Mathematical Analysis II

  • Filename: mathematical-analysis-ii.
  • ISBN: 9783319127576
  • Release Date: 2015-02-07
  • Number of pages: 559
  • Author: Claudio Canuto
  • Publisher: Springer



The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis. The contents are organised to suit, in particular, students of Engineering, Computer Science and Physics, all areas in which mathematical tools play a crucial role. The basic notions and methods concerning integral and differential calculus for multivariable functions, series of functions and ordinary differential equations are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The pedagogical layout echoes the one used in the companion text Mathematical Analysis I. The book’s structure has a specifically-designed modular nature, which allows for great flexibility in the preparation of a lecture course on Mathematical Analysis. The style privileges clarity in the exposition and a linear progression through the theory. The material is organised on two levels. The first, reflected in this book, allows students to grasp the essential ideas, familiarise with the corresponding key techniques and find the proofs of the main results. The second level enables the strongly motivated reader to explore further into the subject, by studying also the material contained in the appendices. Definitions are enriched by many examples, which illustrate the properties discussed. A host of solved exercises complete the text, at least half of which guide the reader to the solution. This new edition features additional material with the aim of matching the widest range of educational choices for a second course of Mathematical Analysis.

Mathematical Analysis II

  • Filename: mathematical-analysis-ii.
  • ISBN: 884701784X
  • Release Date: 2011-01-01
  • Number of pages: 543
  • Author: Claudio Canuto
  • Publisher: Springer Science & Business Media



The purpose of this textbook is to present an array of topics in Calculus, and conceptually follow our previous effort Mathematical Analysis I.The present material is partly found, in fact, in the syllabus of the typical second lecture course in Calculus as offered in most Italian universities. While the subject matter known as `Calculus 1' is more or less standard, and concerns real functions of real variables, the topics of a course on `Calculus 2'can vary a lot, resulting in a bigger flexibility. For these reasons the Authors tried to cover a wide range of subjects, not forgetting that the number of credits the current programme specifications confers to a second Calculus course is not comparable to the amount of content gathered here. The reminders disseminated in the text make the chapters more independent from one another, allowing the reader to jump back and forth, and thus enhancing the versatility of the book. On the website: http://calvino.polito.it/canuto-tabacco/analisi 2, the interested reader may find the rigorous explanation of the results that are merely stated without proof in the book, together with useful additional material. The Authors have completely omitted the proofs whose technical aspects prevail over the fundamental notions and ideas. The large number of exercises gathered according to the main topics at the end of each chapter should help the student put his improvements to the test. The solution to all exercises is provided, and very often the procedure for solving is outlined.

Solving Numerical PDEs Problems Applications Exercises

  • Filename: solving-numerical-pdes-problems-applications-exercises.
  • ISBN: 9788847024120
  • Release Date: 2012-04-05
  • Number of pages: 434
  • Author: Luca Formaggia
  • Publisher: Springer Science & Business Media



This book stems from the long standing teaching experience of the authors in the courses on Numerical Methods in Engineering and Numerical Methods for Partial Differential Equations given to undergraduate and graduate students of Politecnico di Milano (Italy), EPFL Lausanne (Switzerland), University of Bergamo (Italy) and Emory University (Atlanta, USA). It aims at introducing students to the numerical approximation of Partial Differential Equations (PDEs). One of the difficulties of this subject is to identify the right trade-off between theoretical concepts and their actual use in practice. With this collection of examples and exercises we try to address this issue by illustrating "academic" examples which focus on basic concepts of Numerical Analysis as well as problems derived from practical application which the student is encouraged to formalize in terms of PDEs, analyze and solve. The latter examples are derived from the experience of the authors in research project developed in collaboration with scientists of different fields (biology, medicine, etc.) and industry. We wanted this book to be useful both to readers more interested in the theoretical aspects and those more concerned with the numerical implementation.

A Textbook on Ordinary Differential Equations

  • Filename: a-textbook-on-ordinary-differential-equations.
  • ISBN: 9783319164083
  • Release Date: 2015-06-05
  • Number of pages: 331
  • Author: Shair Ahmad
  • Publisher: Springer



This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.

