Assignment 1 MATH 2270 SOLUTION Please write out complete solutions for each of the following 6 problems (one more will still be added). You may, of course, consult with your classmates, the textbook or other resources, but please write up your own soluti
INTEGRATION BY PARTS (TABLE METHOD)
Suppose you want to evaluate
Using the
x
2
cos 3 x dx using integration by parts.
u dv notation, we get
u x2
So,
dv cos 3 x dx
1
v sin 3 x
du 2 x dx
3
1
2
21
x cos 3x dx x 3 sin 3x 2 x 3 sin 3x dx
or
2
1
x 2 sin 3 x x
Math 2A Tentative Homework
At this level of math, you should consider it your responsibility to do as many of the textbook problems as possible.
The problems listed below are the minimum you should do to develop the necessary understanding to grasp future
2.3: Modeling with Dierential Equations
Some General Comments:
A mathematical model is an equation or set of equations that mimic the behavior of some phenomenon
under certain assumptions/approximations. Phenomena that contain rates/change can often be mo
2.5: Autonomous Dierential Equations and Equilibrium Analysis
dy
= f (y).
An autonomous rst order ordinary dierential equation is any equation of the form:
dt
Note: In my home dictionary, the word autonomous is dened as existing or acting separately from
Math 2A
Review for Exam 2: Chapters 3 & 4
Winter 2004
Chapter 3: 3.1 3.3
Growth and Decay Equations
Newtons Law of Cooling
Mixtures
Logistic
Simple System of Equations (Lotka-Volterra Predator-Prey Model)
Chapter 4: 4.1 4.4, 4.6 4.7
Given a general
2.7: Eulers Method
Given dy = f (t, y) with y(t0 ) = y0 . The methods for nding explicit (or implicit) solutions are limited.
dt
We can solve only a small collection of special types of dierential equations. In many applied problems numerical methods are
Chapter 2. First-Order Dierential Equations
Section 2.3 Linear Equations
A linear rst-order equation is an equation that can be expressed in the form
dy
+ a0 (x)y = b(x),
(1)
dx
where a0 (x), a1 (x), b(x) depend only on x.
We will assume that a0 (x), a1 (