Differential Equations: From Calculus to Dynamical Systems
eBook - PDF

Differential Equations: From Calculus to Dynamical Systems

Second Edition

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

Differential Equations: From Calculus to Dynamical Systems

Second Edition

About this book

A thoroughly modern textbook for the sophomore-level differential equations course. The examples and exercises emphasize modeling not only in engineering and physics but also in applied mathematics and biology. There is an early introduction to numerical methods and, throughout, a strong emphasis on the qualitative viewpoint of dynamical systems. Bifurcations and analysis of parameter variation is a persistent theme.Presuming previous exposure to only two semesters of calculus, necessary linear algebra is developed as needed. The exposition is very clear and inviting. The book would serve well for use in a flipped-classroom pedagogical approach or for self-study for an advanced undergraduate or beginning graduate student.This second edition of Noonburg's best-selling textbook includes two new chapters on partial differential equations, making the book usable for a two-semester sequence in differential equations. It includes exercises, examples, and extensive student projects taken from the current mathematical and scientific literature.

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34
Chapter
2
First-order
Differential
Equations
In
Exercises
10–12,
you
are
given
a
differential
equation.
The
corresponding
slope
field
has
also
been
drawn.
Sketch
enough
solution
curves
in
the
slope
field
to
be
able
to
describe
the
behavior
of
the
family
of
solutions
in
the
entire
(,
)
-plane.
As
part
of
your
description,
explain
how
the
long-term
behavior
depends
on
the
initial
condition
(0)
.
Be
as
specific
as
possible.
10.
′
=
2(1
−
/2)
x
t
1
2
3
1
2
3
0
–1
–2
–3
–1
–2
–3
11.
′
+
=
x
t
1
2
3
0
–1
–2
–3
1
2
3
–1
–2
–3
12.
′
=
/
–1
–2
–3
1
2
3
0
1
2
3
–1
–2
–3
x
t

Table of contents

  1. Cover
  2. Title page
  3. Copyright
  4. Contents
  5. Preface
  6. Chapter 1. Introduction to Differential Equations
  7. Chapter 2. First-order Differential Equations
  8. Chapter 3. Second-order Differential Equations
  9. Chapter 4. Linear Systems ofFirst-order Differential Equations
  10. Chapter 5. Geometry of Autonomous Systems
  11. Chapter 6. Laplace Transforms
  12. Chapter 7. Introduction to Partial Differential Equations
  13. Chapter 8. Solving Second-order Partial Differential Equations
  14. Appendix
  15. Index
  16. Back Cover

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