This is an extremely good intro book on heat transfer. I sorely wish my other intro textbooks were as comprehensive, elucidating, detailed and accessible as this book. Good for newcomers to heat transfer or those who just want a quick review of core concepts. Numerical methods are lightly...
Sorry for the typos everywhere earlier (edited now).
L(c_1 u + c_2 v) = c_1 u_x + c_1 u_y + c_1 + c_2 v_x + c_2 v_y + c_2
= c_1 (u_x + u_y + 1) + c_2 (v_x + v_y + 1)
= c_1 L(u) + c_2 L(v)
So is that what you were guiding me to? If I did that correctly, it makes a lot more sense now...
Homework Statement
Verify whether or not the operator
L(u) = u_x + u_y + 1
is linear.
Homework Equations
An operator L is linear if for any functions u, v and any constants c, the property
L(c_1 u + c_2 v) = c_1 L(u) + c_2 L(v)
holds true.
The Attempt at a Solution
I feel...
The core problem is that educators believe, when choosing quantity over quality, all those techniques and methods STICK.
What good is learning 20 different ways to tackle an ODE if you easily forget them right after you take the final exam? That's the point I'm trying to make. A conceptual...
[I'm more concerned with how mathematics is taught in university in this topic]
I'm a junior Mechanical Engineer and have taken Differential & Integral Calculus, Multivariable Calculus, Differential Equations, and Linear Algebra. Just from these classes and talking with a variety of peers in...
I'm only an ME undergraduate right now, but I'm pursuing this path that may lock me in industry (CAD/CAM/machine design/etc.) for a minimum of 3 years after graduation. It's not quite the technical path that I wanted to go into, but the opportunity seems too great to pass up for now.
How...
Homework Statement
Write a C++ program to determine and print the sum of the series (1/3 + 1/6 + 1/9 + ... + 1/(3*n)) for a given value of n. In case you don't see the patter, the series can also be written as 1/(3*1) + 1/(3*2) +1/(3*3)+ ... + 1/(3*n). The value of n should be given...
Homework Statement
Derive via integration the first moment of area Q of a semicircle with radius r.
Homework Equations
Q = \int_{A} y dA
A_{semicircle} = \frac{\pi r^{2} }{2}
The Attempt at a Solution
A = \frac{\pi r^{2} }{2}
A(y) = \frac{\pi y^{2} }{2}
dA = \pi y dy
Q =...
I have, and I end up with the original series.
But if that were already a Taylor series, why would my professor waste a question to ask me to rewrite the series in the same exact way...
Homework Statement
[sorry about the formatting, I had no idea how I would latex the sigma notation]
Let f(x) = [n=1 to infinity] summation of (-1)n n2 / 3n * (x+1)n
Find the Taylor series of f(x) centered at c = -1Homework Equations
Taylor series defined by
[n=0 to infinity] summation of...
I'm a sophomore right now majoring in ME, but I'm wondering if I should do a Co-op to get experience in the actual field. But will this help me as much as pure research when I apply to top grad schools in the US? What about internships?
Basically I'm asking if I should be seeking pre-career...