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Homogenization is a fairly new, yet deep field of mathematics which
is used as a powerful tool for analysis of applied problems which
involve multiple scales. Generally, homogenization is utilized as a
modeling procedure to describe processes in complex structures.
Applications of Homogenization Theory to the Study of Mineralized
Tissue functions as an introduction to the theory of
homogenization. At the same time, the book explains how to apply
the theory to various application problems in biology, physics and
engineering. The authors are experts in the field and collaborated
to create this book which is a useful research monograph for
applied mathematicians, engineers and geophysicists. As for
students and instructors, this book is a well-rounded and
comprehensive text on the topic of homogenization for graduate
level courses or special mathematics classes. Features: Covers
applications in both geophysics and biology. Includes recent
results not found in classical books on the topic Focuses on
evolutionary kinds of problems; there is little overlap with books
dealing with variational methods and T-convergence Includes new
results where the G-limits have different structures from the
initial operators
Multivariable Calculus with Mathematica is a textbook addressing
the calculus of several variables. Instead of just using
Mathematica to directly solve problems, the students are encouraged
to learn the syntax and to write their own code to solve problems.
This not only encourages scientific computing skills but at the
same time stresses the complete understanding of the mathematics.
Questions are provided at the end of the chapters to test the
student's theoretical understanding of the mathematics, and there
are also computer algebra questions which test the student's
ability to apply their knowledge in non-trivial ways. Features
Ensures that students are not just using the package to directly
solve problems, but learning the syntax to write their own code to
solve problems Suitable as a main textbook for a Calculus III
course, and as a supplementary text for topics scientific
computing, engineering, and mathematical physics Written in a style
that engages the students' interest and encourages the
understanding of the mathematical ideas
This book illustrates how MAPLE can be used to supplement a
standard, elementary text in ordinary and partial differential
equation. MAPLE is used with several purposes in mind. The authors
are firm believers in the teaching of mathematics as an
experimental science where the student does numerous calculations
and then synthesizes these experiments into a general theory.
Projects based on the concept of writing generic programs test a
student's understanding of the theoretical material of the course.
A student who can solve a general problem certainly can solve a
specialized problem. The authors show MAPLE has a built-in program
for doing these problems. While it is important for the student to
learn MAPLES in built programs, using these alone removes the
student from the conceptual nature of differential equations. The
goal of the book is to teach the students enough about the computer
algebra system MAPLE so that it can be used in an investigative
way. The investigative materials which are present in the book are
done in desk calculator mode DCM, that is the calculations are in
the order command line followed by output line. Frequently, this
approach eventually leads to a program or procedure in MAPLE
designated by proc and completed by end proc. This book was
developed through ten years of instruction in the differential
equations course. Table of Contents 1. Introduction to the Maple
DEtools 2. First-order Differential Equations 3. Numerical Methods
for First Order Equations 4. The Theory of Second Order
Differential Equations with Con- 5. Applications of Second Order
Linear Equations 6. Two-Point Boundary Value Problems, Catalytic
Reactors and 7. Eigenvalue Problems 8. Power Series Methods for
Solving Differential Equations 9. Nonlinear Autonomous Systems 10.
Integral Transforms Biographies Robert P. Gilbert holds a Ph.D. in
mathematics from Carnegie Mellon University. He and Jerry Hile
originated the method of generalized hyperanalytic function theory.
Dr. Gilbert was professor at Indiana University, Bloomington and
later became the Unidel Foundation Chair of Mathematics at the
University of Delaware. He has published over 300 articles in
professional journals and conference proceedings. He is the
Founding Editor of two mathematics journals Complex Variables and
Applicable Analysis. He is a three-time Awardee of the
Humboldt-Preis, and. received a British Research Council award to
do research at Oxford University. He is also the recipient of a
Doctor Honoris Causa from the I. Vekua Institute of Applied
Mathematics at Tbilisi State University. George C. Hsiao holds a
doctorate degree in Mathematics from Carnegie Mellon University.
Dr. Hsiao is the Carl J. Rees Professor of Mathematics Emeritus at
the University of Delaware from which he retired after 43 years on
the faculty of the Department of Mathematical Sciences. Dr. Hsiao
was also the recipient of the Francis Alison Faculty Award, the
University of Delaware's most prestigious faculty honor, which was
bestowed on him in recognition of his scholarship, professional
achievement and dedication. His primary research interests are
integral equations and partial differential equations with their
applications in mathematical physics and continuum mechanics. He is
the author or co-author of more than 200 publications in books and
journals. Dr. Hsiao is world-renowned for his expertise in Boundary
Element Method and has given invited lectures all over the world.
Robert J. Ronkese holds a PhD in applied mathematics from the
University of Delaware. He is a professor of mathematics at the US
Merchant Marine Academy on Long Island. As an undergraduate, he was
an exchange student at the Swiss Federal Institute of Technology
(ETH) in Zurich. He has held visiting positions at the US Military
Academy at West Point and at the University of Central Florida in
Orlando.
This book illustrates how MAPLE can be used to supplement a
standard, elementary text in ordinary and partial differential
equation. MAPLE is used with several purposes in mind. The authors
are firm believers in the teaching of mathematics as an
experimental science where the student does numerous calculations
and then synthesizes these experiments into a general theory.
Projects based on the concept of writing generic programs test a
student's understanding of the theoretical material of the course.
