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Books > Science & Mathematics > Mathematics > General
The valuation of the liability structure can be determined by real
options because the shares of a company can be regarded as similar
to the purchase of a financial call option. Therefore, from this
perspective, debt can be viewed as the sale of a financial put
option. As a result, financial analysts are able to establish
different valuations of a company, according to these two financing
methods. Valuation of the Liability Structure by Real Options
explains how the real options method works in conjunction with
traditional methods. This innovative approach is particularly
suited to the valuation of companies in industries where an
underlying asset has high volatility (such as the mining or oil
industries) or where research and development costs are high (for
example, the pharmaceutical industry). Integration of the economic
value of net debt (rather than the accounting value) and
integration of the asset volatility are the main advantages of this
approach.
These materials were developed, in part, by a grant from the
federally-funded Mathematics and Science Partnership through the
Center for STEM Education. Some of the activities were adapted from
the National Council of Teachers of Mathematics Illuminations, the
National Library of Virtual Manipulatives, Hands-On Math Projects
with Real Applications by Judith A. Muschla and Gary R. Muschla,
Learning Math with Calculators: Activities for Grades 3-8 by Len
Sparrow and Paul Swan, and Mathematical Ideas by Charles D. Miller,
Vern E. Heeren and John Hornsby.
Matrix-analytic methods (MAM) were introduced by Professor Marcel
Neuts and have been applied to a variety of stochastic models
since. In order to provide a clear and deep understanding of MAM
while showing their power, this book presents MAM concepts and
explains the results using a number of worked-out examples. This
book's approach will inform and kindle the interest of researchers
attracted to this fertile field. To allow readers to practice and
gain experience in the algorithmic and computational procedures of
MAM, Introduction to Matrix Analytic Methods in Queues 1 provides a
number of computational exercises. It also incorporates simulation
as another tool for studying complex stochastic models, especially
when the state space of the underlying stochastic models under
analytic study grows exponentially. The book's detailed approach
will make it more accessible for readers interested in learning
about MAM in stochastic models.
For anyone interested in the history and effects of the
introduction of so-called "Modern Mathematics" (or "Mathematique
Moderne," or "New Mathematics," etc.) this book, by Dirk De Bock
and Geert Vanpaemel, is essential reading. The two authors are
experienced and highly qualified Belgian scholars and the book
looks carefully at events relating to school mathematics for the
period from the end of World War II to 2010. Initially the book
focuses on events which helped to define the modern mathematics
revolution in Belgium before and during the 1960s. The book does
much more than that, however, for it traces the influence of these
events on national and international debates during the early
phases of the reform. By providing readers with translations into
English of relevant sections of key Continental documents outlining
the major ideas of leading Continental scholars who contributed to
the "Mathematique Moderne" movement, this book makes available to a
wide readership, the theoretical, social, and political backdrops
of Continental new mathematics reforms. In particular, the book
focuses on the contributions made by Belgians such as Paul Libois,
Willy Servais, Frederique Lenger, and Georges Papy. The influence
of modern mathematics fell away rapidly in the 1970s, however, and
the authors trace the rise and fall, from that time into the 21st
century, of a number of other approaches to school mathematics-in
Belgium, in other Western European nations, and in North America.
In summary, this is an outstanding, landmark publication displaying
the fruits of deep scholarship and careful research based on
extensive analyses of primary sources.
AN INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH USE OF THE TENSOR
CALCULUS By LUTHER PFAHLER EISENHART. Preface: Since 1909, when my
Differential Geometry of Curves and Surfaces was published, the
tensor calculus, which had previously been invented by Ricci, was
adopted by Einstein in his General Theory of Relativity, and has
been developed further in the study of Riemannian Geometry and
various generalizations of the latter. In the present book the
tensor calculus of cuclidean 3-space is developed and then
generalized so as to apply to a Riemannian space of any number of
dimensions. The tensor calculus as here developed is applied in
Chapters III and IV to the study of differential geometry of
surfaces in 3-space, the material treated being equivalent to what
appears in general in the first eight chapters of my former book
with such additions as follow from the introduction of the concept
of parallelism of Levi-Civita and the content of the tensor
calculus. LUTHER PFAHLER EISENHART. Contents include: CHAPTER I
CURVES IN SPACE SECTION PAGE 1. Curves ami surfaces. The summation
convention 1 2. Length of a curve. Linear element, 8 3. Tangent to
a curve. Order of contact. Osculating plane 11 4. Curvature.
Principal normal. Circle of curvature 16 5. TBi normal. Torsion 19
6r The Frenet Formulas. The form of a curve in the neighborhood of
a point 25 7. Intrinsic equations of a curve 31 8. Involutes and
evolutes of a curve 34 9. The tangent surface of a curve. The polar
surface. Osculating sphere. . 38 10. Parametric equations of a
surface. Coordinates and coordinate curves trT a surface 44 11. 1
Tangent plane to a surface 50 tSffDovelopable surfaces. Envelope of
a one-parameter family ofsurfaces. . 53 CHAPTER II TRANSFORMATION
OF COORDINATES. TENSOR CALCULUS 13. Transformation of coordinates.
Curvilinear coordinates 63 14. The fundamental quadratic form of
space 70 15. Contravariant vectors. Scalars 74 16. Length of a
contravariant vector. Angle between two vectors 80 17. Covariant
vectors. Contravariant and covariant components of a vector 83 18.
Tensors. Symmetric and skew symmetric tensors 89 19. Addition,
subtraction and multiplication of tensors. Contraction.... 94 20.
The Christoffel symbols. The Riemann tensor 98 21. The Frenet
formulas in general coordinates 103 22. Covariant differentiation
107 23. Systems of partial differential equations of the first
order. Mixed systems 114 CHAPTER III INTRINSIC GEOMETRY OF A
SURFACE 24. Linear element of a surface. First fundamental
quadratic form of a surface. Vectors in a surface 123 25. Angle of
two intersecting curves in a surface. Element of area 129 26.
Families of curves in a surface. Principal directions 138 27. The
intrinsic geometry of a surface. Isometric surfaces 146 28. The
Christoffel symbols for a surface. The Riemannian curvature tensor.
The Gaussian curvature of a surface 149 29. Differential parameters
155 30. Isometric orthogonal nets. Isometric coordinates 161 31...
This book has been a work in progress since 1971 in which the
author reveals his then, way out ideas and imaginations about the
origin of the universe, religion, gender bias in language, future
economic and social systems, future space travel and the
rectification of PI in a peanutshell. Many of his ideas have now
been proven, like the black hole theory and many other ideas are
now being considered by the established authorities in their
respective fields. And there are many other ramblings and
reflections of an active mind that are still crazy but provocative
and entertaining.
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