First-Order Partial Differential Equations
Lecture 3
First-Order Partial Differential Equations
Text book: Advanced Analytic Methods in Continuum Mathematics, by Hung Cheng (LuBan
Press, 25 West St. 5th Fl., Boston, MA 02111, USA).
In this lecture and the
Complex Analysis
Lecture 2
Complex Analysis
A Complex Numbers and Complex Variables
In this chapter we give a short discussion of complex numbers and the theory of a function of a
complex variable.
Before we get to complex numbers, let us first say a few
Second-Order Partial Differential Equations
Lecture 4 Second-Order Partial Differential Equations
In this lecture and in the next, well briefly review second-order PDEs. Well begin with one of the simplest of such PDEs: the Laplace equation.
A The Laplace
Chapter1
The Di fferential Operator
A . C alculus
Let us fir st introduce a shorthand notation for the differential operator:
d
( 1.1)
.
D
dx
W e note that
D em x = mem x .
This means that, when it operates on emx , the dierential operator D is
simply equ
Separation of Variables
Lecture 5
Separation of Variables
Unlike first-order partial differential equations, solvable second-order partial differential
equations are much more limited in number. Many such second-order partial differential equations
are so