The Book | Calculus with Differential Equations |

The Author | Dale E. Varberg |

The Publisher | Prentice Hall |

Release Date | 2006-04 |

Genre | Education |

Pages | 880 |

ISBN | 0132306336 |

Language | English, Spanish, And French |

**READING**: This the shortest mainstream calculus book available. The authors make effective use of computing technology, graphics, and applications, and provide at least two technology projects per chapter. This popular book is correct without being excessively rigorous, up-to-date without being faddish. Maintains a strong geometric and conceptual focus. Emphasizes explanation rather than detailed proofs. Presents definitions consistently throughout to maintain a clear conceptual framework. Provides hundreds of new problems, including problems on approximations, functions defined by tables, and conceptual questions. Ideal for readers preparing for the AP Calculus exam or who want to brush up on their calculus with a no-nonsense, concisely written book.

The Book | Solutions to Calculus and Ordinary Differential Equations |

The Author | N. Gupta; R.S. Dahiya |

The Publisher | Firewall Media |

Release Date | 2006-08-01 |

Genre | |

Pages | 680 |

ISBN | 8170088674 |

Language | English, Spanish, And French |

The Book | Calculus of Variations and Partial Differential Equations |

The Author | Luigi Ambrosio |

The Publisher | Springer Science & Business Media |

Release Date | 2000-01-24 |

Genre | Mathematics |

Pages | 348 |

ISBN | 3540648038 |

Language | English, Spanish, And French |

**READING**: At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

The Book | Ordinary Differential Equations |

The Author | Virginia W. Noonburg |

The Publisher | The Mathematical Association of America |

Release Date | 2014-05-02 |

Genre | Mathematics |

Pages | 315 |

ISBN | 9781939512048 |

Language | English, Spanish, And French |

**READING**: This book presents a modern treatment of material traditionally covered in the sophomore-level course in ordinary differential equations. While this course is usually required for engineering students the material is attractive to students in any field of applied science, including those in the biological sciences. The standard analytic methods for solving first and second-order differential equations are covered in the first three chapters. Numerical and graphical methods are considered, side-by-side with the analytic methods, and are then used throughout the text. An early emphasis on the graphical treatment of autonomous first-order equations leads easily into a discussion of bifurcation of solutions with respect to parameters. The fourth chapter begins the study of linear systems of first-order equations and includes a section containing all of the material on matrix algebra needed in the remainder of the text. Building on the linear analysis, the fifth chapter brings the student to a level where two-dimensional nonlinear systems can be analyzed graphically via the phase plane. The study of bifurcations is extended to systems of equations, using several compelling examples, many of which are drawn from population biology. In this chapter the student is gently introduced to some of the more important results in the theory of dynamical systems. A student project, involving a problem recently appearing in the mathematical literature on dynamical systems, is included at the end of Chapter 5. A full treatment of the Laplace transform is given in Chapter 6, with several of the examples taken from the biological sciences. An appendix contains completely worked-out solutions to all of the odd-numbered exercises. The book is aimed at students with a good calculus background that want to learn more about how calculus is used to solve real problems in today's world. It can be used as a text for the introductory differential equations course, and is readable enough to be used even if the class is being "flipped." The book is also accessible as a self-study text for anyone who has completed two terms of calculus, including highly motivated high school students. Graduate students preparing to take courses in dynamical systems theory will also find this text useful.

The Book | Thomas Calculus |

The Author | Maurice D. Weir |

The Publisher | Addison-Wesley Longman |

Release Date | 2006-08-01 |

Genre | Mathematics |

Pages | 1228 |

ISBN | 032149069X |

Language | English, Spanish, And French |

**READING**: KEY Message: Thomas' Calculus including Second-order Differential Equations responds to the needs of today's readers by developing their conceptual understanding while strengthening their skills in algebra and trigonometry,two areas of knowledge vital to the mastery of calculus. This book offers a full range of exercises, a precise and conceptual presentation, and a new media package designed specifically to meet the needs of today's readers. The exercises gradually increase in difficulty, helping readers learn to generalize and apply the concepts. The refined table of contents introduces the exponential, logarithmic, and trigonometric functions in Chapter 7 of the text. KEY TOPICS: Limits and Derivatives, Differentiation, Applications of Derivatives, Integration, Applications of Definite Integrals, Transcendental Functions, Techniques of Integration, Further Applications of Integration, Conic Sections and Polar Coordinates, Infinite Sequences and Series, Vectors and the Geometry of Space, Vector-Valued Functions and Motion in Space, Partial Derivatives, Multiple Integrals, Integration in Vector Fields, Second-order Differential Equations. MARKET: For all readers interested in Calculus.

