Advanced Calculus Partial Differential Equations

Author : Lynn Harold Loomis
Publisher : World Scientific Publishing Company
ISBN 13 : 9814583952
Total Pages : 596 pages
Book Rating : 4.54/5 ( download)

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Download or read book Advanced Calculus written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Author : B.R. THAKUR
Publisher : Ram Prasad Publications(R.P.H.)
ISBN 13 : 8195625150
Total Pages : 559 pages
Book Rating : 4.54/5 ( download)

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Download or read book ADVANCED CALCULUS & PARTIAL DIFFERENTIAL EQUATIONS written by B.R. THAKUR and published by Ram Prasad Publications(R.P.H.). This book was released on with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unit-I 0. Historical Background .... i-iii 1. Field Structure and Ordered Structure of R, Intervals, Bounded and unbounded sets, Supremum and infimum, Completeness in R, Absolute value of a real Number .... 1-33 2. Sequence of Real Numbers, Limit of a Sequence, Bounded and Monotonic Sequences, Cauchy’s General Principle of Convergence, Algebra of Sequence and Some Important Theorems .... 34-80 Unit-II 3. Series of non-negative terms, Convergence of positive term series .... 81-146 4. Alternating Series and Leibrintr’s test, Absolute and conditional convergence of Series of real Terms .... 147-163 5. Uniform Continuity .... 164-185 6. Chain Rule of Differentiability .... 186-202 7. Mean Value Theorems and Their Geometrical Interpretations .... 203-228 Unit-III 8. Limit and continuity of functions of two variables .... 229-256 9. Change of Variables .... 257-280 10. Euler’s Theorem on Homogeneous Functions .... 281-294 11. Taylor’s Theorem For functions of two Variables .... 295-307 12. Jacobians .... 308-337 13. Maxima and Minima of Functions of Two Variables .... 338-354 14. Lagrange’s Multipliers Method .... 355-367 15. Beta and Gamma Functions .... 368-395 Unit-IV 16. Partial Differential Equations of The first order .... 396-415 17. Lagrange’s Solution .... 416-440 18. Some Special types of equations which can be solved easily by methods other than the general method .... 441-462 19. Charpit’s General Method .... 463-474 20. Partial Differential Equation of Second and Higher Order .... 475-485 Unit-V 21. Classification of Partial Differential Equations of Second Order .... 486-494 22. Homogeneous and Non-homogeneous Partial Differential Equations of Constant coefficients .... 495-541 23. Partial Differential Equations Reducible to Equtions with Constant Coefficients .... 542-551

Author : Jeffrey Rauch
Publisher : Springer Science & Business Media
ISBN 13 : 9780387974729
Total Pages : 280 pages
Book Rating : 4.25/5 ( download)

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Download or read book Partial Differential Equations written by Jeffrey Rauch and published by Springer Science & Business Media. This book was released on 1991 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a course I have given five times at the University of Michigan, beginning in 1973. The aim is to present an introduction to a sampling of ideas, phenomena, and methods from the subject of partial differential equations that can be presented in one semester and requires no previous knowledge of differential equations. The problems, with hints and discussion, form an important and integral part of the course. In our department, students with a variety of specialties-notably differenƯ tial geometry, numerical analysis, mathematical physics, complex analysis, physics, and partial differential equations-have a need for such a course. The goal of a one-term course forces the omission of many topics. Everyone, including me, can find fault with the selections that I have made. One of the things that makes partial differential equations difficult to learn is that it uses a wide variety of tools. In a short course, there is no time for the leisurely development of background material. Consequently, I suppose that the reader is trained in advanced calculus, real analysis, the rudiments of complex analysis, and the language offunctional analysis. Such a background is not unusual for the students mentioned above. Students missing one of the "essentials" can usually catch up simultaneously. A more difficult problem is what to do about the Theory of Distributions

Author : Stig Larsson
Publisher : Springer Science & Business Media
ISBN 13 : 3540887059
Total Pages : 263 pages
Book Rating : 4.58/5 ( download)

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Download or read book Partial Differential Equations with Numerical Methods written by Stig Larsson and published by Springer Science & Business Media. This book was released on 2008-12-05 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

Author : E. C. Zachmanoglou
Publisher : Courier Corporation
ISBN 13 : 048613217X
Total Pages : 432 pages
Book Rating : 4.74/5 ( download)

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Download or read book Introduction to Partial Differential Equations with Applications written by E. C. Zachmanoglou and published by Courier Corporation. This book was released on 2012-04-20 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

Author : Edwin Bidwell Wilson
Publisher :
ISBN 13 :
Total Pages : 302 pages
Book Rating : 4.48/5 ( download)

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Download or read book Advanced Calculus written by Edwin Bidwell Wilson and published by . This book was released on 1911 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : David V. Widder
Publisher : Courier Corporation
ISBN 13 : 0486134660
Total Pages : 548 pages
Book Rating : 4.66/5 ( download)

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Download or read book Advanced Calculus written by David V. Widder and published by Courier Corporation. This book was released on 2012-05-23 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic text offers exceptionally precise coverage of partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more. Includes exercises and selected answers.

Author : Ralph E. Showalter
Publisher : Courier Corporation
ISBN 13 : 0486135799
Total Pages : 226 pages
Book Rating : 4.93/5 ( download)

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Download or read book Hilbert Space Methods in Partial Differential Equations written by Ralph E. Showalter and published by Courier Corporation. This book was released on 2011-09-12 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.

Author : Francis Begnaud Hildebrand
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 760 pages
Book Rating : 4.98/5 ( download)

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Download or read book Advanced Calculus for Applications written by Francis Begnaud Hildebrand and published by Prentice Hall. This book was released on 1976 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text provides advanced undergraduates with the necessary background in advanced calculus topics, providing the foundation for partial differential equations and analysis. Readers of this text should be well-prepared to study from graduate-level texts and publications of similar level. KEY TOPICS: Ordinary Differential Equations; The Laplace Transform; Numerical Methods for Solving Ordinary Differential Equations; Series Solutions of Differential Equations: Special Functions; Boundary-Value Problems and Characteristic-Function Representations; Vector Analysis; Topics in Higher-Dimensional Calculus; Partial Differential Equations; Solutions of Partial Differential Equations of Mathematical Physics; Functions of a Complex Variable; Applications of Analytic Function Theory MARKET: For all readers interested in advanced calculus.

Author : Kenneth S. Miller
Publisher : Courier Dover Publications
ISBN 13 : 0486843297
Total Pages : 273 pages
Book Rating : 4.92/5 ( download)

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Download or read book Partial Differential Equations in Engineering Problems written by Kenneth S. Miller and published by Courier Dover Publications. This book was released on 2020-03-18 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise text derives common partial differential equations, discussing and applying techniques of Fourier analysis. Also covers Legendre, Bessel, and Mathieu functions and general structure of differential operators. 1953 edition.