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Differential Geometry: A First Course is an introduction to the classical theory of space curves and surfaces offered at the Graduate and Post- Graduate courses in Mathematics. Based on Serret-Frenet formulae, the theory of space curves is developed and concluded with a detailed discussion on fundamental existence theorem. The theory of surfaces includes the first fundamental form with local intrinsic properties, geodesics on surfaces, the second fundamental form with local non-intrinsic properties and the fundamental equations of the surface theory with several applications.
Slay the calculus monster with this user-friendly guideCalculus For Dummies, 2nd Edition makes calculus manageable—even if you’re one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English instead of math-speak.
A Guide to Real Variables is an aid and conceptual support for students taking an undergraduate course on real analysis. It focuses on concepts, results, examples and illustrative figures, rather than the details of proofs, in order to remain a concise guide which students can dip into. The core topics of a first real analysis course are covered, including sequences, series, modes of convergence, the derivative, the integral and metric spaces. The next book in this series, Folland’s A Guide to Advanced Real Analysis is designed to naturally follow on from this book, and introduce students to graduate level real analysis.
Authors: Bouchard, Bruno, Chassagneux, Jean-FrançoisPresents the various mathematical techniques used in mathematical finance in a single volumeTreats both theoretical aspects and practical applicationsIncludes a chapter on stochastic targets and risk-based pricing techniquesThis book covers the theory of derivatives pricing and hedging as well as techniques used in mathematical finance. The authors use a top-down approach, starting with fundamentals before moving to applications, and present theoretical developments alongside various exercises, providing many examples of practical interest.A
Der vorliegende Band stellt den zweiten Teil eines Analysis-Kurses für Studierende der Mathematik und Physik im ersten Studienjahr dar und beschäftigt sich mit der mehrdimensionalen Differentialrechnung sowie mit gewöhnlichen Differentialgleichungen.
Bei der Darstellung wurde angestrebt, allzu große Abstraktionen zu vermeiden und die Theorie durch viele konkrete Beispiele zu erläutern, insbesondere solche, die für die Physik relevant sind.
Das Buch enthält zahlreiche Übungsaufgaben. Die Neuauflage wurde durch einige neue Abbildungen mit erläuterndem Text ergänzt.
Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. Calculus Essentials For Dummies provides explanations of key concepts for students who may have taken calculus in high school and want to review the most important concepts as they gear up for a faster–paced college course. Free of review and ramp–up material, Calculus Essentials For Dummies sticks to the point with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical two–semester high school calculus class or a college level Calculus I course, from limits and differentiation to integration and infinite series.
Now in its 4th edition, Smith/Minton, Calculus: Early Transcendental Functions offers students and instructors a mathematically sound text, robust exercise sets and elegant presentation of calculus concepts. When packaged with ALEKS Prep for Calculus, the most effective remediation tool on the market, Smith/Minton offers a complete package to ensure students success in calculus. The new edition has been updated with a reorganization of the exercise sets, making the range of exercises more transparent.
This book describes innovative approaches that have been used successfully by a variety of instructors in the undergraduate mathematics courses that follow calculus. These approaches are designed to make upper division mathematics courses more interesting, more attractive, and more beneficial to our students. The authors of the articles in this volume show how this can be done while still teaching mathematics courses. These approaches range from various classroom techniques to novel presentations of material to discussing topics not normally encountered in the typical mathematics curriculum.
For two-semester/three-quarter, first undergraduate courses in Advanced Calculus or Real Analysis.
This book is an easy, readable, intimidation-free analysis textbook. Ideas and methods of proof build upon each other and are explained thoroughly. This is the first text to cover both single and multivariable analysis in such a student friendly setting.
A book on the subject of normal families more than sixty years after the publication of Montel’s treatise Ler;ons sur les familles normales de fonc tions analytiques et leurs applications is certainly long overdue. But, in a sense, it is almost premature, as so much contemporary work is still being produced. To misquote Dickens, this is the best of times, this is the worst of times. The intervening years have seen developments on a broad front, many of which are taken up in this volume. A unified treatment of the classical theory is also presented, with some attempt made to preserve its classical flavour.
Elliptic operators arise naturally in several different mathematical settings, notably in the representation theory of Lie groups, the study of evolution equations, and the examination of Riemannian manifolds. This book develops the basic theory of elliptic operators on Lie groups and thereby extends the conventional theory of parabolic evolution equations to a natural noncommutative context. In order to achieve this goal, the author presents a synthesis of ideas from partial differential equations, harmonic analysis, functional analysis, and the theory of Lie groups.
This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander’s sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner and Taylor.