The Book | A Treatise on Differential Equations and on the Calculus of Finite Differences |

The Author | John Hymers |

The Publisher | |

Release Date | 1839 |

Genre | Difference equations |

Pages | 240 |

ISBN | HARVARD:32044091890483 |

Language | English, Spanish, And French |

The Book | Cohomological Analysis of Partial Differential Equations and Secondary Calculus |

The Author | A. M. Vinogradov |

The Publisher | American Mathematical Soc. |

Release Date | 2001-10-16 |

Genre | |

Pages | |

ISBN | 0821897993 |

Language | English, Spanish, And French |

**READING**: This book is dedicated to fundamentals of a new theory, which is an analog of affine algebraic geometry for (nonlinear) partial differential equations. This theory grew up from the classical geometry of PDE's originated by S. Lie and his followers by incorporating some nonclassical ideas from the theory of integrable systems, the formal theory of PDE's in its modern cohomological form given by D. Spencer and H. Goldschmidt and differential calculus over commutative algebras (Primary Calculus). The main result of this synthesis is Secondary Calculus on diffieties, new geometrical objects which are analogs of algebraic varieties in the context of (nonlinear) PDE's. Secondary Calculus surprisingly reveals a deep cohomological nature of the general theory of PDE's and indicates new directions of its further progress. Recent developments in quantum field theory showed Secondary Calculus to be its natural language, promising a nonperturbative formulation of the theory. In addition to PDE's themselves, the author describes existing and potential applications of Secondary Calculus ranging from algebraic geometry to field theory, classical and quantum, including areas such as characteristic classes, differential invariants, theory of geometric structures, variational calculus, control theory, etc. This book, focused mainly on theoretical aspects, forms a natural dipole with Symmetries and Conservation Laws for Differential Equations of Mathematical Physics, Volume 182 in this same series, Translations of Mathematical Monographs, and shows the theory "in action".

The Book | Calculus and Differential Equations with MATLAB |

The Author | Pramote Dechaumphai |

The Publisher | |

Release Date | 2016-05-04 |

Genre | |

Pages | 454 |

ISBN | 1783322659 |

Language | English, Spanish, And French |

The Book | Ordinary Differential Equations |

The Author | W. T. Ang |

The Publisher | Universal-Publishers |

Release Date | 2008 |

Genre | Mathematics |

Pages | 204 |

ISBN | 9781599429755 |

Language | English, Spanish, And French |

**READING**: This introductory course in ordinary differential equations, intended for junior undergraduate students in applied mathematics, science and engineering, focuses on methods of solution and applications rather than theoretical analyses. Applications drawn mainly from dynamics, population biology and electric circuit theory are used to show how ordinary differential equations appear in the formulation of problems in science and engineering. The calculus required to comprehend this course is rather elementary, involving differentiation, integration and power series representation of only real functions of one variable. A basic knowledge of complex numbers and their arithmetic is also assumed, so that elementary complex functions which can be used for working out easily the general solutions of certain ordinary differential equations can be introduced. The pre-requisites just mentioned aside, the course is mainly self-contained. To promote the use of this course for self-study, suggested solutions are not only given to all set exercises, but they are also by and large complete with details.

**Malliavin Calculus with Applications to Stochastic Partial Differential Equations by Marta Sanz-Sole**

The Book | Malliavin Calculus with Applications to Stochastic Partial Differential Equations |

The Author | Marta Sanz-Sole |

The Publisher | CRC Press |

Release Date | 2005-08-17 |

Genre | Mathematics |

Pages | 150 |

ISBN | 1439818940 |

Language | English, Spanish, And French |

**READING**: Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics. This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself based on a general Gaussian space, going from the simple, finite-dimensional setting to the infinite-dimensional one. The final three chapters discuss recent research on regularity of the solution of stochastic partial differential equations and the existence and smoothness of their probability laws. About the author: Marta Sanz-Solé is Professor at the Faculty of Mathematics, University of Barcelona. She is a leading member of the research group on stochastic analysis at Barcelona, and in 1998 she received the Narcis Monturiol Award of Scientific and Technological Excellence from the autonomous government of Catalonia.

The Book | Differential Equations and the Calculus of Variations |

The Author | Lev Elsgolts |

The Publisher | |

Release Date | 2003-12-01 |

Genre | Mathematics |

Pages | 444 |

ISBN | 1410210677 |

Language | English, Spanish, And French |

**READING**: Originally published in the Soviet Union, this text is meant for students of higher schools and deals with the most important sections of mathematics - differential equations and the calculus of variations. The first part describes the theory of differential equations and reviews the methods for integrating these equations and investigating their solutions. The second part gives an idea of the calculus of variations and surveys the methods for solving variational problems. The book contains a large number of examples and problems with solutions involving applications of mathematics to physics and mechanics. Apart from its main purpose the textbook is of interest to expert mathematicians. Lev Elsgolts (deceased) was a Doctor of Physico-Mathematical Sciences, Professor at the Patrice Lumumba University of Friendship of Peoples. His research work was dedicated to the calculus of variations and differential equations. He worked out the theory of differential equations with deviating arguments and supplied methods for their solution. Lev Elsgolts was the author of many printed works. Among others, he wrote the well-known books Qualitative Methods in Mathematical Analysis and Introduction to the Theory of Differential Equations with Deviating Arguments. In addition to his research work Lev Elsgolts taught at higher schools for over twenty years.

