Paperback
Hardback
Format: Paperback / softback, 157 pages, height x width: 235x155 mm, weight: 272 g, 43 Illustrations, black and white; XI, 157 p. 43 illus., 1 Paperback / softback
Series: Compact Textbooks in Mathematics
Pub. Date: 13-Jan-2024
ISBN-13: 9783031439162
This textbook offers undergraduates a self-contained introduction to advanced topics not covered in a standard calculus sequence. The authors enthusiastic and engaging style makes this material, which typically requires a substantial amount of study, accessible to students with minimal prerequisites. Readers will gain a broad knowledge of the area, with approaches based on those found in recent literature, as well as historical remarks that deepen the exposition. Specific topics covered include the binomial theorem, the harmonic series, Euler's constant, geometric probability, and much more. Over the fifteen chapters, readers will discover the elegance of calculus and the pivotal role it plays within mathematics.
A Compact Capstone Course in Classical Calculus is ideal for exploring interesting topics in mathematics beyond the standard calculus sequence, particularly for undergraduates who may not be taking more advanced math courses. It would also serve as a useful supplement for a calculus course and a valuable resource for self-study. Readers are expected to have completed two one-semester college calculus courses.
Chapter 1. Prelude: Vi`etes ProductChapter. 2. Calculus Warm-upChapter.
3. The Probability Integral & Gamma FunctionChapter. 4. Walliss
ProductChapter. 5. Interlude: How Big is a Ball ?Chapter. 6. Convexity
TangentsChapter. 7. Some Important SeriesChapter. 8. Geometric
ProbabilityChapter. 9. Convexity ChordsChapter. 10. Interlude: Minkowski
DistanceChapter. 11. The Basel ProblemChapter. 12. Interlude: Beyond
BaselChapter. 13. Stirlings FormulaChapter. 14. Eulers Sine ProductChapter.
15. Postlude: Stirlings Formula AgainIndex
Hardback
Format: Hardback, 162 pages, height x width: 235x155 mm, 3 Illustrations, black and white; X, 162 p. 3 illus., 1 Hardback
Series: Mathematical Physics Studies
Pub. Date: 27-Feb-2024
ISBN-13: 9789819997374
Large numbers of studies of the KdV equation have appeared since the pioneering paper by Gardner, Greene, Kruskal, and Miura in 1967. Most of those works have employed the inverse spectral method for 1D Schrodinger operators or an advanced Fourier analysis. Although algebraic approaches have been discovered by HirotaSato and Marchenko independently, those have not been fully investigated and analyzed.
The present book offers a new approach to the study of the KdV equation, which treats decaying initial data and oscillating data in a unified manner. The authors method is to represent the tau functions introduced by HirotaSato and developed by SegalWilson later in terms of the WeylTitchmarsh functions (WT functions, in short) for the underlying Schrodinger operators. The main result is stated by a class of WT functions satisfying some of the asymptotic behavior along a curve approaching the spectrum of the Schrodinger operators at + in an order of -(n-1/2)for the nth KdV equation. This class contains many oscillating potentials (initial data) as well as decaying ones. Especially bounded smooth ergodic potentials are included, and under certain conditions on the potentials, the associated Schrodinger operators have dense point spectrum. This provides a mathematical foundation for the study of the soliton turbulence problem initiated by Zakharov, which was the authors motivation for extending the class of initial data in this book. A large class of almost periodic potentials is also included in these ergodic potentials. P. Deift has conjectured that any solutions to the KdV equation starting from nearly periodic initial data are almost periodic in time. Therefore, our result yields a foundation for this conjecture.
For the readers benefit, the author has included here (1) a basic knowledge of direct and inverse spectral problem for 1D Schrodinger operators, including the notion of the WT functions; (2)Satos Grassmann manifold method revised by SegalWilson; and (3) basic results of ergodic Schrodinger operators.
Introduction.- Satos Theory.- KdV Flow I: Reflectionless Case.- KdV
Flow II: Extension.- Applications.- Further Topics.- Appendix.
