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This volume presents a systematic and unified treatment of
Leray-Schauder continuation theorems in nonlinear analysis. In
particular, fixed point theory is established for many classes of
maps, such as contractive, non-expansive, accretive, and compact
maps, to name but a few. This book also presents coincidence and
multiplicity results. Many applications of current interest in the
theory of nonlinear differential equations are presented to
complement the theory. The text is essentially self-contained, so
it may also be used as an introduction to topological methods in
nonlinear analysis. This volume will appeal to graduate students
and researchers in mathematical analysis and its applications.
This volume presents a systematic and unified treatment of
Leray-Schauder continuation theorems in nonlinear analysis. In
particular, fixed point theory is established for many classes of
maps, such as contractive, non-expansive, accretive, and compact
maps, to name but a few. This book also presents coincidence and
multiplicity results. Many applications of current interest in the
theory of nonlinear differential equations are presented to
complement the theory. The text is essentially self-contained, so
it may also be used as an introduction to topological methods in
nonlinear analysis. This volume will appeal to graduate students
and researchers in mathematical analysis and its applications.
This introductory text combines models from physics and biology
with rigorous reasoning in describing the theory of ordinary
differential equations along with applications and computer
simulations with Maple. Offering a concise course in the theory of
ordinary differential equations, it also enables the reader to
enter the field of computer simulations. Thus, it is a valuable
read for students in mathematics as well as in physics and
engineering. It is also addressed to all those interested in
mathematical modeling with ordinary differential equations and
systems. Contents Part I: Theory Chapter 1 First-Order Differential
Equations Chapter 2 Linear Differential Systems Chapter 3
Second-Order Differential Equations Chapter 4 Nonlinear
Differential Equations Chapter 5 Stability of Solutions Chapter 6
Differential Systems with Control Parameters Part II: Exercises
Seminar 1 Classes of First-Order Differential Equations Seminar 2
Mathematical Modeling with Differential Equations Seminar 3 Linear
Differential Systems Seminar 4 Second-Order Differential Equations
Seminar 5 Gronwall's Inequality Seminar 6 Method of Successive
Approximations Seminar 7 Stability of Solutions Part III: Maple
Code Lab 1 Introduction to Maple Lab 2 Differential Equations with
Maple Lab 3 Linear Differential Systems Lab 4 Second-Order
Differential Equations Lab 5 Nonlinear Differential Systems Lab 6
Numerical Computation of Solutions Lab 7 Writing Custom Maple
Programs Lab 8 Differential Systems with Control Parameters
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