Vibox

Linear Turning Point Theory by Wolfgang Wasow (English) Paperback Book

Description: Linear Turning Point Theory by Wolfgang Wasow The formal theory of linear analytic differential equations without a parameter near singularities with respect to the independent variable has, in recent years, been greatly deepened by bringing to it methods of modern algebra and topology. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description My book "Asymptotic Expansions for Ordinary Differential Equations" published in 1965 is out of print. In the almost 20 years since then, the subject has grown so much in breadth and in depth that an account of the present state of knowledge of all the topics discussed there could not be fitted into one volume without resorting to an excessively terse style of writing. Instead of undertaking such a task, I have concentrated, in this exposi­ tion, on the aspects of the asymptotic theory with which I have been particularly concerned during those 20 years, which is the nature and structure of turning points. As in Chapter VIII of my previous book, only linear analytic differential equations are considered, but the inclusion of important new ideas and results, as well as the development of the neces­ sary background material have made this an exposition of book length. The formal theory of linear analytic differential equations without a parameter near singularities with respect to the independent variable has, in recent years, been greatly deepened by bringing to it methods of modern algebra and topology. It is very probable that many of these ideas could also be applied to the problems concerning singularities with respect to a parameter, and I hope that this will be done in the near future. It is less likely, however, that the analytic, as opposed to the formal, aspects of turning point theory will greatly benefit from such an algebraization. Table of Contents I Historical Introduction.- 1.1. Early Asymptotic Theory Without Turning Points.- 1.2. Total Reflection and Turning Points.- 1.3. Hydrodynamic Stability and Turning Points.- 1.4. The So-Called WKB Method.- 1.5. The Contribution of R. E. Langer.- 1.6. Remarks on Recent Trends.- II Formal Solutions.- 2.1. Introduction.- 2.2. The Jordan Form of Holomorphic Functions.- 2.3. A Formal Block Diagonalization.- 2.4. Parameter Shearing: Its Nature and Purpose.- 2.5. Simplification by a Theorem of Arnold.- 2.6. Parameter Shearing: Its Application.- 2.7. Parameter Shearing: The Exceptional Case.- 2.8. Formal Solution of the Differential Equation.- 2.9. Some Comments and Warnings.- III Solutions Away From Turning Points.- 3.1. Asymptotic Power Series: Definition of Turning Points.- 3.2. A Method for Proving the Analytic Validity of Formal.- Solutions: Preliminaries.- 3.3. A General Theorem on the Analytic Validity of Formal.- Solutions.- 3.4. A Local Asymptotic Validity Theorem.- 3.5. Remarks on Points That Are Not Asymptotically Simple.- IV Asymptotic Transformations of Differential Equations.- 4.1. Asymptotic Equivalence.- 4.2. Formal Invariants.- 4.3. Formal Circuit Relations with Respect to the Parameter.- V Uniform Transformations at Turning Points: Formal Theory.- 5.1. Preparatory Simplifications.- 5.2. A Method for Formal Simplification in Neighborhoods of a Turning Point.- 5.3. The Case h > 1.- 5.4. The General Theory for n = 2.- VI Uniform Transformations at Turning Points: Analytic Theory.- 6.1. Preliminary General Results.- 6.2. Differential Equations Reducible to Airys Equation.- 6.3. Differential Equations Reducible to Webers Equation.- 6.4. Uniform Transformations in a Full Neighborhood of.- a Turning Point.- 6.5. Complete Reduction to Airys Equation.- 6.6.Reduction to Webers Equation in Wider Sectors.- 6.7. Reduction to Webers Equation in a Full Disk.- VII Extensions of the Regions of Validity of the Asymptotic Solutions.- 7.1. Introduction.- 7.2. Regions of Asymptotic Validity Bounded by Separation Curves: The Problem.- 7.3. Solutions Asymptotically Known in Sectors Bounded by.- Separation Curves.- 7.4. Singularities of Formal Solutions at a Turning Point.- 7.5. Asymptotic Expansions in Growing Domains.- 7.6. Asymptotic Solutions in Expanding Regions: A General Theorem.- 7.7. Asymptotic Solutions in Expanding Regions: A Local Theorem.- VIII Connection Problems.- 8.1. Introduction.- 8.2. Stretching and Parameter Shearing.- 8.3. Calculation of the Restraint Index.- 8.4. Inner and Outer Solutions for a Particular nth-Order System.- 8.5. Calculation of a Central Connection Matrix.- 8.6. Connection Formulas Calculated Through Uniform Simplification.- IX Fedoryuks Global Theory of Second-Order Equations.- 9.1. Global Formal Solutions of ?2u"=a(x)u2u" = a(x)u.- 9.2. Separation Curves for ?2u"=a(x)u2u" = a(x)u.- 9.3. A Global Asymptotic Existence Theorem for ?2u"=a(x)u2u" = a(x)u.- X Doubly Asymptotic Expansions.- 10.1. Introduction.- 10.2. Formal Solutions for Large Values of the.- Independent Variable.- 10.3. Asymptotic Solutions for Large Values of the.- Independent Variable.- 10.4. Some Properties of Doubly Asymptotic Solutions.- 10.5. Central Connection Problems in Unbounded Regions.- XI A Singularly Perturbed Turning Point Problem.- 11.1. The Problem.- 11.2. A Simple Example.- 11.3. The General Case: Formal Part.- 11.4. The General Case: Analytic Part.- XII Appendix: Some Linear Algebra for Holomorphic Matrices.- 12.1. Vectors and Matrices of Holomorphic Functions.- 12.2. Reduction to JordanForm.- 12.3. General Holomorphic Block Diagonalization.- 12.4. Holomorphic Transformation of Matrices into Arnolds Form.- References. Promotional Springer Book Archives Long Description My book "Asymptotic Expansions for Ordinary Differential Equations" published in 1965 is out of print. In the almost 20 years since then, the subject has grown so much in breadth and in depth that an account of the present state of knowledge of all the topics discussed there could not be fitted into one volume without resorting to an excessively terse style of writing. Instead of undertaking such a task, I have concentrated, in this exposi Details ISBN1461270081 Author Wolfgang Wasow Short Title LINEAR TURNING POINT THEORY SO Language English ISBN-10 1461270081 ISBN-13 9781461270089 Media Book Format Paperback Series Number 54 DEWEY 518 Pages 246 Year 2012 Publication Date 2012-10-23 Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States Illustrations IX, 246 p. AU Release Date 2012-10-23 NZ Release Date 2012-10-23 US Release Date 2012-10-23 UK Release Date 2012-10-23 Publisher Springer-Verlag New York Inc. Edition Description Softcover reprint of the original 1st ed. 1985 Series Applied Mathematical Sciences Alternative 9780387960463 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96394726;

