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 Differential Equations |

The Author | Alexander Ioffe |

The Publisher | CRC Press |

Release Date | 1999-07-15 |

Genre | Mathematics |

Pages | 272 |

ISBN | 0849306051 |

Language | English, Spanish, And French |

**READING**: The calculus of variations is a classical area of mathematical analysis-300 years old-yet its myriad applications in science and technology continue to hold great interest and keep it an active area of research. These two volumes contain the refereed proceedings of the international conference on Calculus of Variations and Related Topics held at the Technion-Israel Institute of Technology in March 1998. The conference commemorated 300 years of work in the field and brought together many of its leading experts. The papers in the first volume focus on critical point theory and differential equations. The other volume deals with variational aspects of optimal control. Together they provide a unique opportunity to review the state-of-the-art of the calculus of variations, as presented by an international panel of masters in the field.

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 | 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 | Topics in Mathematics Calculus and Ordinary Differential Equations |

The Author | Om P. Chug; P.N. Gupta; R.S. Dahiya |

The Publisher | Laxmi Publications |

Release Date | 2008-12-01 |

Genre | |

Pages | 530 |

ISBN | 8170086590 |

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 and Calculus of Variations |

The Author | M. V. Makarets |

The Publisher | World Scientific |

Release Date | 1995 |

Genre | Mathematics |

Pages | 372 |

ISBN | 9789810221911 |

Language | English, Spanish, And French |

**READING**: This problem book contains exercises for courses in differential equations and calculus of variations at universities and technical institutes. It is designed for non-mathematics students and also for scientists and practicing engineers who feel a need to refresh their knowledge. The book contains more than 260 examples and about 1400 problems to be solved by the students ? much of which have been composed by the authors themselves. Numerous references are given at the end of the book to furnish sources for detailed theoretical approaches, and expanded treatment of applications.

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 | Functional differential equations |

The Author | A. V. Kim |

The Publisher | Kluwer Academic Pub |

Release Date | 1999 |

Genre | Mathematics |

Pages | 165 |

ISBN | 0792356896 |

Language | English, Spanish, And French |

**READING**: This monograph presents the basics of i-smooth calculus, a new differential calculus of nonlinear functionals based on the notion of invariant derivative, and its application to some problems of the qualitative theory of functional differential equations. This book is unique in its separation of finite and infinite dimensional components in the structures of functional differential equations and functionals, as well as in its use of conditional representation of FDEs, which is expedient for the application of methods and constructions of i-smooth calculus. Part I contains a foundation of i-smooth calculus. Part II is an introduction to FDEs based on i-smooth calculus. Part III describes the direct Lyapunov method for systems with delays in terms of i- smooth functionals. Part IV considers an approach to the development of a dynamical programming method for systems with delays in terms of i-smooth Bellman's functionals. Audience: This volume will be of interest to students and researchers in mathematics, applied mathematicians, and engineers whose work involves ordinary differential equations, functional analysis, partial differential equations, optimal control and mathematics systems theory.

The Book | Calculus of Variations and Nonlinear Partial Differential Equations |

The Author | Luigi Ambrosio |

The Publisher | Springer Science & Business Media |

Release Date | 2008 |

Genre | Mathematics |

Pages | 196 |

ISBN | 9783540759133 |

Language | English, Spanish, And French |

The Book | Thomas Calculus with Second Order Differential Equations |

The Author | Weir |

The Publisher | Addison Wesley Longman |

Release Date | 2011 |

Genre | Calculus |

Pages | 988 |

ISBN | 0321726413 |

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 | 2012-12-06 |

Genre | Mathematics |

Pages | 348 |

ISBN | 9783642571862 |

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 | Integral Calculus and Differential Equations Using Mathematica |

