Foundations of Differential Calculus

In the latter a way of investigating integrals of given differentials is shown. ... Besides differential and integral calculus, one sometimes finds differentio-differential calculus and exponential calculus. In differentio-differential ...

Author: Euler

Publisher: Springer Science & Business Media

ISBN: 9780387226453

Category: Mathematics

Page: 194

View: 747


The positive response to the publication of Blanton's English translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's "Foundations of Differential Calculus" as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community.

A Treatise on the Differential Calculus

ON DIFFERENTIAL EQUATIONS BETWEEN THREE OR MORE VARIABLES . CHAPTER I. DEFINITIONS AND GENERAL CHARACTERS . da WE know , by the Differential Calculus , that if : be a function of two independent variables x and y , there will be dz two ...

Author: William Campbell Ottley


ISBN: CHI:36532499

Category: Calculus, Integral

Page: 253

View: 500


Elements of the differential calculus Sixth edition with index

effect the same as the inverse processes of integrating differentials and differential equations in the Integral Calculus , And these abstract analytical problems , which embody the essential principles of the Calculus as an instrument ...

Author: Wesley Stoker Barker Woolhouse


ISBN: BL:A0022039278


Page: 164

View: 857


A Treatise on the Differential Calculus

( 1 ) involve n constants together with two variables x and y differentiate this equation successively n times , we shall obtain n differential equations Du = 0 , D'u = 0 , Dou = 0 , ... , D " U = 0 , involving the n constants ...

Author: William Walton


ISBN: STANFORD:36105038879040

Category: Differential calculus

Page: 263

View: 605


A Treatise on the Differential Calculus

The differential equations to such surfaces may be thus found ; taking the partial differentials of ( 84 ) we have 1 ( 3 ) dz dx ( 3 ) , dz ز y otro ( ) ; ( ) dz .. + y = 0 . ( 85 ) Or taking the implicit form , viz . equation ( 472 ON ...

Author: Bartholomew Price


ISBN: NYPL:33433069104473

Category: Differential calculus

Page: 540

View: 732


Universal Formulas in Integral and Fractional Differential Calculus

Already, during the last three centuries and more, classical differential and integral calculations by famous ... Here, we use the Mellin representation of sign variable functions and sketch some useful formulas, equations and ...

Author: Khavtgai Namsrai

Publisher: World Scientific

ISBN: 9789814675611

Category: Mathematics

Page: 296

View: 630


' This reference book presents unique and traditional analytic calculations, and features more than a hundred universal formulas where one can calculate by hand enormous numbers of definite integrals, fractional derivatives and inverse operators. Despite the great success of numerical calculations due to computer technology, analytical calculations still play a vital role in the study of new, as yet unexplored, areas of mathematics, physics and other branches of sciences. Readers, including non-specialists, can obtain themselves universal formulas and define new special functions in integral and series representations by using the methods expounded in this book. This applies to anyone utilizing analytical calculations in their studies. Contents:Mathematical PreparationCalculation of Integrals Containing Trigonometric and Power FunctionsIntegrals Involving xγ, (p + txp)–λ Sine and Cosine FunctionsDerivation of General Formulas for Integrals Involving Powers of x, (a + bx)-Type Binomials and Trigonometric FunctionsIntegrals Involving xγ, 1/(p + txp)–λ, exp[–axγ] and Trigonometric FunctionsIntegrals Containing Bessel FunctionsIntegrals Involving the Neumann Function Nσ(x)Integrals Containing Other Cylindrical and Special FunctionsIntegrals Involving Two Trigonometric FunctionsDerivation of Universal Formulas for Calculation of Fractional Derivatives and Inverse Operators Readership: Undergraduate and graduate students interested in analytic calculations in integral calculus. Researchers from the fields of modern mathematical analysis, theoretical physics and engineering. Non-experts interested in integrals, fractional derivatives and inverse operators. Key Features:Content in this book is easy to readHas simple tables of integration and taking fractional derivatives and calculating complicated inverse operatorsMost valuable tip from the book is a simple and nice way to perform integration showing it as a design culture but not as tedious workKeywords:Mellin Representation;Contour Integration;Analytic Continuation;Taking Residue;L''Hôpital''s Rule;Gamma Function;Psi-Function;Exponential Function;Neumann;Trigonometric;Cylindrical;Struve;Modified Struve;Bessel and Modified Bessel Functions;Probability Integrals;Integral of Frenal;General Formulas for Taking Integrals;Fractional Derivatives;Inverse Operators;Euler Number'