A student who can solve a general problem certainly can solve a
specialized problem. The authors show MAPLE has a built-in program
for doing these problems. While it is important for the student to
learn MAPLES in built programs, using these alone removes the
student from the conceptual nature of differential equations. The
goal of the book is to teach the students enough about the computer
algebra system MAPLE so that it can be used in an investigative
way. The investigative materials which are present in the book are
done in desk calculator mode DCM, that is the calculations are in
the order command line followed by output line. Frequently, this
approach eventually leads to a program or procedure in MAPLE
designated by proc and completed by end proc. This book was
developed through ten years of instruction in the differential
equations course. Table of Contents 1. Introduction to the Maple
DEtools 2. First-order Differential Equations 3. Numerical Methods
for First Order Equations 4. The Theory of Second Order
Differential Equations with Con- 5. Applications of Second Order
Linear Equations 6. Two-Point Boundary Value Problems, Catalytic
Reactors and 7. Eigenvalue Problems 8. Power Series Methods for
Solving Differential Equations 9. Nonlinear Autonomous Systems 10.
Integral Transforms Biographies Robert P. Gilbert holds a Ph.D. in
mathematics from Carnegie Mellon University. He and Jerry Hile
originated the method of generalized hyperanalytic function theory.
Dr. Gilbert was professor at Indiana University, Bloomington and
later became the Unidel Foundation Chair of Mathematics at the
University of Delaware. He has published over 300 articles in
professional journals and conference proceedings. He is the
Founding Editor of two mathematics journals Complex Variables and
Applicable Analysis. He is a three-time Awardee of the
Humboldt-Preis, and. received a British Research Council award to
do research at Oxford University. He is also the recipient of a
Doctor Honoris Causa from the I. Vekua Institute of Applied
Mathematics at Tbilisi State University. George C. Hsiao holds a
doctorate degree in Mathematics from Carnegie Mellon University.
Dr. Hsiao is the Carl J. Rees Professor of Mathematics Emeritus at
the University of Delaware from which he retired after 43 years on
the faculty of the Department of Mathematical Sciences. Dr. Hsiao
was also the recipient of the Francis Alison Faculty Award, the
University of Delaware's most prestigious faculty honor, which was
bestowed on him in recognition of his scholarship, professional
achievement and dedication. His primary research interests are
integral equations and partial differential equations with their
applications in mathematical physics and continuum mechanics. He is
the author or co-author of more than 200 publications in books and
journals. Dr. Hsiao is world-renowned for his expertise in Boundary
Element Method and has given invited lectures all over the world.
Robert J. Ronkese holds a PhD in applied mathematics from the
University of Delaware. He is a professor of mathematics at the US
Merchant Marine Academy on Long Island. As an undergraduate, he was
an exchange student at the Swiss Federal Institute of Technology
(ETH) in Zurich. He has held visiting positions at the US Military
Academy at West Point and at the University of Central Florida in
Orlando.
Multivariable Calculus with Mathematica is a textbook addressing
the calculus of several variables. Instead of just using
Mathematica to directly solve problems, the students are encouraged
to learn the syntax and to write their own code to solve problems.
This not only encourages scientific computing skills but at the
same time stresses the complete understanding of the mathematics.
Questions are provided at the end of the chapters to test the
student's theoretical understanding of the mathematics, and there
are also computer algebra questions which test the student's
ability to apply their knowledge in non-trivial ways. Features
Ensures that students are not just using the package to directly
solve problems, but learning the syntax to write their own code to
solve problems Suitable as a main textbook for a Calculus III
course, and as a supplementary text for topics scientific
computing, engineering, and mathematical physics Written in a style
that engages the students' interest and encourages the
understanding of the mathematical ideas
Homogenization is a fairly new, yet deep field of mathematics which
is used as a powerful tool for analysis of applied problems which
involve multiple scales. Generally, homogenization is utilized as a
modeling procedure to describe processes in complex structures.
Applications of Homogenization Theory to the Study of Mineralized
Tissue functions as an introduction to the theory of
homogenization. At the same time, the book explains how to apply
the theory to various application problems in biology, physics and
engineering. The authors are experts in the field and collaborated
to create this book which is a useful research monograph for
applied mathematicians, engineers and geophysicists. As for
students and instructors, this book is a well-rounded and
comprehensive text on the topic of homogenization for graduate
level courses or special mathematics classes. Features: Covers
applications in both geophysics and biology. Includes recent
results not found in classical books on the topic Focuses on
evolutionary kinds of problems; there is little overlap with books
dealing with variational methods and T-convergence Includes new
results where the G-limits have different structures from the
initial operators
This is a new type of calculus book: Students who master this text will be well versed in calculus and, in addition, possess a useful working knowledge of how to use modern symbolic mathematics software systems for solving problems in calculus. This will equip them with the mathematical competence they need for science and engineering and the competitive workplace. MACSYMA is used as the software in which the example programs and calculations are given. However, by the experience gained in this book, the student will also be able to use any of the other major mathematical software systems, like for example AXIOM, MATHEMATICA, MAPLE, DERIVE or REDUCE, for "doing calculus on computers".
This book presents current research trends in the field of
underwater acoustic wave direct and inverse problems. Until very
recently, little had been published concerning model-based
inversions of the boundaries and material constants of finite-sized
targets located in either the water column or the sediments. This
text is the first to investigate inverse problems in an ocean
environment, with a heavy emphasis placed on the description and
resolution of the forward scattering problem. Marine Acoustics
emphasizes computation of Green's Functions with new material added
for elastic and poro-elastic seabeds. This timely publication
addresses many areas of practical interest related to underwater
acoustical imaging, including ecological survey and cleanup,
protection of open water harbors, maintenance of offshore petroleum
and gas enterprises, and other areas of environmental and military
concern. The ocean-seabed system is an acoustic waveguide, and this
is the only book that treats inverse problems in a waveguide. The
propagation of acoustic waves in this system is treated for various
types of seabeds and the direct and inverse problems are considered
in realistic ocean environments. The inverse problem is to
determine the shape of an impenetrable or penetrable object, or to
determine the coefficients describing the seabed. This is done by
acoustically illuminating the seabed and investigating the
scattered field.
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