Mathematical Analysis tools for engineering
eBook - PDF

Mathematical Analysis tools for engineering

Franco Tomarelli

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Mathematical Analysis tools for engineering

Franco Tomarelli

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Table of contents
Citations

About This Book

This book is an introduction to the study of ordinary differential equations and partial differential equations, ranging from elementary techniques to advanced tools. The presentation focusses on initial value problems, boundary value problems, equations with delayed argument and analysis of periodic solutions: main goal is the analysis of diffusion equation, wave equation Laplace equation and signals. The study of relevant examples of differential models highlights the notion of well-posed problem. An expanded tutorial chapter collects the topics from basic undergraduate calculus that are used in subsequent chapters. A wide exposition concerning classical methods for solving problems related to differential equations is available: mainly separation of variables and Fourier series, with basic worked exercises. A whole chapter deals with the analytic functions of complex variable. An introduction to function spaces, distributions and basic notions of functional analysis is present. Several chapters are devoted to Fourier and Laplace transforms methods to solve boundary value problems and initial value problems for differential equations. Tools for the analysis appear gradually: first in function spaces, then in the more general framework of distributions, where a powerful arsenal of techniques allows dealing with impulsive signals and singularities in both data and solutions of differential problems.

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Information

Publisher
SocietĂ  Editrice Esculapio
Year
2019
ISBN
9788834187500
Topic
Mathematik
Subtopic
Mathematische Analyse
2.2
Linear
rst
order
PDES
91
discontinuity
is
transported
along
the
characteristic
x
=
wt
propagating
on
the
domain
of
the
solution.
The
solution
u
is
a
function
of
two
real
variables,
therefore
its
graphs
is
a
surface.
To
visualize
such
a
graph,
one
can
”freeze”
one
variable
and
look
only
at
the
dependence
on
the
other
one:
freezing
the
time
variable
provides
a
”snapshot”
of
the
solution
at
xed
time;
freezing
the
space
variable
provides
a
”movie”
of
the
solution
as
it
is
seen
from
a
xed
point.
x
u
(
x,
e
t
)
w
e
t
β
exp(
-
Îł
e
t
)
β
Fig.
2.9
A
snapshot
at
time
e
t
>
0
of
the
solution
u
(
x,
e
t
)
of
the
problem
(2.19):
transport
equation
with
damping
and
localized
source.
x
u
(
e
x,
t
)
e
x/w
β
exp(
-
Îł
w
e
t
)
Fig.
2.10
A
movie
at
location
e
x
>
0
of
the
solution
u
(
e
x,
t
)
of
the
problem
(2.19):
trans-
port
equation
with
damping
and
localized
source.

Table of contents

Citation styles for Mathematical Analysis tools for engineering

APA 6 Citation

Tomarelli, F. (2019). Mathematical Analysis tools for engineering ([edition unavailable]). SocietĂ  Editrice Esculapio. Retrieved from https://www.perlego.com/book/1385956/mathematical-analysis-tools-for-engineering-pdf (Original work published 2019)

Chicago Citation

Tomarelli, Franco. (2019) 2019. Mathematical Analysis Tools for Engineering. [Edition unavailable]. SocietĂ  Editrice Esculapio. https://www.perlego.com/book/1385956/mathematical-analysis-tools-for-engineering-pdf.

Harvard Citation

Tomarelli, F. (2019) Mathematical Analysis tools for engineering. [edition unavailable]. SocietĂ  Editrice Esculapio. Available at: https://www.perlego.com/book/1385956/mathematical-analysis-tools-for-engineering-pdf (Accessed: 14 October 2022).

MLA 7 Citation

Tomarelli, Franco. Mathematical Analysis Tools for Engineering. [edition unavailable]. SocietĂ  Editrice Esculapio, 2019. Web. 14 Oct. 2022.