Differential Equations and Vector Calculus

If Q denotes the instantaneous electric charge on the capacitor C, it is possible to get a differential equation governing Q given by L d dt 2 2 Q + R dQ dt In Mathematics we identify all the differential equations of the type (1),(4) ...

Author: Dr T.K.V. Iyengar & Dr B. Krishna Gandhi & S. Ranganadham & Dr M.V.S.S.N. Prasad

Publisher: S. Chand Publishing

ISBN: 9789352838264

Category: Science


View: 724


In this book, how to solve such type equations has been elaborately described. In this book, vector differential calculus is considered, which extends the basic concepts of (ordinary) differential calculus, such as, continuity and differentiability to vector functions in a simple and natural way. This book comprises previous question papers problems at appropriate places and also previous GATE questions at the end of each chapter for the

Partial Differential Equations and Calculus of Variations

Vol 1151: Ordinary and Partial Differential Equations. Proceedings, 1984. Edited by B.D. Sleeman and R.J. Jarvis. XIV, 357 pages. 1985. Vol. 1152. H. Widom, Asymptotic Expansions for Pseudodifferential Operators on Bounded Domains.

Author: Stefan Hildebrandt

Publisher: Springer

ISBN: 9783540460244

Category: Mathematics

Page: 428

View: 756


This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.

A First Course in Differential Equations

Differential Equations, Dynamical Systems, & An Introduction to Chaos, Elsevier, New York. (A readable, intermediate text with an excellent format.) D. Hughes-Hallet, et al. 2005. Calculus: Single Variable, 4th ed, John Wiley, New York.

Author: J. David Logan

Publisher: Springer Science & Business Media

ISBN: 9780387259635

Category: Mathematics

Page: 289

View: 754


While the standard sophomore course on elementary differential equations is typically one semester in length, most of the texts currently being used for these courses have evolved into calculus-like presentations that include a large collection of methods and applications, packaged with state-of-the-art color graphics, student solution manuals, the latest fonts, marginal notes, and web-based supplements. All of this adds up to several hundred pages of text and can be very expensive. Many students do not have the time or desire to read voluminous texts and explore internet supplements. Thats what makes the format of this differential equations book unique. It is a one-semester, brief treatment of the basic ideas, models, and solution methods. Its limited coverage places it somewhere between an outline and a detailed textbook. The author writes concisely, to the point, and in plain language. Many worked examples and exercises are included. A student who works through this primer will have the tools to go to the next level in applying ODEs to problems in engineering, science, and applied mathematics. It will also give instructors, who want more concise coverage, an alternative to existing texts. This text also encourages students to use a computer algebra system to solve problems numerically. It can be stated with certainty that the numerical solution of differential equations is a central activity in science and engineering, and it is absolutely necessary to teach students scientific computation as early as possible. Templates of MATLAB programs that solve differential equations are given in an appendix. Maple and Mathematica commands are given as well. The author taught this material on several ocassions to students who have had a standard three-semester calculus sequence. It has been well received by many students who appreciated having a small, definitive parcel of material to learn. Moreover, this text gives students the opportunity to start reading mathematics at a slightly higher level than experienced in pre-calculus and calculus; not every small detail is included. Therefore the book can be a bridge in their progress to study more advanced material at the junior-senior level, where books leave a lot to the reader and are not packaged with elementary formats. J. David Logan is Professor of Mathematics at the University of Nebraska, Lincoln. He is the author of another recent undergraduate textbook, Applied Partial Differential Equations, 2nd Edition (Springer 2004).