Frank Morgan

Calculus Lite, Second Edition

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


Martin Majewski, Free University of Berlin, Germany

Rational Homotopical Models and Uniqueness

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


Y. A. Abramovich, Indiana University-Purdue University, Indianapolis, IN,
and A. K. Kitover, Community College of Philadelphia, PA

Inverses of Disjointness Preserving Operators

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


Joachim Zacharias, University d'Orleans, France

Continuous Tensor Products and Arveson's Spectral C*-Algebras

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


David P. Blecher, University of Houston, TX, Paul S. Muhly, University of Iowa, Iowa City, IA,and Vern I. Paulsen, University of Houston, TX

Categories of Operator Modules
(Morita Equivalence and Projective Modules)

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

Matrix Diagonal Stability inSystems and Computation

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


by Daniel Holtom & Elizabeth Fisher (Imperial College)

ENJOY WRITING YOUR SCIENCE THESIS OR DISSERTATION!

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)

FUNDAMENTALS OF TEACHING MATHEMATICS AT UNIVERSITY LEVEL

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