- #1

- 48

- 9

I am just now taking a math methods course for Physicists and we're using Mary Boas book. I wanted to supplement it for better understanding as saw

**Partial Differential Equations for Scientists and Engineers by Stanley J. Farlow.**

Reading reviews for this book on Amazon made me think, perfect for me. I've done well in Calculus and ODEs. So I pick it up and get to the problems at the end of lesson 1 and lesson 2 and think to myself "How the l;kj would I do these?" I look at the solutions and have no idea how they got to them for some of these.

So is this book really that good? Am I missing something? Should it be able to be used for self-study alone or in conjunction with another text?

In isolation of the info an average student would recall from calculus and ODEs and info in this book prior to other lessons how for example would you solve

**problem 2 in lesson 2:**

Suppose the rod has a constant internal heat source, so the basic equation describing the heat flow within the rod is: U

o<x<1

Suppose we fix the boundaries' temperatures by u(0,t)=0 and u(1,t)=0. What is the steady-state temperature of the rod? In other words, does the temperature u(x,t) converge to a constant temperature U(x) independent of time?

Hint: Set u<-----How do I even draw this?

Suppose the rod has a constant internal heat source, so the basic equation describing the heat flow within the rod is: U

_{t}=a^{2}U_{xx}+1o<x<1

Suppose we fix the boundaries' temperatures by u(0,t)=0 and u(1,t)=0. What is the steady-state temperature of the rod? In other words, does the temperature u(x,t) converge to a constant temperature U(x) independent of time?

Hint: Set u

_{t}=0. It would be useful to graph this temperature. Also start with an initial temperature of zero and draw some temperature profiles.Let me note that Farlow uses U

_{xx}to mean ∇

^{2}u and U

_{t}to be the differential of U with respect to time. At least as far as I can see...