[2]:= y'[t_]:=D[y'[t],t];In[3]:= y'[t_]:=D[y'[t],t];In[6]:= k1=h*f[t,y[t];In[7]:= k2=h*f[t+alpha1 h, y[t]+beta1 k1];In[8]:= yp[h_]:=y[t]+c1*k1+c2*k2;In[9]:= erk2[h_]:=(y
Neumont - MAT - 6470
Verification de l'ordre methode classique RK4In[1]:= y'[t_]:=f[t,y[t];In[2]:= y'[t_]:=D[y'[t],t];In[3]:= y'[t_]:=D[y'[t],t];In[4]:= y'[t_]:=D[y'[t],t];In[5]:= y'[t_]:=D[y'[t],t];In[6]:= k1=h f[t,y[t];In[7]:= k2=h f[t+h/2,y[t]+k1/2];In[8]:=
Neumont - MAT - 6470
Exemple 1 - Verification de l'ordre de convergence de RK2 et RK4 =Generer les donnees (Euler, RK2, RK4)-t0=0;tf=20;y0=0.5;yref=solex(tf);n=2.^(1:24);for i=1:24;ni=n(i);[ti,yi]=euler(@f1,[t0 tf],y0,ni);yf(i)=yi(ni+1);err_eul(i)=abs(yf(i)-yr
Neumont - MAT - 6470
Exemple 2 - convergence vers un cycle limite, avec RK=Parametres physiques-format compact; format short e;alpha=0.01;beta=0.02;eq2=[1/beta;1/alpha];Solution de reference--options=odeset('RelTol',1.e-9,'AbsTol',1.e-9);[tref,yref]=ode45(@lotk
Neumont - MAT - 6470
Neumont - MAT - 6470
Neumont - MAT - 6470
Neumont - MAT - 6470
Neumont - MAT - 6470
Neumont - MAT - 6470
Neumont - MAT - 6470
Neumont - MAT - 6470
Modele de Lotka-Volterra. Petite perturbation Eq2. Euler avant.-format compact; format short e;Calcul du point d'equilibre 2=eq2=[1/beta;1/alpha]Calcul de la solution de reference avec solution initiale= equilibre + 1%. Tolerance tres serree
Neumont - MAT - 6470
type ode23.mfunction varargout = ode23(ode,tspan,y0,options,varargin)%ODE23 Solve non-stiff differential equations, low order method.% [TOUT,YOUT] = ODE23(ODEFUN,TSPAN,Y0) with TSPAN = [T0 TFINAL] integrates % the system of differential equ
Neumont - MAT - 6470
Ordre de convergence - Euler avant - exemple 1=1. Generer les donnees-> n=2.^(1:24);> for i=1:24;> ni=n(i);> tic;[ti,yi]=euler(@f1,[t0 tf],y0,ni);time=toc;> yf(i)=yi(ni+1);err(i)=abs(yf(i)-yref)/yref);> disp([i,ni,time,yf(i),err(i)]);> end;
Neumont - MAT - 6470
Modele de Lotka-Volterra (suite). Petite perturbation Eq2. Methode Taylor2-1. Taylor2 specialise=type taylor2_lotka.mfunction [t,y]=taylor2_lotka(intervalledetemps,y0,n);alpha=0.01;beta=0.02;t0=intervalledetemps(1);tf=intervalledetemps(2);h
Neumont - MAT - 6470
Voici une session sur Mathematica pour generer les methodes de Taylor d'ordre de plus en plus eleve=Mathematica 5.2 for LinuxCopyright 1988-2005 Wolfram Research, Inc. - Motif graphics initialized -Expansion en series de base=In[1]:= s1=Seri
Brandeis - CS - 170
eComputer Science 170 (Summer Term, 2005)Introduction to the Theory of Computation Context-free Parsing and Dynamic ProgrammingSuppose you are given a fixed context-free grammar G and an arbitrary string w = w1 w2 wn , where wi . How hard is
Brandeis - CS - 170
eComputer Science 170 (Summer Term, 2005)Problem Set 2Introduction to the Theory of ComputationDue Wednesday, June 8 Exercise 1. Here's a question in three parts: a. Prove that {0m 1n 0m+n | m, n 0} is not regular. b. Prove that {0f (n) | n
Brandeis - CS - 170
eComputer Science 170 (Summer Term, 2005)Problem Set 4Introduction to the Theory of ComputationDue Wednesday, June 29 (at the final exam) Exercise 1. A 2-counter machine (2CM) has a finite state control, and two stacks on which it can push an
Brandeis - CS - 170
eComputer Science 170 (Summer Term, 2005)Introduction to the Theory of Computation P, NP, and Completeness: Simulating Turing Machines by Circuits and FormulasSuppose we are given a Turing Machine M that runs in nk steps on an input x {0, 1}n .
Penn State - MATH - 141
Math 141 Integration PracticeFor each of the following integrals, decide what method to use. (You could use integration by parts, substitution, a trig identity, or another algebraic method). After you've made your educated guesses, go back and try t
Penn State - MATH - 141
SAMPLE PROBLEMS Determine whether each of the following series converges absolutely, converges conditionally, or diverges. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.(-1)n n(-1)n n(-1)n n2 (-1)2n+1 n (-1)2n+1 n+3n-4 (-1)n+1 n+3n-4 (-1)n n
Penn State - MATH - 141
The series in the following problems converge absolutely: 3,5,6,9,11,13,14 The series in the following problems converge conditionally: 1,7,8,10 The series in the other problems diverge.1
Penn State - MATH - 141
Math 141 Exam 1 Spring 2004 Answers1.a, 2.c, 3.d, 4.c, 5.b, 6.c, 7.d, 8.a, 9.b, 10.a 11.(a) 0, (b) x ln , (c) 2xex 12.9 x x - sin-1 2 3 22+3, (d) - , (e) 225 29 - x2 + C13. ln |x| + ln(x2 + 1) - 3 tan-1 x + C 14. x ln(1 + x2 ) - 2x + 2 ta
Penn State - MATH - 141
Math 141 Exam 1 Fall 2003 Answers1.a, 2.d, 3.e, 4.a, 5.a, 6.a, 7.b, 8.d, 9.d, cos x 10. xcos x - (sin x)(ln x)x x2 2x 2 11. - cos(3x) + sin(3x) + cos(3x) + C 3 9 27 1 12. 1 - - 12 3 x 13. - sin-1 x + C 1 - x2
Penn State - MATH - 141
Math 141 Exam 1 Spring 2002 Answers1.b, 2.a, 3.d, 4.b, 5.a, 6.b, 7.d, 8.a, 9.a, 10.c 11.(a) F, (b) F, (c) T, (d) T, (e) F2x tan-1 x ln(1 + x2 ) + 1 + x2 1 + x2 13. ln |x + 1| - ln |x + 2| + C12. (1 + x2 )tan-1x14. 1 ex (cos x + sin x) + C 2
Penn State - MATH - 141
MATH 141 EXAMINATION I September 24, 2001NAME STUDENT NUMBER INSTRUCTOR SECTION NUMBERThere are four short-answer questions, six multiple-choice problems, and four problems where you should show all your work. Partial credit may be given for work