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| Ch. 1 | Approximate Block Method for Solving the Laplace Equation on Polygons | 1 |
| 1 | Setting up a Mixed Boundary-Value Problem for the Laplace Equation on a Polygon | 1 |
| 2 | A Finite Covering of a Polygon by Blocks of Three Types | 13 |
| 3 | Representation of the Solution of a Boundary-Value Problem on Blocks | 19 |
| 4 | An Algebraic Problem | 34 |
| 5 | The Main Result | 40 |
| 6 | Proofs of Theorem 5.1 and of Lemmas 4.1-4.4 | 48 |
| 7 | The Stability and the Labor Content of Computations Required by the Block Method | 73 |
| 8 | Approximation of a Conjugate Harmonic Function on Blocks | 85 |
| 9 | Neumann's Problem | 92 |
| 10 | The Case of Arbitrary Analytic Mixed Boundary Conditions | 98 |
| Ch. 2 | Approximate Block Method of Conformal Mapping of Polygons onto Canonical Domains | 108 |
| 11 | Approximate Conformal Mapping of a Simply-Connected Polygon onto a Disk | 108 |
| 12 | Basic Harmonic Functions | 111 |
| 13 | Approximate Conformal Mapping of a Multiply-Connected Polygon onto a Plane with Cuts along Parallel Line Segments | 113 |
| 14 | Approximate Conformal Mapping of a Multiply-Connected Polygon onto a Ring with Cuts along the Arcs of Concentric Circles | 119 |
| Ch. 3 | Development and Application of the Approximate Block Method for Conformal Mapping of Simply-Connected and Doubly-Connected Domains | 124 |
| 15 | Approximate Conformal Mapping of Some Polygons onto a Strip | 124 |
| 16 | Scheme of Constructing a Conformal Mapping of a Doubly-Connected Domain onto a Ring | 141 |
| 17 | Mapping a Square Frame onto a Ring | 143 |
| 18 | Mapping a Square with a Circular Hole Using Circular Lune Block | 149 |
| 19 | Representation of a Harmonic Function on a Ring | 155 |
| 20 | Using a Block-Ring for Mapping Domain (18.1) onto a Ring | 157 |
| 21 | A Block-Bridge | 161 |
| 22 | Limit Cases | 167 |
| 23 | Mapping a Disk with an Elliptic Hole or with a Retrosection onto a Ring | 169 |
| 24 | Mapping a Disk with a Regular Polygonal Hole | 173 |
| 25 | Mapping the Exterior of a Parabola with a Hole onto a Ring | 181 |
| Ch. 4 | Approximate Conformal Mapping of Domains with a Periodic Structure by the Block Method | 188 |
| 26 | Mapping a Domain of the Type of Half-Plane with a Periodic Structure onto a Half-Plane | 188 |
| 27 | Mapping a Domain of the Type of Strip with a Periodic Structure onto a Strip | 202 |
| 28 | Mapping the Exterior of a Lattice of Ellipses onto the Exterior of a Lattice of Plates | 210 |
| References | 220 | |
| Index | 225 |
| Price | Condition | Delivery | Seller | Action |
| $191.95 | Digital |
| WonderClub |
Cory Lucas
reviewed Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings on February 10, 2011
Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings
If you are coming at these topics with an applied interest in finance or probability, you'll find this book to be a double-edged sword. The book is clearly aimed at budding mathematicians (specifically, analysts), and thus the presentation of material is very general -- Schilling looks at general measure spaces, not just probability spaces. If you have an applied interest like me, this can make reading somewhat awkward because concepts that are normally presented quite prominently in more applied texts (i.e. conditional expectation) are presented as asides in this book. Being general, the notation also takes getting used to. For those with an applied interest, treat this as a secondary text and use it to get some general mathematical exposure to the topics of measure and integration. I found the chapters on Lesbesgue Integration and convergence to be particularly useful in building my mathematical intuition, as these topic seems to be glossed-over in more applied probability/finance texts.
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Add Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings, This book presents a new, efficient numerical-analytical method for solving the Laplace equation on an arbitrary polygon. This method, called the approximate block method, overcomes indicated difficulties and has qualitatively more rapid convergence than , Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings to the inventory that you are selling on WonderClubX
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Add Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings, This book presents a new, efficient numerical-analytical method for solving the Laplace equation on an arbitrary polygon. This method, called the approximate block method, overcomes indicated difficulties and has qualitatively more rapid convergence than , Block Method for Solving the Laplace Equation and for Constructing Conformal Mappings to your collection on WonderClub |