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Format: Paperback / softback, 432 pages, height x width: 235x155 mm, 8 Illustrations, color; 118 Illustrations, black and white; X, 432 p. 126 illus., 8 illus. in color., 1 Paperback / softback
Series: Springer Undergraduate Mathematics Series
ISBN-13: 9783031548307
The primary aim of this text is to help transition undergraduates to study graduate level mathematics. It unites real and complex analysis after developing the basic techniques and aims at a larger readership than that of similar textbooks that have been published, as fewer mathematical requisites are required. The idea is to present analysis as a whole and emphasize the strong connections between various branches of the field. Ample examples and exercises reinforce concepts, and a helpful bibliography guides those wishing to delve deeper into particular topics. Graduate students who are studying for their qualifying exams in analysis will find use in this text, as well as those looking to advance their mathematical studies or who are moving on to explore another quantitative science.
Chapter 1 contains many tools for higher mathematics; its content is easily accessible, though not elementary. Chapter 2 focuses on topics in real analysis such as p-adic completion, Banach Contraction Mapping Theorem and its applications, Fourier series, Lebesgue measure and integration. One of this chapter’s unique features is its treatment of functional equations. Chapter 3 covers the essential topics in complex analysis: it begins with a geometric introduction to the complex plane, then covers holomorphic functions, complex power series, conformal mappings, and the Riemann mapping theorem. In conjunction with the Bieberbach conjecture, the power and applications of Cauchy’s theorem through the integral formula and residue theorem are presented.
Preface.- Introductory Analysis.- Real Analysis.- Complex Analysis.- Bibliography.-Index
Format: Hardback, 318 pages, height x width: 235x155 mm, 23 Illustrations, color; 10 Illustrations, black and white; X, 318 p. 33 illus., 23 illus. in color., 1 Hardback
Series: CIM Series in Mathematical Sciences 7
Pub. Date: 12-May-2024
This proceedings volume gathers selected, carefully reviewed works presented at the Portugal-Italy Conference on Nonlinear Differential Equations and Applications (PICNDEA22), held on July 4-6, 2022, at the University of Evora, Portugal.
The main focus of this work lies in non-linear problems originating in applications and their treatment with numerical analysis. The reader will also find new advances on topics such as ordinary and partial differential equations, numerical analysis, topological and variational methods, fluid mechanics, operator theory, stability, and more.
The Portugal-Italy Conference on Nonlinear Differential Equations and Applications convenes Italian and Portuguese researchers in differential equations and their applications to amplify previous collaboration and to follow and discuss new topics in the area. Reflecting the increasing teamwork involving the two mathematical communities, the conference has been opened to researchers from all nationalities.
While researchers in analysis and related fields are the primary readership of this volume, PhD students can rely on this book as a valuable source to keep pace with recent advances in differential equations and cutting-edge applications.
Preface.- Some Optimal Design Problems with Perimeter Penalisation.- On
a Rotational Smagorinsky model for turbulent fluids: an overview of recent
results in the steady and unsteady case.- On a forward and a backward
stochastic Euler equation.- Keller-Segel System: A Survey on Radial Steady
States.- The Kernel of The Strain Tensor for Solenoidal Vector Fields with
Homogeneous Normal Trace.- Power Law Approximation Results for Optimal Design
Problems.- Long-time behaviour for solutions of systems of PDEs modeling
suspension bridges.- Positive Solutions for The Fractional P-Laplacian Via
Mixed Topological and Variational Methods.- Some Remarks on The Virtual
Element Method for The Linear Elasticity Problem in Mixed Form.- On the
Existence and Stability of 2d Compressible Current-Vortex Sheets.-
Navier-Stokes Equations with Regularized Directional Boundary Condition.-
Local and Nonlocal Liquid Drop Models.- Mathematical Analysis of Turbulent
Flows Through Permeable Media.- Quantitative Study of The Stabilization
Parameter in The Virtual Element Method.- Geometric Optics for Surface Waves
on The PlasmaVacuum Interface: Higher Order Expansion.- Combined
Numerical/Experimental Analysis for Intracranial Aneurysms in a Computational
Hemodynamics Patient-Specific Framework.