The Book | Foundations of Differential Calculus |

The Author | Euler |

The Publisher | Springer Science & Business Media |

Release Date | 2000-05-23 |

Genre | Mathematics |

Pages | 194 |

ISBN | 0387985344 |

Language | English, Spanish, And French |

**READING**: What differential calculus, and, in general, analysis ofthe infinite, might be can hardly be explainedto those innocent ofany knowledge ofit. Nor can we here offer a definition at the beginning of this dissertation as is sometimes done in other disciplines. It is not that there is no clear definition of this calculus; rather, the fact is that in order to understand the definition there are concepts that must first be understood. Besides those ideas in common usage, there are also others from finite analysis that are much less common and are usually explained in the courseofthe development ofthe differential calculus. For this reason, it is not possible to understand a definition before its principles are sufficiently clearly seen. In the first place, this calculus is concerned with variable quantities. Although every quantity can naturally be increased or decreased without limit, still, since calculus is directed to a certain purpose, we think of some quantities as being constantly the same magnitude, while others change through all the .stages of increasing and decreasing. We note this distinc tion and call the former constant quantities and the latter variables. This characteristic difference is not required by the nature of things, but rather because of the special question addressed by the calculus.

The Book | Differential Equations |

The Author | Charles Henry Edwards |

The Publisher | Prentice Hall |

Release Date | 2008 |

Genre | Computers |

Pages | 575 |

ISBN | UCSC:32106018838745 |

Language | English, Spanish, And French |

**READING**: This practical book reflects the new technological emphasis that permeates differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; it does not concentrate on traditional manual methods but rather on new computer-based methods that lead to a wider range of more realistic applications. The book starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the book. For mathematicians and those in the field of computer science and engineering.

The Book | Fractional Differential Equations |

The Author | Igor Podlubny |

The Publisher | Elsevier |

Release Date | 1998-10-27 |

Genre | Mathematics |

Pages | 340 |

ISBN | 0080531989 |

Language | English, Spanish, And French |

**READING**: This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'. This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models. In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research. A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. A unique survey of many applications of fractional calculus Presents basic theory Includes a unified presentation of selected classical results, which are important for applications Provides many examples Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives

The Book | An Introduction to the Fractional Calculus and Fractional Differential Equations |

The Author | Kenneth S. Miller |

The Publisher | Wiley-Interscience |

Release Date | 1993-06-02 |

Genre | Mathematics |

Pages | 384 |

ISBN | 0471588849 |

Language | English, Spanish, And French |

**READING**: Commences with the historical development of fractional calculus, its mathematical theory—particularly the Riemann-Liouville version. Numerous examples and theoretical applications of the theory are presented. Features topics associated with fractional differential equations. Discusses Weyl fractional calculus and some of its uses. Includes selected physical problems which lead to fractional differential or integral equations.

The Book | The Elements of the Integral Calculus |

The Author | John Radford Young |

The Publisher | |

Release Date | 1839 |

Genre | Calculus, Integral |

Pages | 292 |

ISBN | HARVARD:32044091886440 |

Language | English, Spanish, And French |

The Book | Differential Equations and Boundary Value Problems |

The Author | Charles Henry Edwards |

The Publisher | Prentice Hall |

Release Date | 2008 |

Genre | Boundary value problems |

Pages | 804 |

ISBN | 0132061155 |

Language | English, Spanish, And French |

**READING**: This practical book reflects the new technological emphasis that permeates differential equations, including the wide availability of scientific computing environments like "Maple, Mathematica, " and MATLAB; it does not concentrate on traditional manual methods but rather on new computer-based methods that lead to a wider range of more realistic applications. The book starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the book. For mathematicians and those in the field of computer science and engineering.

The Book | Calculus and Ordinary Differential Equations |

The Author | David Pearson |

The Publisher | Elsevier |

Release Date | 1995-12-01 |

Genre | Mathematics |

Pages | 240 |

ISBN | 9780080928654 |

Language | English, Spanish, And French |

**READING**: Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.

The Book | Calculus and Differential Equations with Mathematica |

The Author | Pramote Dechaumphai |

The Publisher | |

Release Date | 2016 |

Genre | Calculus |

Pages | 428 |

ISBN | 1783322640 |

Language | English, Spanish, And French |

The Book | Calculus |

The Author | M. Henriksen |

The Publisher | |

Release Date | 1967 |

Genre | Calculus |

Pages | 723 |

ISBN | PSU:000009491311 |

Language | English, Spanish, And French |