Mathematical Analysis tools for engineering
eBook - PDF

Mathematical Analysis tools for engineering

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

Mathematical Analysis tools for engineering

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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Yes, you can access Mathematical Analysis tools for engineering by Franco Tomarelli in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.
2.2
Linear
first
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
fixed
time;
freezing
the
space
variable
provides
a
”movie”
of
the
solution
as
it
is
seen
from
a
fixed
point.
x
u
(
x,
e
t
)
w
e
t
β
exp(
-
γ
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(
-
γ
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

  1. Cover
  2. Title Page
  3. Preface
  4. Contents
  5. 1 - Preliminary Calculus Tools
  6. 2 - Partial Differential Equations
  7. 3 - Analytic Functions of complex variable
  8. 4 - Special Functions
  9. 5 - Functional Analysis
  10. 6 - Fourier Transform in L¹ and L²
  11. 7 - Laplace Transform
  12. 8 - Distributions or Generalized Functions
  13. 9 - Heat Equationand other Diffusion Models
  14. 10 - Wave Equation
  15. Symbols and notation
  16. References
  17. Index
  18. Back Cover