This manual contains solutions to all exercises from the textbook Vector Calculus by Miroslav Lovric, published by John Wiley & Sons.In most cases, all details of a solution are given. Occasionally, a related theoretical concept, a method or a formula are recalled in order to make the exposition clearer. Details of evaluation of definite integrals are sometimes skipped and the reader is referred to a table of integrals or advised to use a numeric method or appropriate software. (The objective of this course is not to master a dozen integration techniques but rather to understand what the integral involved is all about.)
These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of some classical results on everywhere regularity for scalar-valued weak solutions, the presentation focuses on vector-valued weak solutions to a system of several coupled equations. In the vectorial case, weak solutions may have discontinuities and so are expected, in general, to be regular only outside of a set of measure zero. Several methods are presented concerning the proof of such partial regularity results, and optimal regularity is discussed.
With students of Physics chiefly in mind, we have collected the material on special functions that is most important in mathematical physics and quan tum mechanics. We have not attempted to provide the most extensive collec tion possible of information about special functions, but have set ourselves the task of finding an exposition which, based on a unified approach, ensures the possibility of applying the theory in other natural sciences, since it pro vides a simple and effective method for the independent solution of problems that arise in practice in physics, engineering and mathematics.
Calculus for Cats describes the processes, vocabulary and strategies of calculus for people who like to learn the concepts of a subject before they start trying to operate it. In an irreverent tone, it explains what calculus is, why it’s important, what the procedures are and when to use them. Many people learn subjects like calculus by repeating the procedures but sometimes feel like they don’t really understand what’s going on. This book answers their questions. Over the last decade of the book’s existence, the most common comment it’s received is, "Wow! So that’s how it works! I wish I had this book back when i took the course.&
EVERYTHING YOU NEED TO SCORE A PERFECT 5. Equip yourself to ace the AP Calculus BC Exam with The Princeton Review’s comprehensive study guide—including thorough content reviews, targeted strategies for every question type, access to our AP Connect online portal, and 3 full-length practice tests with complete answer explanations.We don’t have to tell you how tough AP Calculus is—or how important a stellar score on the AP Exam can be to your chances of getting into a top college of your choice. Written by Princeton Review experts who know their way around Calc BC, Cracking the AP Calculus BC Exam will give you:Techniques That Actually Work.•
This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications, chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of topological methods. Only basic knowledge of general analysis is needed, making the book understandable to non-specialists. The main topics in the study of boundary value problems are present in this text, so readers with some experience in functional analysis or differential equations may also find some elements that complement and enrich their tools for solving nonlinear problems.
Authors: Bercovici, Hari, Brown, Arlen, Pearcy, CarlAxiomatic treatment of Lebesgue integration allows quick access to the main convergence of theoremsIncludes a brief introduction to Fourier analysis in the Euclidean settingProvides a treatment of standard measure spaces and analytic setsDetailed index provides easy navigation to the main resultsAbout this TextbookThis book covers the material of a one year course in real analysis. It includes an original axiomatic approach to Lebesgue integration which the authors have found to be effective in the classroom.
The author helps students to comprehend the ideas and concepts behind calculus rather than simply memorize formulas, and to break complicated problems into simple components. A large number of examples are included and this edition includes a new design and systematic use of colour, together with many new exercises and applications.
Applied mathematical modeling is concerned with solving unsteady problems. This book shows how to construct additive difference schemes to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods)and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for systems of equations.
Evolution equations of hyperbolic or more general p-evolution type form an active field of current research. This volume aims to collect some recent advances in the area in order to allow a quick overview of ongoing research. The contributors are first rate mathematicians. This collection of research papers is centred around parametrix constructions and microlocal analysis; asymptotic constructions of solutions; energy and dispersive estimates; and associated spectral transforms. Applications concerning elasticity and general relativity complement the volume.
Many calculus textbooks look to engage students with margin notes, anecdotes, and other devices. But many instructors find these distracting, preferring to captivate their science and engineering students with the beauty of the calculus itself. Taalman and Kohn’s refreshing new textbook is designed to help instructors do just that.
Taalman and Kohn’s Calculus offers a streamlined, structured exposition of calculus that combines the clarity of classic textbooks with a modern perspective on concepts, skills, applications, and theory.
Drawing on their decades of teaching experience, authors have created a calculus text that carries the teacher’s voice beyond the classroom. This book is an expanded version of Calculus: Early Transcendentals by the same authors, with an entire chapter devoted to differential equations, additional sections on other topics, and additional exercises in most sections.That voice—evident in the narrative, the figures, and the questions interspersed in the narrative—is a master teacher leading readers to deeper levels of understanding.
Showing 1–24 of 31 results