Format: Hardback, 268 pages, height x width: 235x155 mm, 20 Illustrations, color; 46 Illustrations, black and white; X, 268 p. 66 illus., 20 illus. in color
Series: Springer Undergraduate Texts in Mathematics and Technology
Pub. Date: 26-Sep-2023
ISBN-13: 9783031366543
This text provides a detailed and self-contained introduction to the core topics of optimal control for finite-dimensional deterministic dynamical systems. Skillfully designed to guide the student through the development of the subject, the book provides a rich collection of examples, exercises, illustrations, and applications, to support comprehension of the material. Solutions to odd-numbered exercises are included, while a complete set of solutions is available to instructors who adopt the text for their class. The book is adaptable to coursework for final year undergraduates in (applied) mathematics or beginning graduate students in engineering. Required mathematical background includes calculus, linear algebra, a basic knowledge of differential equations, as well as a rudimentary acquaintance with control systems.
The book has developed out of lecture notes that were tested, adapted, and expanded over many years of teaching. Chapters 1-4 constitute the material for a basic course on optimal control, covering successively the calculus of variations, minimum principle, dynamic programming, and linear quadratic control. The additional Chapter 5 provides brief views to a number of selected topics related to optimal control, which are meant to peak the readerfs interest. Some mathematical background is summarized in Appendix A for easy review. Appendix B recalls some of the basics of differential equations and also provides a detailed treatment of Lyapunov stability theory including LaSallefs invariance principle, as occasionally used in Chapters 3 and 4.
1. Calculus of Variations.-
2. Minimum Principle.-
3. Dynamic Programming.-
4. Linear Quadratic Control.-
5. Glimpses of Related Topics.- A. Background Material.- B. Differential Equations and Lyapunov Functions.- Solutions to Odd Numbered Exercises.- Bibliography.- Index.
Format: Hardback, 162 pages, height x width: 235x155 mm, 34 Illustrations, color; X, 162 p. 34 illus. in color
Pub. Date: 12-Oct-2023
ISBN-13: 9783031384158
This book tells the story of the probability integral, the approaches to analyzing it throughout history, and the many areas of science where it arises. The so-called probability integral, the integral over the real line of a Gaussian function, occurs ubiquitously in mathematics, physics, engineering and probability theory. Stubbornly resistant to the undergraduate toolkit for handling integrals, calculating its value and investigating its properties occupied such mathematical luminaries as De Moivre, Laplace, Poisson, and Liouville. This book introduces the probability integral, puts it into a historical context, and describes the different approaches throughout history to evaluate and analyze it. The author also takes entertaining diversions into areas of math, science, and engineering where the probability integral arises: as well as being indispensable to probability theory and statistics, it also shows up naturally in thermodynamics and signal processing. Designed to be accessible to anyone at the undergraduate level and above, this book will appeal to anyone interested in integration techniques, as well as historians of math, science, and statistics.
Preface
Chapter 1: De Moivre and the Discovery of the Probability Integral Evaluating the Probability Integral- Part 1
Chapter 2: Laplace's First Derivation
Chapter 3: How Euler Could Have Done It Before Laplace (but did he?)
Chapter 4: Laplace's Second Derivation
Chapter 5: Generalizing the Probability Integral
Chapter 6: Poisson's Derivation Interlude
Chapter 7: Rice's Radar Integral Chapter 8: Liouville's Proof That e x2dx Has No Finite Form
Chapter 9: How the Error Function Appeared in the Electrical Response of the Trans-Atlantic Telegraph Cable Evaluating the Probability Integral- Part 2
Chapter 10: Doing the Probability Integral with Differentiation
Chapter 11: The Probability Integral as a Volume
Chapter 12: How Cauchy Could Have Done It (but didn't)
Chapter 13: Fourier Has the Last Word
Format: Paperback / softback, 171 pages, height x width: 235x155 mm, 77 Tables, color; 66 Illustrations, color;
14 Illustrations, black and white; X, 171 p. 80 illus., 66 illus. in color.,
Series: Compact Textbooks in Mathematics
Pub. Date: 07-Oct-2023
ISBN-13: 9783031398377
This open access book covers the main topics for a course on the differential geometry of curves and surfaces. Unlike the common approach in existing textbooks, there is a strong focus on variational problems, ranging from elastic curves to surfaces that minimize area, or the Willmore functional. Moreover, emphasis is given on topics that are useful for applications in science and computer graphics. Most often these applications are concerned with finding the shape of a curve or a surface that minimizes physically meaningful energy. Manifolds are not introduced as such, but the presented approach provides preparation and motivation for a follow-up course on manifolds, and topics like the Gauss-Bonnet theorem for compact surfaces are covered.
