February 1
section covered in text
1.2. Solutions and Initial Value Problems
(continued)
objective
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to be able to determine whether given functions are
solutions to differential equations
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to be able to determine whether a solution satisfies
initial conditions
key ideas and/or vocabulary
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nth order differential equation :=
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explicit solution (defined on some interval)
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implicit solution
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Implicit Function Theorem
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initial value problem
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existence and uniqueness of a solution (first order,
initial value)
solved problems-using key ideas
determining if a function is an explicit solution
to a differential equation, #1
testing whether a function is an explicit
solution to a differential equation, #5,7
determining if a function is an implicit
solution to a differential equation, #9,13
using Theorem 1 to determine if there is a unique
solution, #25,26
some problems have no solutions, #19
initial value problem with more than one solution,
#29
one parameter family of solutions, #16
finding solutions of the form f(x)
= xm, #21
announcements
Homework: #2,4,6,10,14,20,24 (due 2/5)
download software by pointing to http://hepg.awl.com/AWHome/BookSite.qry?function=form
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QUESTION OF THE DAY
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| Use logarithmic differentiation to find y' if
y = x(x + 1)2(x2 + 1)3. |
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SOLUTION
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SOLUTION.
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