A Primer on PDEs

  • Filename: a-primer-on-pdes.
  • ISBN: 9788847028623
  • Release Date: 2013-05-13
  • Number of pages: 489
  • Author: Sandro Salsa
  • Publisher: Springer Science & Business Media



This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations during the last decade at the Politecnico of Milan. The main purpose of these courses was twofold: on the one hand, to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences and on the other hand to give them a solid background for numerical methods, such as finite differences and finite elements.

Calculus Problems

  • Filename: calculus-problems.
  • ISBN: 3319154273
  • Release Date: 2016-11-08
  • Number of pages: 366
  • Author: Marco Baronti
  • Publisher: Springer



This book, intended as a practical working guide for calculus students, includes 450 exercises. It is designed for undergraduate students in Engineering, Mathematics, Physics, or any other field where rigorous calculus is needed, and will greatly benefit anyone seeking a problem-solving approach to calculus. Each chapter starts with a summary of the main definitions and results, which is followed by a selection of solved exercises accompanied by brief, illustrative comments. A selection of problems with indicated solutions rounds out each chapter. A final chapter explores problems that are not designed with a single issue in mind but instead call for the combination of a variety of techniques, rounding out the book’s coverage. Though the book’s primary focus is on functions of one real variable, basic ordinary differential equations (separation of variables, linear first order and constant coefficients ODEs) are also discussed. The material is taken from actual written tests that have been delivered at the Engineering School of the University of Genoa. Literally thousands of students have worked on these problems, ensuring their real-world applicability.

Mathematical Analysis I

  • Filename: mathematical-analysis-i.
  • ISBN: 9783319127729
  • Release Date: 2015-04-08
  • Number of pages: 492
  • Author: Claudio Canuto
  • Publisher: Springer



The purpose of the volume is to provide a support for a first course in Mathematics. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variable are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices when planning an introductory lecture course. The book may in fact be employed at three levels of depth. At the elementary level the student is supposed to grasp the very essential ideas and familiarise with the corresponding key techniques. Proofs to the main results befit the intermediate level, together with several remarks and complementary notes enhancing the treatise. The last, and farthest-reaching, level requires the additional study of the material contained in the appendices, which enable the strongly motivated reader to explore further into the subject. Definitions and properties are furnished with substantial examples to stimulate the learning process. Over 350 solved exercises complete the text, at least half of which guide the reader to the solution. This new edition features additional material with the aim of matching the widest range of educational choices for a first course of Mathematics.

Mathematical Analysis II

  • Filename: mathematical-analysis-ii.
  • ISBN: 9783319127576
  • Release Date: 2015-02-07
  • Number of pages: 559
  • Author: Claudio Canuto
  • Publisher: Springer



The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis. The contents are organised to suit, in particular, students of Engineering, Computer Science and Physics, all areas in which mathematical tools play a crucial role. The basic notions and methods concerning integral and differential calculus for multivariable functions, series of functions and ordinary differential equations are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The pedagogical layout echoes the one used in the companion text Mathematical Analysis I. The book’s structure has a specifically-designed modular nature, which allows for great flexibility in the preparation of a lecture course on Mathematical Analysis. The style privileges clarity in the exposition and a linear progression through the theory. The material is organised on two levels. The first, reflected in this book, allows students to grasp the essential ideas, familiarise with the corresponding key techniques and find the proofs of the main results. The second level enables the strongly motivated reader to explore further into the subject, by studying also the material contained in the appendices. Definitions are enriched by many examples, which illustrate the properties discussed. A host of solved exercises complete the text, at least half of which guide the reader to the solution. This new edition features additional material with the aim of matching the widest range of educational choices for a second course of Mathematical Analysis.

Partial Differential Equations in Action

  • Filename: partial-differential-equations-in-action.
  • ISBN: 9783319312385
  • Release Date: 2016-10-04
  • Number of pages: 686
  • Author: Sandro Salsa
  • Publisher: Springer



The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.The third edition contains a few text and formulas revisions and new exercises.

