Embedded Files
Starting to study for final exam!!!!!!!!!
-------- after midterm -------- Ch.3, Sec 3.6 Ch.8, Sec 8.3 (8.6 was discussed but will be excluded from the final) Ch.9, Sec 9.2 Ch.10, Sec 10.2, 10.3, 10.4.2, 10.5 Ch.12, Sec 12.1, 12.2, 12.6 (excluding Sec 12.6.4) Slide sets #10, #11, #12, #13, #14, and #15 -------- Plan ahead: Intro to nonlinear PDE If time allows: Various chapters, PDEs in non-Cartesian geometry
HW5 PDEs
Define powers of i
http://www.regentsprep.org/Regents/math/algtrig/ATO6/powerlesson.htm
http://www.public.asu.edu/~hhuang38/MAE502.html
Fourier Transform
Book with Problmes
Cosine Fourier Transform
1. http://www.public.asu.edu/~hhuang38/MAE502.html
2. http://www.public.asu.edu/~hhuang38/pde_slides_ftsine1_revised.pdf
3.http://www.public.asu.edu/~hhuang38/pde_slides_ftfull1_revised.pdf
4. http://www.math.ucsb.edu/~helena/teaching/math124b/heat.pdf
-------- after midterm -------- Ch.3, Sec 3.6 Ch.10, Sec 10.2, 10.3 (excluding 10.3.3), 10.4.2, 10.5
Wed 3/27 HW4 due, HW5 posted
Wed 4/10 HW5 due, HW6 posted Wed 4/24 HW6 due Mon 4/29 Last lecture before final
Good heat transfer class website:
https://docs.google.com/forms/d/1J0gtmufY3TnWHeZLYoWQ9dZZ7PoT436101OVWpqudhM/viewform
http://www.public.asu.edu/~hhuang38/MAE502.html
HW 2 Solutions
http://www.public.asu.edu/~hhuang38/mae502_2013_hw1_sol.pdf
http://www.public.asu.edu/~hhuang38/mae502_2013_hw2.pdf
http://www.public.asu.edu/~hhuang38/mae502_2013_hw2.pdf
Ch.3 (Fourier series Sec 3.1,3.2,3.3,3.4,3.6) followed by Ch.5 (Sturm-Liouville Problem, Sec. 5.3, 5.5)
Midterm will cover:
Ch.1, whole chapter (excludes the discussion on spherical coordinate, Eqs. (1.5.21) and (1.5.22))
Ch.2, whole chapter except Sec 2.5.2 and 2.5.3 (will finish 2.5.1 on 2/4)
Ch.8, Sec 8.2 (excludes the discussion on time-dependent b.c.) -------- Plan ahead:
Ch.4 (wave equation, Sec 4.2,4.3,4.4) followed by
Ch.3 (Fourier series Sec 3.1,3.2,3.3,3.4,3.6)
Ch.5 (Sturm-Liouville Problem, Sec. 5.3, 5.5)
Problem 3. (3 points) 2-D Laplace equation.
code for laplace equation pde hw 2
x = [0:0.01:1];
y = [0:0.01:1];
ntrunc = 30;
for n = 1:ntrunc
if (mod(n,2) == 0)
b(n) = 0;
else
b(n) = 0;
end
end
for p = 1:101
for q = 1:101
x2d(p,q) = x(p);
y2d(p,q) = y(q);
u2(p,q) = 0;
for n = 1:ntrunc
u2(p,q) = u2(p,q)+b(n)*sin(n*pi*x(p))*sinh(n*pi*(y(q)-1));
end
u1(p,q) = sinh(pi*x(p))*sin(pi*y(q))/sinh(pi) + ...
0.5*sinh(3*pi*x(p))*sin(3*pi*y(q))/sinh(3*pi);
u(p,q) = u1(p,q)+u2(p,q);
end
end
u(61,41)
contourf(x2d,y2d,u,[0:0.1:1.4]);colorbar
xlabel('x');ylabel('y');title('u(x,y) Contour interval = 0.1')
PDE HW 1
PDE HW prob 1
code for prob 1
x = [0:0.01:1];
%With 2 terms for an
u = inline('(-8/(pi*pi)*sin(pi/2))*sin(pi*x)*exp(-pi*pi*t)-(8/(4*pi*pi)*sin(pi))*sin(2*pi*x)*exp(-4*pi*pi*t)-2*x+3','x','t');
for k = 1:101
u1(k) = u(x(k),0);
u2(k) = u(x(k),0.02);
u3(k) = u(x(k),0.06);
u4(k) = u(x(k),0.12);
u5(k) = u(x(k),50);
end
plot(x,u1,'y-.',x,u2,'g:^',x,u3,'ko',x,u4,'r--',x,u5,'b:','LineWidth',2)
xlabel('x')
ylabel('u(x,t)')
title( 'Temperature as a function of x for two terms')
legend('t = 0','t = 0.02','t = 0.06','t = 0.12','t=50')
%%
%For x=0.6 and t=0.2 to find u(x,t)
x=0.6
t=0.2
x = [0:0.01:1];
%With 2 terms for an
u = inline('(-8/(pi*pi)*sin(pi/2))*sin(pi*x)*exp(-pi*pi*t)-(8/(4*pi*pi)*sin(pi))*sin(2*pi*x)*exp(-4*pi*pi*t)-2*x+3','x','t');
for k = 1:101
u1(k) = u(x(k),0.2);
end
plot(x,u1,'r--')
xlabel('x')
ylabel('u(x,t)')
title( 'Temperature as a function of x for two terms')
legend('t = 0.2')
PDE HW 1 prob 2
code for prob 2
x = [0:0.01:1];
% 2 terms
u = inline('(-32/(pi*pi)*sin(pi/4)*sin(pi*x/2))*exp(-pi*pi*1/4*t)+(-(32/9)/(pi*pi)*sin(3*pi/4)*sin(3*pi*x/2))*exp(-pi*pi*9/4*t)+3','x','t');
for k = 1:101
u1(k) = u(x(k),0);
u2(k) = u(x(k),0.05);
u3(k) = u(x(k),0.2);
u4(k) = u(x(k),0.5);
u5(k) = u(x(k),1);
u6(k) = u(x(k),50);
end
plot(x,u1,'y-.',x,u2,'g:^',x,u3,'ko',x,u4,'r--',x,u5,'b:',x,u6,'r+-','LineWidth',2)
xlabel('x')
ylabel('u(x,t)')
title( 'Temperature as a function of x for two terms')
legend('t = 0','t = 0.05','t = 0.2','t = 0.5','t=1','t=50')
PDE HW Prob 3
PDE HW Prob 4
Heat Equation with Non-Zero Temperature Boundaries
Heat Equation with Non-Zero Temperature Boundaries
http://tutorial.math.lamar.edu/Classes/DE/HeatEqnNonZero.aspx
http://en.wikibooks.org/wiki/Calculus/Ordinary_differential_equations
Quiz Time:
Ex. 20 Double loop
sum1 = 0;
for n = 1:2
for m = 1:3
sum1 = sum1+n*m;
end
end
sum1
Output:
16
Remark: this program performs the summation of
Sum1 = 1*1+1*2+1*3 +2*1+2*2+2*3 = 16
http://tutorial.math.lamar.edu/Classes/DE/ReductionofOrder.aspx
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