Part I Curves.- Curves in Rn.- Variations of Curves.- Curves in R2.-
Parallel Normal Fields. - Curves in R3.- Part II Surfaces.- Surfaces and
Riemannian Geometry.- Integration and Stokes' Theorem.- Curvature.-
Levi-Civita Connection.- Total Gaussian Curvature.- Closed Surfaces. -
Variations of Surfaces.- Willmore Surfaces
Format: Paperback / softback, 120 pages, height x width: 240x168 mm, 8 Tables, color; 11 Illustrations, color;
34 Illustrations, black and white; X, 120 p. 45 illus., 11 illus. in color.
Series: Oberwolfach Seminars 52
Pub. Date: 06-Oct-2023
ISBN-13: 9783031394003
This book is based on the lectures given at the Oberwolfach Seminar held in Fall 2021. Logarithmic Gromov-Witten theory lies at the heart of modern approaches to mirror symmetry, but also opens up a number of new directions in enumerative geometry of a more classical flavour. Tropical geometry forms the calculus through which calculations in this subject are carried out. These notes cover the foundational aspects of this tropical calculus, geometric aspects of the degeneration formula for Gromov-Witten invariants, and the practical nuances of working with and enumerating tropical curves. Readers will get an assisted entry route to the subject, focusing on examples and explicit calculations.
Part I: Toric geometry and logarithmic curve counting.- Geometry of toric varieties.- Compactifying subvarieties of tori.- Points on the Riemann sphere.- Stable maps and logarithmic stable maps.- Cheat codes for logarithmic GW theory.- Part II: Hurwitz theory.- Classical Hurwitz Theory and Moduli Spaces.- Tropical Hurwitz Theory.- Hurwitz Numbers from Piecewise Polynomials.- Part III Tropical plane curve counting.- Introduction to plane tropical curve counts.- Lattice paths and the Caporaso-Harris formula.- The Caporaso-Harris formula for tropical plane curves and floor diagrams.
Format: Paperback / softback, 216 pages, height x width: 235x155 mm, 24 Illustrations, color;
9 Illustrations, black and white; XVIII, 216 p. 33 illus., 24 illus. in color.
Series: Lecture Notes in Statistics 226
Pub. Date: 19-Sep-2023
ISBN-13: 9783031359170
This textbook provides a concise introduction to optimal experimental design and efficiently prepares the reader for research in the area. It presents the common concepts and techniques for linear and nonlinear models as well as Bayesian optimal designs. The last two chapters are devoted to particular themes of interest, including recent developments and hot topics in optimal experimental design, and real-world applications. Numerous examples and exercises are included, some of them with solutions or hints, as well as references to the existing software for computing designs. The book is primarily intended for graduate students and young researchers in statistics and applied mathematics who are new to the field of optimal experimental design. Given the applications and the way concepts and results are introduced, parts of the text will also appeal to engineers and other applied researchers.
Preface.- Motivating Introduction.- Linear Models.- Nonlinear Models.- Bayesian Optimal Designs.- Hot Topics.- Real Case Examples.- Appendices.- References.- Index.
Format: Hardback, 220 pages, height x width: 235x155 mm, 3 Tables, color; 3 Illustrations, color;
1 Illustrations, black and white; X, 220 p. 4 illus., 3 illus. in color.
Series: Operator Theory: Advances and Applications 292
Pub. Date: 19-Sep-2023
ISBN-13: 9783031380198
This volume collects contributions from participants in the IWOTA conference held virtually at Lancaster, UK, originally scheduled in 2020 but postponed to August 2021. It includes both survey articles and original research papers covering some of the main themes of the meeting.
Criteria for eventual domination of operator semigroups and resolvents.-
Bounded functional calculi for unbounded operators.- A noncommutative Bishop
peak interpolation-set theorem.- Operator algebras associated with graphs and
categories of paths: a survey.- Non-autonomous Desch-Schappacher
perturbations.- Finite sections of periodic Schroedinger operators.- The
Jacobi operator and its Donoghue m-functions.- Entanglement breaking rank via
complementary channels and multiplicative domains.- On the Bergman projection
and kernel in periodic planar domains.- Brown measure of R-diagonal
operators, revisited.
Format: Hardback, 440 pages, height x width: 235x155 mm, 1 Tables, color; 1 Illustrations, color;
27 Illustrations, black and white; X, 440 p. 28 illus., 1 illus. in color.
Series: Progress in Mathematics 348
Pub. Date: 02-Oct-2023
ISBN-13: 9783031379000
This work gives a coherent introduction to isoperimetric inequalities in Riemannian manifolds, featuring many of the results obtained during the last 25 years and discussing different techniques in the area.
Written in a clear and appealing style, the book includes sufficient introductory material, making it also accessible to graduate students. It will be of interest to researchers working on geometric inequalities either from a geometric or analytic point of view, but also to those interested in applying the described techniques to their field.
Introduction.- The isoperimetric profile of compact manifolds.- The
isoperimetric profile of non-compact manifolds.- Symmetrization.- Small
volumes.- Surfaces.- Space forms.- Manifolds with boundary.- Bibliography.