Format: Paperback / softback, 243 pages, height x width: 240x168 mm, 9 Illustrations, black and white; XIX, 243 p. 9 illus., 1 Paperback / softback
Series: Frontiers in Mathematics
Pub. Date: 29-Apr-2024
This monograph deals with the Hadamard products of algebraic varieties. A typical subject of study in Algebraic Geometry are varieties constructed from other geometrical objects. The most well-known example is constituted by the secant varieties, which are obtained through the construction of the join of two algebraic varieties, which, in turn, is based on the operation of summing two vectors. However, other constructions are possible through a change of the basic operation. One remarkable case is based on the Hadamard product of two vectors. While secant varieties of algebraic varieties have been studied extensively and systematically, the same is not yet true for the Hadamard products of algebraic varieties. This monograph aims to bridge this gap in the literature.
The topic is presented in a self-contained manner, and it is accessible to all readers with sound knowledge of Commutative Algebra and Algebraic Geometry. Both experienced researchers and students can profit from this monograph, which will guide them through the subject. The foundational aspects of the Hadamard products of algebraic varieties are covered and some connections both within and outside Algebraic Geometry are presented. The theoretical and algorithmic aspects of the subject are considered to demonstrate the effectiveness of the results presented. Thus, this monograph will also be useful to researchers in other fields, such as Algebraic Statistics, since it provides several algebraic and geometric results on such products.
Hadamard products.- Linear spaces.- Not generic cases in P2.- Grids and rulings.- Degenerate varieties.- Hypersurfaces.- Binomial varieties.- Hilbert functions.- Star configurations.- Gorenstein sets of points in P3.- Pure Commutative Algebra.- Open questions.
Format: Hardback, 641 pages, height x width: 235x155 mm, 39 Tables, color; 38 Illustrations, color; 64 Illustrations, black and white; X, 641 p. 102 illus., 38 illus. in color., 1 Hardback
Pub. Date: 29-Apr-2024
ISBN-13: 9783031542657
This monograph meticulously examines the contributions of French mathematician Michel Chasles to 19th-century geometry. Through an in-depth analysis of Chasles' extensive body of work, the author examines six pivotal arguments which collectively reshape the foundations of geometry. Chasles introduces a novel form of polarity, termed "parabolic," to the graphic context, so expressing the metric properties by means of this specific polarity?a foundational argument. Beyond the celebrated "Chasles theorem," he extends his analysis to the movement of a rigid body, employing concepts derived from projective geometry. This approach is consistently applied across diverse domains. Chasles employs the same methodology to analyze systems of forces. The fourth argument examined by the author concerns the principle of virtual velocities, which can also be addressed through a geometric analysis. In the fifth chapter, Chasles' philosophy of duality is explained. It is grounded on the duality principles of projective geometry. Finally, the author presents Chasles’ synthetic solution for the intricate problem of ellipsoid attraction?the sixth and concluding chapter. Throughout these explorations, Chasles engages in a dynamic scientific dialogue with leading physicists and mathematicians of his era, revealing diverse perspectives and nuances inherent in these discussions.
Tailored for historians specializing in mathematics and geometry, this monograph also beckons philosophers of mathematics and science, offering profound insights into the philosophical, epistemological, and methodological dimensions of Chasles' groundbreaking contributions. Providing a comprehensive understanding of Chasles' distinctive perspective on 19th-century geometry, this work stands as a valuable resource for scholars and enthusiasts alike.
Introduction.- Chasles foundational programme for geometry.-
Displacement of a rigid body.- Chasles and the systems of forces.- The
principle of virtual velocities.- Chasles philosophy of duality.- Chasles
and the ellipsoid attraction.- Conclusion.