Peter B. Kahn

Mathematical Methods for Scientists and Engineers:
Linear and Nonlinear Systems

Appropriate for advanced undergraduate and graduate students in a variety of scientific and engineering
fields, this text introduces linear and nonlinear problems and their associated models.

Contents: I. Linear Systems. 0. Miscellaneous Resources. 1. Matrix Theory. 2. The Gamma and Related Functions.
3. Elements of Asymptotics. 4. Evaluation of Sums: The Euler.MacLaurin Sum Expansion. 5. Evaluation of Integrals:
The Laplace Method. 6. Differential Equations. II. Nonlinear Systems. 7. The Simple Harmonic Oscillator
and the Logistic Equation. 8. Aspects of Harmonic Motion and the Concept of Secular Terms. 9. Equilibrium
Points and the Phase Plane. 10. Conservative Systems. 11. Nonconservative Systems. 12. The Method of Averaging
(MOA). 13. The Method of Multiple Times Scales (MMTS). 14. Higher-Order Calculations. 15. Error Analysis.
16. One-Dimensional Iterative Maps and the Onset of Chaos. Appendix. Index.

Unabridged republication of the edition published by John Wiley & Sons, New York, 1990. 70 figures.
4 tables.

496pp.
61.8 x 91.4 (15.6 cm. x 23.5 cm.)
0-486-43516-4
July 2004

Felix Klein

Elementary Mathematics from an Advanced Standpoint: Geometry

“Nothing comparable to it.”.Mathematics Teacher
This companion volume to Klein’s related book (see below) offers a comprehensive view of its subject,
accompanying the space perception inherent in geometry with analytical formulas enabling
precise formulation of geometric facts.

Contents: 1. The Simplest Geometric Manifolds. I. Line-Segment, Area, Volume, as Relative Magnitudes. II.
The Grassmann Determinant Principle for the Plane. III. The Grassmann Principle for Space. IV. Classification
of the Elementary Configurations of Space According to their Behavior under Transformation of
Rectangular Coordinates. V. Derivative Manifolds. 2. Geometric Transformations. I. Affine Transformations.
II. Projective Transformations. III. Higher Point Transformations. IV. Transformations with Change
of Space Element. V. Theory of the Imaginary. 3. Systematic Discussion of Geometry and Its Foundations.
I. The Systematic Discussion. II. Foundations of Geometry. Indexes.

Unabridged republication of the Dover reprint of the 1925 third edition. Translated from German by
E. R. Hedrick & C. A. Noble. 141 figures.

224pp.
53.8 x 81.2 (13.7 cm. x 21.6 cm.)
0-486-43481-8
July 2004

Felix Klein

Elementary Mathematics from an Advanced Standpoint:
Arithmetic, Algebra, Analysis

"Makes the reader feel the inspiration that comes from listening to a great teacher." -Bulletin,
American Mathematical Society
This companion volume to the author's book on geometry (see above) enlivens abstract discussion
of arithmetic, algebra, and analysis by means of graphical and geometrically perceptive methods.

Contents: 1. Arithmetic. I. Calculating with Natural Numbers. II. The First Extension of the Notion of Number.
III. Concerning Special Properties of Integers. IV. Complex Numbers. 2. Algebra. I. Real Equations with Real
Unknowns. II. Equations in the Field of Complex Quantities. III. Analysis. I. Logarithmic and Exponential Functions.
II. The Goniometric Functions. III. Concerning Infinitesimal Calculus Proper. Supplement. Indexes.

Unabridged republication of the Dover reprint of the 1925 third edition. Translated from German
by E. R. Hedrick & C. A. Noble. 125 figures.

288pp.
53/8 x 81/2 (13.7 cm. x 21.6 cm.)
0-486-43480-X
July 2004

George W. Mackey

Mathematical Foundations of Quantum Mechanics

Designed for students familiar with abstract mathematical concepts but possessing little
knowledge of physics, this graduate-level text focuses on generality and careful formulation
rather than problem-solving. Author George W. Mackey of Harvard University is a member of
the distinguished National Academy of Science.

Contents: 1. Classical Mechanics. 2. Quantum Mechanics. 3. Group Theory and the Quantum Mechanics of
the Atom. Appendix.

Unabridged republication of the edition published by W. A. Benjamin, Inc., New York, 1963.
3 figures. 1 table.

160pp.
61/8 x 91/4 (15.6 cm. x 23.5 cm.)
0-486-43517-2
February 2004

Walter J. Meyer

Concepts of Mathematical Modeling

All mathematics students need to understand mathematical modeling, and this text does it
clearly with a straightforward overview of the subject痴 main themes and methods. Undergraduate
and graduate students will benefit from its approach, which features independent
sections, a variety of applications, and an examination of classic models.

Contents: 1. The Scope of Mathematical Modeling. 2. The Relation of Models to Data. 3. Evaluation of Mathematical
Models. 4. Optimization. 5. Choosing the Mathematics for the Model. Answers to Selected Exercises.
Index.