Discrete Calculus

  • Filename: discrete-calculus.
  • ISBN: 9783319030388
  • Release Date: 2016-09-11
  • Number of pages: 665
  • Author: Carlo Mariconda
  • Publisher: Springer



This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet user-friendly approach. This is particularly useful in combinatorics, a field where, all too often, exercises are solved by means of ad hoc tricks. The book contains more than 400 examples and about 300 problems, and the reader will be able to find the proof of every result. To further assist students and teachers, important matters and comments are highlighted, and parts that can be omitted, at least during a first and perhaps second reading, are identified.

Principles of Mathematical Analysis

  • Filename: principles-of-mathematical-analysis.
  • ISBN: 0070856133
  • Release Date: 1976
  • Number of pages: 342
  • Author: Walter Rudin
  • Publisher: McGraw-Hill Publishing Company



The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Python for Data Analysis

  • Filename: python-for-data-analysis.
  • ISBN: 9781449319793
  • Release Date: 2012-10-22
  • Number of pages: 452
  • Author: Wes McKinney
  • Publisher: "O'Reilly Media, Inc."



Presents case studies and instructions on how to solve data analysis problems using Python.

Unicode Explained

  • Filename: unicode-explained.
  • ISBN: 9780596101213
  • Release Date: 2006-06-28
  • Number of pages: 658
  • Author: Jukka Korpela
  • Publisher: "O'Reilly Media, Inc."



Fundamentally, computers just deal with numbers. They store letters and other characters by assigning a number for each one. There are hundreds of different encoding systems for mapping characters to numbers, but Unicode promises a single mapping. Unicode enables a single software product or website to be targeted across multiple platforms, languages and countries without re-engineering. It's no wonder that industry giants like Apple, Hewlett-Packard, IBM andMicrosoft have all adopted Unicode. Containing everything you need to understand Unicode, this comprehensive reference from O'Reilly takes you on a detailed guide through the complex character world. For starters, it explains how to identify and classify characters - whether they're common, uncommon, or exotic. It then shows you how to type them, utilize their properties, and process character data in a robust manner. The book is broken up into three distinct parts. The first few chapters provide you with a tutorial presentation of Unicode and character data. It gives you a firm grasp of the terminology you need to reference various components, including character sets, fonts and encodings, glyphs and character repertoires. The middle section offers more detailed information about using Unicode and other character codes. It explains the principles and methods of defining character codes, describes some of the widely used codes, and presents code conversion techniques. It also discusses properties of characters, collation and sorting, line breaking rules and Unicode encodings. The final four chapters cover more advanced material, such as programming to support Unicode. You simply can't afford to be without the nuggets of valuable information detailed in Unicode Explained.

Unicode Demystified

  • Filename: unicode-demystified.
  • ISBN: 0201700522
  • Release Date: 2003
  • Number of pages: 853
  • Author: Richard Gillam
  • Publisher: Addison-Wesley Professional



Unicode provides a unique number for every character a computer deals with, no matter what platform, what program or what language. This text provides a hands-on programmer's guide to Unicode. It offers specific guidance on integrating Unicode with other technologies, including Java.

Mathematical Finance Theory Review and Exercises

  • Filename: mathematical-finance-theory-review-and-exercises.
  • ISBN: 9783319013572
  • Release Date: 2014-02-10
  • Number of pages: 285
  • Author: Emanuela Rosazza Gianin
  • Publisher: Springer Science & Business Media



The book collects over 120 exercises on different subjects of Mathematical Finance, including Option Pricing, Risk Theory, and Interest Rate Models. Many of the exercises are solved, while others are only proposed. Every chapter contains an introductory section illustrating the main theoretical results necessary to solve the exercises. The book is intended as an exercise textbook to accompany graduate courses in mathematical finance offered at many universities as part of degree programs in Applied and Industrial Mathematics, Mathematical Engineering, and Quantitative Finance.

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