1999, ISBN: 1-56881-112-8, paperback; 320pp.;
1997, ISBN: 1-56881-070-9, hardcover; 320pp.;
Morgan has created a no-nonsense text for
teaching single-variable calculus. Abandoning
the
outmoded approach of the traditional, unwieldy
mathematics book, Calculus Lite is a
straightforward instructional tool that introduces
standard preliminary topics like trigonometry
and limits by using them in the calculus.
The text is filled with a plethora of relevant
examples
and problems to illustrate the general concepts
and includes careful explanations and solutions.
This book will be an excellent addition to
any calculus course allowing teachers to
mold the
material to their individual needs.
Praise for Calculus Lite:
"A nice, concise introduction to differential
and integral calculus with a nod towards
infinite
series and differential equations."
--American Mathematical Monthly
"This is a nontraditional text and I
highly recommend it to anyone who has become
bored with
the canonical business, social science, and
life science texts which all seem to be the
same. My
students have raved about it and appreciate
the 'lite' style. They have also mentioned
that the
price is right. Gien the high cost of texts
it is nice to be able to purchase an excellent
one for
around $30. The author and the publisher
deserve to be commended for producing such
an
outstanding book at a reasonable price."
--Jerry Rosen, Professor at California State
University, Northridge
Table of Contents
I. The Derivative
1. Instantaneous Velocity and the Derivative
2. Geometric Interpretation of the Derivative
as the Slope of the Graph
3. The Product and Quotient Rules
4. The Chain Rule and Implicit Differentiation
5. The Extended Power Rule
6. Sines, Cosines, and Their Derivatives
7. Maxima and Minima
8. Maxima-Minima Real-World Problems
9. Exponentials and Logarithms
10. Exponential Growth and Decay
11. The Second Derivative and Curve Sketching
12. Antidifferentiation
13. Differentiation and Continuity
14. Review
II. The Integral
15. Area and the Riemann Integral
16. The Fundamental Theorem of Calculus
17. Properties of the Definite Integral
18. Recognizing Antiderivatives (Indefinite
Integrals)
19. Integration by Substitution
20. Review of Integration
21. Trigonometric Functions and Their Inverses
22. Volume, Length, Average
23. Integration by Table
24. Partial Fractions and Integration by
Parts
25. Numerical Methods
26. Review Problems
III. Infinite Series
27. Infinite Series (Sums)
28. Power Series and Taylor Series
IV. Differential Equations
29. Differential Equations
30. Linear Second Order Homogenous Constant-Coefficient
Differential Equations
V. Multivariable Calculus
31. Partial Derivatives
32. Double Integrals
33. Critical Points
34. Maxima and Minima
Description
Abstract. The main goal of this paper is
to prove the following conjecture of Baues
and Lemaire: the differential graded Lie
algebra associated with the Sullivan model
of
a space is homotopy equivalent to its Quillen
model. In addition we show the same for the
cellular Lie algebra model which we build
from the simplicial analog of the
classical Adams-Hilton model. It turns out
that this cellular Lie algebra model is one
link in a chain of models connecting the
models of Quillen and Sullivan. The key result
which makes all this possible is Anick's
correspondence between differential graded
Lie algebras and Hopf algebras up to homotopy.
In addition we show that the Quillen
model is a rational homotopical equivalence,
and we conclude the same for the other models
using our main result. The construction of
the three models is given in detail.
The background from homotopy theory, differential
algebra, and algebra is presented in great
generality.
Contents
Introduction
Homotopy theory
Differential algebra
Complete algebra
Three models for spaces
Notations
Bibliography
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Memoirs of the American Mathematical
Society, Volume: 682
Publication Year: 2000
ISBN: 0-8218-1920-8
Paging: 149 pp.
Binding: Softcover
Contents
Setting forth the problems
Some history
Synopsis of the main results
Preliminaries
The McPolin-Wickstead and Huijsmans-de Pagter-Koldunov
Theorems revisited
d-bases
Band preserving operators and band-projections
Central operators and Problems A and B
Range-domain exchange in the Huijsmans-de
Pagter-Koldunov Theorem
d-splitting number of disjointness preserving
operators
Essentially one-dimensional and discrete
vector lattices
Essentially constant functions and operators
on $C[0,1]$
Counterexamples
Dedekind complete vector lattices and Problems
A and B
Generalizations to $(r_u)$-complete vector
lattices
Open problems
References
Index
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Memoirs of the American Mathematical
Society, Volume: 679
Publication Year: 2000
ISBN: 0-8218-1397-8
Paging: 162 pp.
Binding: Softcover
Contents
Introduction
Continuous tensor products
Algebras associated to continuous tensor
products
Arveson's spectral $C^*$-algebras
Appendix
References
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Memoirs of the American Mathematical
Society, Volume: 680
Publication Year: 2000
ISBN: 0-8218-1545-8
Paging: 118 pp.
Binding: Softcover
Description
Abstract. We employ recent advances in the
theory of operator spaces, also known as
quantized functional analysis, to provide
a context in which
one can compare categories of modules over
operator algebras that are not necessarily
self-adjoint. We focus our attention on the
category of
Hilbert modules over an operator algebra
and on the category of operator modules over
an operator algebra. The module operations
are assumed
to be completely bounded - usually, completely
contractive. We develop the notion of a Morita
context between two operator algebras $A$
and
$B$. This is a system $(A,B,{}_{A}X_{B},{}_{B}
Y_{A},(\cdot,\cdot),[\cdot,\cdot])$ consisting
of the algebras, two bimodules $_{A}X_{B$
and $_{B}Y_{A}
and pairings $(\cdot,\cdot)$ and $[\cdot,\cdot]$
that induce (complete) isomorphisms between
the (balanced) Haagerup tensor products,
$X
\otimes_{hB} {} Y$ and $Y \otimes_{hA} {}
X$, and the algebras, $A$ and $B$, respectively.