Unabridged republication of the edition published by McGraw-Hill Book Company, New York, 1984.

464pp.
61/8 x 91/4 (15.6 cm. x 23.5 cm.)
0-486-43515-6
August 2004

M. M. Postnikov

Foundations of Galois Theory

Written by a prominent mathematician, this text offers advanced undergraduate and graduate
students a self-contained treatment of the basics of Galois Theory, which is both the source
of modern abstract algebra and one of abstract algebra痴 most concrete applications.

Contents: I. The Elements of Galois Theory. 1. The Elements of Field Theory. 2. Necessary Facts from the
Theory of Groups. 3. Galois Theory. II. The Solution of Equations by Radicals. 1. Additional Facts from the
General Theory of Groups. 2. Equations Solvable by Radicals. 3. The Construction of Equations Solvable
by Radicals. 4. The Unsolvability by Radicals of the General Equation of Degree n > 5.

Unabridged republication of the edition published by The Macmillan Company, New York, 1962.

128pp.
53/8 x 81/2 (13.7 cm. x 21.6 cm.)
0-486-43518-0
February 2004

Mary Tiles

The Philosophy of Set Theory:
An Historical Introduction to Cantor's Paradise

Philosophers with only a basic grounding in mathematics, as well as mathematicians who
have taken only an introductory course in philosophy, will find many topics of interest in this
text, which is appropriate for undergraduate- and graduate-level courses.

Contents: 1. The Finite Universe. 2. Classes and Aristotelian Logic. 3. Permutations, Combinations and Infinite
Cardinalities. 4. Numbering the Continuum. 5. Cantor痴 Transfinite Paradise. 6. Axiomatic Set Theory.
7. Logical Objects and Logical Types. 8. Independence Results and the Universe of Sets. 9. Mathematical
Structure佑onstruct and Reality. Further Reading. Bibliography. Glossary of Symbols. Index.

Unabridged republication of the edition published by Basil Blackwell Ltd., Oxford, England,
1989. 32 figures.

53/8 x 81/2 (13.7 cm. x 21.6 cm.)
0-486-43520-2
July 2004

Alberto Torchinsky

Real-Variable Methods in Harmonic Analysis

An exploration of the unity of several areas in harmonic analysis, this self-contained text
emphasizes real-variable methods. Appropriate for advanced undergraduate and graduate
students, it contains numerous problems (often with hints) that assist in the development of
important ideas. "A very good choice." ---MathSciNet, American Mathematical Society

Contents: 1. Fourier Series. 2. Cesaro Summability. 3. Norm Convergence of Fourier Series. 4. The Basic
Principles. 5. The Hilbert Transform and Multipliers. 6. Paley's Theorem and Fractional Integration. 7. Harmonic
and Subharmonic Functions. 8. Oscillation of Functions. 9. Ap Weights. 10. More About Rn. 11.
Calderon-Zygmund Singular Integral Operators. 12. The Littlewood-Paley Theory. 13 The Good lPrinciple.
14. Hardy Spaces of Several Real Variables. 15. Carleson Measures. 16. Cauchy Integrals on Lipschitz
Curves. 17. Boundary Value Problems on C 1-Domains. Bibliography. Index.

Unabridged republication of the edition published by Academic Press, Orlando, Florida, 1986.

480pp.
53/8 x 81/2 (13.7 cm. x 21.6 cm.)
0-486-43508-3
April 2004

Paul Waltman

A Second Course in Elementary Differential Equations

Focusing on applicable rather than applied mathematics, this text is appropriate for advanced
undergraduates majoring in any discipline. The author emphasizes basic real analysis as well
as differential equations.

Contents: 1. Systems of Linear Differential Equation. 2. Two-Dimensional Autonomous Systems. 3. Existence
Theory. 4. Boundary Value Problems.

Unabridged, corrected republication of the edition published by Academic Press, Orlando,
Florida. 1986. 39 figures.

272pp.
61/8 x 91/4 (15.6 cm. x 23.5 cm.)
0-486-43478-8
April 2004

Stephen Willard

General Topology

Among the best available reference introductions to general topology, this volume is appropriate
for advanced undergraduate and beginning graduate students. Historical notes and
more than 340 detailed exercises enrich the text.

Contents: 1. Set Theory and Metric Spaces. 2. Topological Spaces. 3. New Spaces from Old. 4. Convergence.
5. Separation and Countability. 6. Compactness. 7. Metrizable Spaces. 8. Connectedness. 9. Uniform Spaces.
10. Function Spaces. Historical Notes. Bibliography. Index.

Unabridged republication of the edition published by Addison-Wesley Publishing Company,
Reading, Massachusetts, 1970. 27 figures.

384pp.
61/8 x 91/4 (15.6 cm. x 23.5 cm.)
0-486-43479-6
March 2004