Price: 115.04 AUD

Location: Melbourne

End Time: 2025-01-13T15:16:55.000Z

Shipping Cost: 9.49 AUD

Product Images

Linear Turning Point Theory by Wolfgang Wasow (English) Paperback Book

Item Specifics

Restocking fee: No

Return shipping will be paid by: Buyer

Returns Accepted: Returns Accepted

Item must be returned within: 30 Days

ISBN-13: 9781461270089

Book Title: Linear Turning Point Theory

Number of Pages: 246 Pages

Language: English

Publication Name: Linear Turning Point Theory

Publisher: Springer-Verlag New York Inc.

Publication Year: 2012

Subject: Mathematics

Item Height: 235 mm

Item Weight: 403 g

Type: Textbook

Author: Wolfgang Wasow

Item Width: 155 mm

Format: Paperback

Recommended

Linear Actuator Wireless Remote Controller 12V Momentary Switch Forward/Reverse
Linear Actuator Wireless Remote Controller 12V Momentary Switch Forward/Reverse

$18.88

View Details
New Clarostat 62JA-5K 10 Turn Linear 5000 Ohm Potentiometer Module Unit in Box
New Clarostat 62JA-5K 10 Turn Linear 5000 Ohm Potentiometer Module Unit in Box

$109.00

View Details
2pcs - RV4LAYSD252A Single Turn Linear Potentiometer  2500 Ohms 2W Ohm Locking
2pcs - RV4LAYSD252A Single Turn Linear Potentiometer 2500 Ohms 2W Ohm Locking

$39.99

View Details
4 Bourns 3852A-282-251A 250Ω 3/4" Single Turn Cermet Panel Potentiometers
4 Bourns 3852A-282-251A 250Ω 3/4" Single Turn Cermet Panel Potentiometers

$24.99

View Details
Lot of (2) New! Bourns 51AADB28E15 10K Linear Taper Potentiometer
Lot of (2) New! Bourns 51AADB28E15 10K Linear Taper Potentiometer

$15.95

View Details
B25K Ohm Linear Potentiometer, Alpha Brand. Includes Dust Seal! USA SELLER!!!
B25K Ohm Linear Potentiometer, Alpha Brand. Includes Dust Seal! USA SELLER!!!

$2.89

View Details
CTS6323 50K OHM 2W LINEAR 3/4 TURN MILITARY POTENTIOMETER
CTS6323 50K OHM 2W LINEAR 3/4 TURN MILITARY POTENTIOMETER

$7.95

View Details
SINO Optical Grating Ruler Linear Scale For Turning Lathe Milling KA-300 5um TTL
SINO Optical Grating Ruler Linear Scale For Turning Lathe Milling KA-300 5um TTL

$107.00

View Details
2 PIHER 25K LINEAR TAPER 1T 1 TURN CARBON PCB PWB TRIMMER POTENTIOMETER POT USA
2 PIHER 25K LINEAR TAPER 1T 1 TURN CARBON PCB PWB TRIMMER POTENTIOMETER POT USA

$1.49

View Details
B250K Ohm Linear Potentiometer, Alpha Brand. Includes Dust Seal! USA Seller!!!
B250K Ohm Linear Potentiometer, Alpha Brand. Includes Dust Seal! USA Seller!!!

$2.89

View Details