Thus, formally, a Morita context is the same
as that
which appears in pure ring theory. The subtleties
of the theory lie in the interplay between
the pure algebra and the operator space geometry.
Our
analysis leads to viable notions of projective
operator modules and dual operator modules.
We show that two C$^*$-algebras are Morita
equivalent
in our sense if and only if they are $C^{\ast}$-algebraically
strong Morita equivalent, and moreover the
equivalence bimodules are the same. The
distinctive features of the non-self-adjoint
theory are illuminated through a number of
examples drawn from complex analysis and
the theory of
incidence algebras over topological partial
orders. Finally, an appendix provides links
to the literature that developed since this
Memoir was
accepted for publication.
Contents
Introduction
Preliminaries
Morita contexts
Duals and projective modules
Representations of the linking algebra
$C^*$-algebras and Morita contexts
Stable isomorphisms
Examples
Appendix-More recent developments
Bibliography
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Memoirs of the American Mathematical
Society, Volume: 681
Publication Year: 2000
ISBN: 0-8218-1916-X
Paging: 94 pp.
Binding: Softcover
Bhaya, A. / Kaszkurewicz, E.,Fed. University of Rio deJaneiro, Brazil
1999. Approx. 272 pages.
Hardcover
ISBN 3-7643-4088-6
Due in January 2000
Matrix diagonal stability and the related
diagonal type Liapunov functions possess
properties that
make them attractive and very useful for
applications. This new book addresses the
matrix-stability concept and its
applications to the analysis and design of
several types of dynamical systems, both
discrete-time and
continuous-time.
The comprehensive presentation begins with
an introductory chapter surveying applied
examples from diverse fields, i.e.,
robust stability analysis, asynchronous iterative
computation, neural networksand variable
structure dynamical systems.
The next few chapters develop the theory
and includes a unified presentation of results
in the area of
matrix-diagonal stability and D-stability.
The remaining chapters examine the various
applications in greater detail.
Both classical and new results are discussed,
and the overall treatment is self-contained,
only requiring linear
algebra, difference equations and differential
equations.
The book provides an essential reference
for new methods and analysis related to dynamical
systems described
by linear and nonlinear ordinary differential
equations and difference equations. Researchers,
professionals
and graduates in applied math, control engineering,
stability of dynamical systems, scientific
computation and
computer science will find the book a successful
guide to current results and developments.
Contents
PREFACE; Chapter 1: Diagonally Stable
Structures in Systems and
Computation; 1.1 Introduction; 1.2
Robust stability of a mechanical system;
1.3 Lotka-Volterra equations of
population biology; 1.4 Convergence of
asynchronous computation; 1.5 Global
stability of neural networks; 1.6 Variable
structure systems; 1.7 Existence of
diagonal type Liapunov functions; 1.8
Notes and References; Chapter 2:
Matrix Diagonal and D-stability; 2.1-2.9;
Chapter 3: Mathematical models
admitting diagonal type Liapunov
functions; 3.1-3.7; Chapter 4:
Convergence of Asynchronous Iterative
Methods; 4.1-4.5; Chapter 5: Neural
networks, Circuits and Systems;
5.11-5.7; Chapter 6: Interconnected
Systems: Stability and Stabilization;
6.1-6.7; EPILOGUE; REFERENCES;
INDEX
Enjoy Writing Your Science Thesis or Dissertation!
is a complete guide to good dissertation
and thesis writing. It is written in an
accessible style with cartoons and real-life
anecdotes to liven up the text. It outlines
the rules and conventions of scientific writing
? particularly for dissertations and theses
? and gives the reader practical advice about
planning, writing, editing, presenting, and
submitting a successful dissertation or thesis.
Enjoy Writing Your Science Thesis or Dissertation!
can be used as either a guide
from day one of the degree course or as a
quick reference life-jacket when deadlines
are looming.
Contents:
Enjoy Writing Your Science Thesis or Dissertation!
Planning and Writing the References (Bibliography)
Planning and Writing Materials and Methods/Experimental
Techniques
Planning and Writing the Results
Planning and Writing the Introduction
Planning and Writing the Discussion
Figures and Tables
Deciding on a Title and Planning and Writing
the Other Bits
Proofreading, Printing, Binding and Submission
And You Thought It was All Over
Supervision
Resources
Layout
The Use of English
Readership: Postgraduate and undergraduate
science students.
296pp
Pub. date: Jul 1999
ISBN 1-86094-090-0
ISBN 1-86094-207-5(pbk)
by Benjamin Baumslag (Mälardalen University,
Sweden)
This unique book presents a personal and
global approach to teaching mathematics at
university level. It is impressively broad
in its scope, and
thought-provoking in its advice. The author
writes with a love of his subject and the
benefit of a long and varied career. He compares
and
contrasts various educational systems and
philosophies. Furthermore, by constantly
drawing on his own experiences and those
of his colleagues, he
offers useful suggestions on how teachers
can respond to the problems they face. This
book will interest educationalists, policy
advisers,
administrators, lecturers, and instructors
of lecturers.
Contents:
Education Systems in Brief
The Expansion of Education
Aims
Universities and Government
Teaching
Study Skills
Rules of Teaching
Organisation and Examinations
Planning
Methods of Teaching and Equipment
Lecturer's Approach
Some Practical Points
Assessment of Teaching
Readership: Academics and lecturers involved
in mathematics teaching at higher education
level.
220pp (approx.)
Pub. date: Scheduled Spring 2000
ISBN 1-86094-214-8