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Introduction to differential equations, including a discussion
of the formation of mathematical models for real phenomena; solution
by special techniques; applications; linear equations; solutions in
series; other topics if time permits.
Differential equations have played a central role in mathematics and
its
applications for the past three hundred years. Their importance in
applications stems from the interpretation of the derivative as a rate
of
change, a familiar example being velocity. Many of the fundamental
laws
of physical science are best formulated as differential equations. In
other areas, too, such as biology and economics, which involve the
study
of growth and change, such equations are of fundamental importance.
In this course we will study some important types of linear
differential
equations and their solutions. Topics will include first-order
(differential) equations; homogeneous second and higher order
equations
with constant coefficients; the particular solution of inhomogeneous
second-order equations; series-form solutions of equations with
variable coefficients; solutions by use of Laplace transforms.
NOTE: Mathematics (APMA, MATH, STAT, etc.) students should register
in section M.
Prerequisite:One of AS/SC/MATH 2010 3.0,
AS/SC/MATH 2015 3.0, or AS/SC/AK/MATH 2310 3.0;
one of AS/SC/MATH 1025 3.0,
AS/SC/MATH 2021 3.0, or AS/SC/AK/MATH 2221 3.0.
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