Math 4B Lecture 1
April 1, 2013
Doug Moore
Announcements.
1. The TAs are Liang Chiang, Amanda Curtis, Cynthia Flores
and Tawny Lim.
2. My oce hours will be Monday, 1pm and Tuesday, Thursday,
1pm.
3. Homework is via WileyPLUS and will usually be due on Fri
Math 4B Lecture 2
April 3, 2013
Doug Moore
Announcements.
1. WileyPLUS Homework 1 has been assigned and is due Monday, April 8 at 6pm. (Read Chapter 1 in the text to prepare
for the homework.) This assignment will NOT count as part
of your grade. Use it t
Math 4B Lecture 3
April 8, 2013
Doug Moore
Our rst goal today is to consider dierential equations of the
form
dy
+ P (t)y = Q(t),
dt
where P (t) and Q(t) are continuously dierentiable functions of
the independent variable x. Dierential equations of this f
Math 4B Lecture 4
April 10, 2013
Doug Moore
Review of rst-order linear dierential equations. To solve
the dierential equation
d
(t2 + 1)y = cos t
dt
we simply integrate both sides to obtain
(1)
But the dierential equation (1) might appear in a slightly di
Math 4B Lecture 5
April 15, 2013
Doug Moore
This contrast between theory and rigor is apparent in the way
mathematicians treat dierentials. In calculus, it is far easier
to be rigorous with quotients dy/dx than with the dierentials
dx and dy themselves. I
Math 4B Lecture 6
April 17, 2013
Doug Moore
Review of method of exact dierentials.
Given the dierential equation
dy
= 0,
M (x, y ) + N (x, y )
dx
we rst rewrite it as
M (x, y )dx + N (x, y )dy = 0,
then try to nd a function (x, y ) such that
d = M (x, y )