The Author | Cesar Perez Lopez |

The Publisher | Createspace Independent Publishing Platform |

Release Date | 2016-01-16 |

Genre | |

Pages | 166 |

ISBN | 1523434171 |

Language | English, Spanish, And French |

**READING**: This book provides all the material needed to work on Integral Calculus and Differential Equations using Mathematica. It includes techniques for solving all kinds of integral and its applications for calculating lengths of curves, areas, volumes, surfaces of revolution... With Mathematica is possible solve ordinary and partial differential equations of various kinds, and systems of such equations, either symbolically or using numerical methods (Euler's method,, the Runge-Kutta method,...). It also describes how to implement mathematical tools such as the Laplace transform, orthogonal polynomials, and special functions (Airy and Bessel functions), and find solutions of differential equations in partial derivatives.The main content of the book is as follows:PRACTICAL INTRODUCTION TO MATHEMATICA 1.1 CALCULATION NUMERIC WITH MATHEMATICA 1.2 SYMBOLIC CALCULATION WITH MATHEMATICA 1.3 GRAPHICS WITH MATHEMATICA 1.4 MATHEMATICA AND THE PROGRAMMING INTEGRATION AND APPLICATIONS 2.1 INDEFINITE INTEGRALS 2.1.1 Inmediate integrals 2.2 INTEGRATION BY SUBSTITUTION (OR CHANGE OF VARIABLES) 2.2.1 Exponential, logarithmic, hyperbolic and inverse circular functions 2.2.2 Irrational functions, binomial integrals 2.3 INTEGRATION BY PARTS 2.4 INTEGRATION BY REDUCTION AND CYCLIC INTEGRATION DEFINITE INTEGRALS. CURVE ARC LENGTH, AREAS, VOLUMES AND SURFACES OF REVOLUTION. IMPROPER INTEGRALS 3.1 DEFINITE INTEGRALS 3.2 CURVE ARC LENGTH 3.3 THE AREA ENCLOSED BETWEEN CURVES 3.4 SURFACES OF REVOLUTION 3.5 VOLUMES OF REVOLUTION 3.6 CURVILINEAR INTEGRALS 3.7 IMPROPER INTEGRALS 3.8 PARAMETER DEPENDENT INTEGRALS 3.9 THE RIEMANN INTEGRAL INTEGRATION IN SEVERAL VARIABLES AND APPLICATIONS. AREAS AND VOLUMES. DIVERGENCE, STOKES AND GREEN'S THEOREMS 4.1 AREAS AND DOUBLE INTEGRALS 4.2 SURFACE AREA BY DOUBLE INTEGRATION 4.3 VOLUME CALCULATION BY DOUBLE INTEGRALS 4.4 VOLUME CALCULATION AND TRIPLE INTEGRALS 4.5 GREEN'S THEOREM 4.6 THE DIVERGENCE THEOREM 4.7 STOKES' THEOREM FIRST ORDER DIFFERENTIAL EQUATIONS. SEPARATES VARIABLES, EXACT EQUATIONS, LINEAR AND HOMOGENEOUS EQUATIONS. NUMERIACAL METHODS 5.1 SEPARATION OF VARIABLES 5.2 HOMOGENEOUS DIFFERENTIAL EQUATIONS 5.3 EXACT DIFFERENTIAL EQUATIONS 5.4 LINEAR DIFFERENTIAL EQUATIONS 5.5 NUMERICAL SOLUTIONS TO DIFFERENTIAL EQUATIONS OF THE FIRST ORDER HIGH-ORDER DIFFERENTIAL EQUATIONS AND SYSTEMS OF DIFFERENTIAL EQUATIONS 6.1 ORDINARY HIGH-ORDER EQUATIONS 6.2 HIGHER-ORDER LINEAR HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS 6.3 NON-HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS. VARIATION OF PARAMETERS 6.4 NON-HOMOGENEOUS LINEAR EQUATIONS WITH VARIABLE COEFFICIENTS. CAUCHY-EULER EQUATIONS 66.5 THE LAPLACE TRANSFORM 6.6 SYSTEMS OF LINEAR HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS 6.7 SYSTEMS OF LINEAR NON-HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS HIGHER ORDEN DIFFERENTIAL EQUATIONS AND SYSTEMS USING APPROXIMATION METHODS. DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES 7.1 HIGHER ORDER EQUATIONS AND APPROXIMATION METHODS 7.2 THE EULER METHOD 7.3 THE RUNGE-KUTTA METHOD 7.4 DIFFERENTIAL EQUATIONS SYSTEMS BY APPROXIMATE METHODS 7.5 DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES 7.6 ORTHOGONAL POLYNOMIALS 7.7 AIRY AND BESSEL FUNCTIONS

The Book | Dictionary of Analysis Calculus and Differential Equations |

The Author | Douglas N. Clark |

The Publisher | CRC Press |

Release Date | 1999-12-15 |

Genre | Mathematics |

Pages | 288 |

ISBN | 1420049992 |

Language | English, Spanish, And French |

**READING**: Clear, rigorous definitions of mathematical terms are crucial to good scientific and technical writing-and to understanding the writings of others. Scientists, engineers, mathematicians, economists, technical writers, computer programmers, along with teachers, professors, and students, all have the occasional-if not frequent-need for comprehensible, working definitions of mathematical expressions. To meet that need, CRC Press proudly introduces its Dictionary of Analysis, Calculus, and Differential Equations - the first published volume in the CRC Comprehensive Dictionary of Mathematics. More than three years in development, top academics and professionals from prestigious institutions around the world bring you more than 2,500 detailed definitions, written in a clear, readable style and complete with alternative meanings, and related references.

The Book | Differential Equations |

The Author | Charles Henry Edwards |

The Publisher | Prentice Hall |

Release Date | 2008 |

Genre | Computers |

Pages | 575 |

ISBN | 0136004385 |

Language | English, Spanish, And French |

**READING**: For introductory courses in Differential Equations. This text provides the conceptual development and geometric visualization of a modern differential equations course that is still essential to science and engineering students. It reflects the new emphases that permeate the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; its focus has shifted from the traditional manual methods to new computer-based methods that illuminate qualitative phenomena and make accessible a wider range of more realistic applications. Seldom-used topics have been trimmed and new topics added: it starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the text.

The Book | Partial Differential Equations and the Calculus of Variations |

The Author | COLOMBINI |

The Publisher | Springer Science & Business Media |

Release Date | 2013-11-11 |

Genre | Mathematics |

Pages | 1019 |

ISBN | 9781461598312 |

Language | English, Spanish, And French |

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 | Stochastic Calculus and Differential Equations for Physics and Finance |

The Author | Joseph L. McCauley |

The Publisher | Cambridge University Press |

Release Date | 2013-02-21 |

Genre | Business & Economics |

Pages | 220 |

ISBN | 9780521763400 |

Language | English, Spanish, And French |

**READING**: Provides graduate students and practitioners in physics and economics with a better understanding of stochastic processes.