February 26, 2018 Forthcoming by Chapman and Hall/CRC
Textbook - 277 Pages - 3 B/W Illustrations
ISBN 9780815396857
The subject matter has been organized in the form of theorems and their proofs, and the presentation is rather unconventional.
It comprises 30 class tested lectures that the authors have given mainly to math majors students at various institutions over a period of almost 40 years
The content in a particular lecture, together with the problems therein, provides fairly adequate coverage of the topic under study
In this book, there are 122 examples which explain each concept and demonstrate the importance of every result. Two types of 289 problems are also included, those that illustrate the general theory and others designed to fill out text material
For the convenience of the reader, the authors have provided answers or hints to all the problems
This book provides a compact, but thorough, introduction to the subject of Real Analysis. It is intended for a senior undergraduate and for a beginning graduate one-semester course.
Logic and Proof Techniques. Sets and Functions. Real Numbers. Open and Closed Sets. Cardinality. Real-valued Functions. Real Sequences. Real Sequences (Contd.). Infinite Series. Infinite Series (Contd.). Limits of Functions. Continuous Functions. Discontinuous Functions. Uniform and Absolute Continuities and Functions of Bounded Variation. Differentiable Functions. Higher Order Differentiable Functions. Convex Functions. Indeterminate Forms. Riemann Integration. Properties of the Riemann Integral. Improper Integrals. Riemann-Lebesgue Theorem. Riemann-Stieltjes Integral. Sequences of Functions. Sequences of Functions (Contd.). Series of Functions. Power and Taylor Series. Power and Taylor Series (Contd.). Metric Spaces. Metric Spaces (Contd.). Bibliography. Index.
March 13, 2018
Reference - 286 Pages - 27 B/W Illustrations
ISBN 9781138033061
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Employs methods of modern asymptotic analysis
Systematically applies the Calculus of Variations
Introduces and systematically employs the basic notion of a locally-plane wave
Concisely describes modern mathematical tools, which may be helpful for a reader with insufficient background
Presents various problems, which have not been yet published in monographs
Elastic Waves: High Frequency Theory is concerned with mathematical aspects of the theory of high-frequency elastic waves, which is based on the ray method. The foundations of elastodynamics are presented along with the basic theory of plane and spherical waves. The ray method is then described in considerable detail for bulk waves in isotropic and anisotropic media, and also for the Rayleigh waves on the surface of inhomogeneous anisotropic elastic solids. Much attention is paid to analysis of higher-order terms and to generation of waves in inhomogeneous media. The aim of the book is to present a clear, systematic description of the ray method, and at the same time to emphasize its mathematical beauty. Luckily, this beauty is usually not accompanied by complexity and mathematical ornateness.
Preface
Introduction
Chapter 1. Basic notions of elastodynamics
Chapter 2. Plane waves
Chapter 3. Point sources and spherical waves in homogeneous isotropic media
Chapter 4. The ray method for volume waves in isotropic media
Chapter 5. The ray method for volume waves in anisotropic media
Chapter 6. Point sources in inhomogeneous isotropic media. The wave S from a center of expansion. The wave P from a center of rotation
Chapter 7. The "nongeometrical" wave S *
Chapter 8. The ray method for Rayleigh waves
A.1. Definition of tensor
A.2. Simple operations with tensors
A.3. Metric tensor. Raising and lowering indices
A.4. Coordinates (q1, q2, n) associated with a surface in R3. The first and second fundamental forms
A.5. Covariant derivative. Divergence
March 13, 2018
Textbook - 524 Pages
ISBN 9781138578333
Series: Chapman & Hall/CRC Texts in Statistical Science
Self-contained coverage of the relevant distributions and matrix algebra
Detailed and accessible derivations or proofs of essentially all results
In-depth coverage of all included topics
Expanded coverage of predictive inference and of multiple comparisons and simultaneous confidence intervals
Extensive coverage of the optimality properties of the F test
Linear Models and the Relevant Distributions and Matrix Algebra provides in-depth and detailed coverage of the use of linear statistical models as a basis for parametric and predictive inference. It can be a valuable reference, a primary or secondary text in a graduate-level course on linear models, or a resource used (in a course on mathematical statistics) to illustrate various theoretical concepts in the context of a relatively complex setting of great practical importance.
March 31, 2018
Textbook - 600 Pages - 149 B/W Illustrations
ISBN 9781138118218
Series: Textbooks in Mathematics
Emphasizes the use of software to aid in problem solving
Includes numerical case studies that highlight possible pitfalls when computing a numerical solution without first considering the appropriate theory
Covers nonlinear differential equations and nonlinear systems
Shows how to solve various mathematical models, such as population growth, epidemic, and predator-prey models
Discusses fundamental existence, uniqueness, and continuation theorems
Contains a CD-ROM with the software programs used in the text
Requires no prior knowledge of programming languages
Solutions manual available for qualifying instructors
In the traditional curriculum, students rarely study nonlinear differential equations and nonlinear systems due to the difficulty or impossibility of computing explicit solutions manually. Although the theory associated with nonlinear systems is advanced, generating a numerical solution with a computer and interpreting that solution are fairly elementary. Bringing the computer into the classroom, Ordinary Differential Equations: Applications, Models, and Computing emphasizes the use of computer software in teaching differential equations.
April 12, 2018
Textbook - 188 Pages - 17 B/W Illustrations
ISBN 9781138482760
Series: Textbooks in Mathematics
Introduces the Lebesque Integral to undergraduate students
Concentrates on the real line
Does not approach through abstract measure spaces
Product measures are treated concretely
It is important and useful to have a text on the Lebesgue theory that is accessible to bright undergraduates. This is such a text. Going back to the days of Isaac Newton and Gottfried Wilhelm von Leibniz, and even to Newton's teacher Isaac Barrow, the integral has been a mainstay of mathematical analysis. The integral is a device for amalgamating information. It is a powerful and irreplaceable tool. The text concentrates on the real line. The student will be familiar with the real numbers and will be comfortable internalizing the new ideas of measure theory in that context. In addition to having copious examples and numerous figures, this book includes a Table of Notation and a Glossary
Introductory Thoughts.The Purpose of Measures.The Lebesgue Integral.Integrable Functions.The Lebesgue Spaces. The Concept of Outer Measure.What is a Measurable Set? Decomposition Theorems.Creation of Measures. Instances of Measurable Sets. Approximation by Open and Closed Sets. Different Methods of Convergence. Measure on a Product Space. Additivity for Outer Measure. Nonmeasurable and Non-Borel Sets
May 18, 2018
Textbook - 544 Pages - 23 B/W Illustrations
ISBN 9781498773287
Contains direct and concise proofs with attention to detail
Features a substantial variety of interesting and nontrivial examples
Includes nearly 700 exercises ranging from routine to challenging with hints for the more difficult exercises
Provides an eclectic set of special topics and applications
Principles of Analysis: Measure, Integration, Functional Analysis, and Applications prepares readers taking advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level. It is also designed so that the reader or instructor may select topics suitable to their needs. The author presents the text in a clear and straightforward manner for the readersf benefit. At the same time, the text is a thorough and rigorous examination of the essentials of measure, integration and functional analysis.
Measurable Sets. Measurable Functions. Integration. Further Topics in Measure Theory. Banach Spaces. Hilbert Spaces. Locally Convex Spaces. Banach Algebras. Harmonic Analysis on Locally Compact Groups. Probability Theory. Operator Theory. Appendices.