Muutke küpsiste eelistusi

E-raamat: Symbolic Asymptotics

Teised raamatud teemal:
  • Formaat - PDF+DRM
  • Hind: 110,53 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Symbolic AsymptoticsSuurem pilt
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

Symbolic asymptotics has recently undergone considerable theoretical development, especially in areas where power series are no longer an appropriate tool. Implementation is beginning to follow.



The present book, written by one of the leading specialists in the area, is currently the only one to treat this part of symbolic asymptotics. It contains a good deal of interesting material in a new, developing field of mathematics at the intersection of algebra, analysis and computing, presented in a lively and readable way. The associated areas of zero equivalence and Hardy fields are also covered.



The book is intended to be accessible to anyone with a good general background in mathematics, but it nonetheless gets right to the cutting edge of active research. Some results appear here for the first time, while others have hitherto only been given in preprints.



Due to its clear presentation, this book is interesting for a broad audience of mathematicians and theoretical computer scientists.

Arvustused

From the reviews:



"This book is the first text book about symbolic asympotics, written by one of its major contributors. It deals with the question to calculate limits and asymptotic Expansions of real functions symbolically. ...



The book contains a wealth of information on symbolic asymptotics. It fills a gap in the literature and should be found in every library. The user of a computer algebra system who is interested to understand the output of a command like Maple's asympt finds much interesting information. Actually many users might not even be aware about the complexity of such a command."



Wolfram Koepf, Computeralgebra Rundbrief, October 2005, Issue 37



"This book comprises the research of Professor Shackell in this field over the last 20 years . it provides a new presentation which is easier to understand and overall comes highly recommended. this book makes a very good starting place indeed. Examples, are fairly plentiful, and usually very helpful, with a good level of detail in the working." (James C. Beaumont, SIGACT News, Vol. 38 (4), 2007)

Introduction 1(6)
Zero Equivalence
7(36)
Zero-equivalence of Constants
8(5)
Richardson's Uniformity Conjecture
11(2)
Zero-equivalence of Functions
13(14)
Examples
22(3)
The sets Si
25(2)
Modular Methods in Zero Equivalence
27(4)
Hensel Lifting
28(2)
Examples
30(1)
Growth in Degrees
31(2)
Canonical Forms
32(1)
Systems of Partial Differential Equations
33(6)
Notation
33(2)
Radical Differential Ideals
35(1)
Computing Characteristic Sets
36(1)
The Rosenfeld-Grobner Algorithm
36(2)
Consequences, Applications
38(1)
Zero Equivalence
39(1)
Finding Symmetries
39(4)
Hardy Fields
43(16)
Definitions and Examples
43(2)
Building Hardy Fields
45(5)
Rough Comparisons
50(4)
The Map γ2
54(5)
Output Data Structures
59(24)
Asymptotic Power Series
59(2)
Multiseries
61(2)
Operations on Multiseries
63(8)
Substituting into a Power Series
65(3)
The Logarithm of a Multiseries
68(1)
The Exponential of a Multiseries
69(1)
Powers of a Multiseries
69(1)
Amalgamating Scales
70(1)
Substituting One Multiseries Into Another
70(1)
Nested Expansions
71(7)
Comparison of Nested Forms
74(2)
Operations on Nested Forms and Expansions
76(2)
The Algebra of Star Products
78(5)
Definitions and Elementary Properties
78(3)
Differentiation and Star Products
81(2)
Algorithms for Function Towers
83(46)
The Exp-Log Algorithm
84(8)
Case 1: fi = log h, h ε Fi-1
85(1)
Case 2: fi = exp h, h ε Fi-1
86(1)
Handling Denominators and Other Powers
87(1)
Summary of the Algorithm
88(1)
Examples
88(4)
Asymptotic Fields
92(24)
Adding Exponentials
100(1)
Adding Integrals
101(9)
Algebraic Equations
110(6)
Compositions with Meromorphic Functions
116(9)
Cartesian Representations
125(4)
Algebraic Differential Equations
129(26)
Nested Forms of Hardy-Field Solutions
130(14)
Examples
140(4)
The Number of Cases
144(6)
Reducing the Complexity
150(5)
A Theorem for Sparse Differential Equations
151(4)
Inverse Functions
155(20)
Inverting a Nested Expansion
156(7)
Summary of the Algorithm for Inversion
161(1)
Example
161(2)
Multiseries of Inverse Functions
163(12)
Proof of the Iteration Formula
169(4)
Asymptotic Fields and Inverse Functions
173(2)
Implicit Functions
175(16)
A Special Case
176(3)
Computation and Checking of Candidates
177(1)
Examples
178(1)
Systems of Exp-Log Equations
179(12)
Zero Equivalence
180(1)
Sketch of the Method
180(2)
Building estimates from the Tower of Fields
182(1)
Extension by a Logarithm
182(1)
Extension by an Exponential
183(1)
Obtaining the Nested Forms
184(1)
Example 1
185(2)
Example 2
187(2)
Example 3
189(2)
Star--Product Expansions
191(24)
Exp-Log Expansions
191(10)
Rewriting Exp--Log Expressions Into Standard Star Expansion Form
193(3)
Order Comparisons
196(5)
Growth Classes in Hardy Fields
201(3)
Generalizing the γnS
201(3)
Generalized Star Products
204(5)
Expansions
207(1)
Non-integral Iterates and Multiple Scales
208(1)
Real Iterates of Increasing Functions
209(6)
Oscillating Functions
215(20)
An Interval Calculus Algorithm
216(4)
Our Calculus of Intervals
217(3)
Lim-sups and Lim-infs
220(4)
Wandering Functions
224(7)
Wandering Expansions
231(4)
References 235(6)
Index 241
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97836621017662e.html
Märksõnad: