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Application of Geometric Algebra to Electromagnetic Scattering [[electronic resource] ] : The Clifford-Cauchy-Dirac Technique / / by Andrew Seagar
| Application of Geometric Algebra to Electromagnetic Scattering [[electronic resource] ] : The Clifford-Cauchy-Dirac Technique / / by Andrew Seagar |
| Autore | Seagar Andrew |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Singapore : , : Springer Singapore : , : Imprint : Springer, , 2016 |
| Descrizione fisica | 1 online resource (187 p.) |
| Disciplina | 620 |
| Soggetto topico |
Microwaves
Optical engineering Physics Computer mathematics Numerical analysis Microwaves, RF and Optical Engineering Numerical and Computational Physics, Simulation Computational Science and Engineering Numeric Computing |
| ISBN | 981-10-0089-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part I. Preparation: History -- Notation -- Geometry -- Space and Time -- Part II. Formulation: Scattering -- Cauchy Integrals -- Hardy Projections -- Construction of Solutions -- Part III. Demonstration: Examples -- Part IV. Contemplation: Perspectives -- Appendices. |
| Record Nr. | UNINA-9910254214403321 |
Seagar Andrew
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| Singapore : , : Springer Singapore : , : Imprint : Springer, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Numerical calculations in Clifford algebra : a practical guide for engineers and scientists / / Andrew Seagar
| Numerical calculations in Clifford algebra : a practical guide for engineers and scientists / / Andrew Seagar |
| Autore | Seagar Andrew |
| Pubbl/distr/stampa | Hoboken, NJ : , : Wiley, , [2023] |
| Descrizione fisica | 1 online resource (531 pages) |
| Disciplina | 512.57 |
| Soggetto topico |
Algebra - Data processing
Clifford algebras |
| ISBN |
1-394-17327-X
1-394-17325-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title Page -- Copyright -- Contents -- List of Figures -- List of Tables -- Preface -- Part I Entities and Operations -- Chapter 1 Introduction -- 1.1 Operations -- 1.2 History -- 1.3 Alternative Forms -- 1.4 Naming -- 1.5 Structure -- 1.5.1 Algebraic -- 1.5.2 Numeric -- 1.6 Entities -- References -- Chapter 2 Input -- 2.1 Syntax -- 2.2 Constants -- 2.2.1 Specific Types -- 2.2.2 General -- 2.3 Variables -- 2.3.1 Checking and Converting -- Reference -- Chapter 3 Output -- 3.1 Tree Format -- 3.2 Numeric Formats -- 3.2.1 Default Format -- 3.2.2 Defined Format -- 3.3 Extended Formats -- 3.3.1 Rounding -- 3.3.2 Parts of Coefficients -- 3.4 Selected Components -- 3.5 Primitive Formats -- 3.6 Recovered Values -- Chapter 4 Unary Operations -- 4.1 Theory -- 4.1.1 Negation -- 4.1.2 Involution -- 4.1.3 Pair Exchange -- 4.1.4 Reversion -- 4.1.5 Clifford Conjugation -- 4.1.6 Supplementation and Pseudo‐scalar -- 4.2 Practice -- 4.2.1 Example Code -- 4.2.2 Example Output -- Chapter 5 Binary Operations -- 5.1 Geometric Origins -- 5.1.1 Outer Multiplication -- 5.1.2 Orthogonal Components -- 5.1.3 Inner Multiplication -- 5.1.4 Names -- 5.2 Multiplication of Units -- 5.2.1 Progressive and Regressive Multiplication -- 5.2.2 Outer, Inner, and Central Multiplication -- 5.2.3 Multiplication By Scalars -- 5.3 Central Multiplication -- 5.3.1 Primal Units -- 5.3.2 Evolved and Other Units -- 5.3.3 Numbers -- 5.4 Practice -- 5.4.1 Example Code -- 5.4.2 Example Output -- 5.4.3 Multiplication Tables -- References -- Chapter 6 Vectors and Geometry -- 6.1 Theory -- 6.1.1 Magnitude -- 6.1.2 Inverse -- 6.1.3 Reflection -- 6.1.4 Projection -- 6.1.5 Rotation -- 6.2 Practice -- 6.2.1 Example Code -- 6.2.2 Example Output -- Chapter 7 Quaternions -- 7.1 Theory -- 7.1.1 Magnitude -- 7.1.2 Inverse -- 7.1.3 Reflection and Projection -- 7.1.4 Rotation -- 7.1.5 Intersection.
7.1.6 Factorisation -- 7.2 Practice -- 7.2.1 Example Code -- 7.2.2 Example Output -- References -- Chapter 8 Pauli Matrices -- 8.1 Theory -- 8.1.1 Recovery of Components -- 8.1.2 Magnitude -- 8.1.3 Inverse -- 8.1.4 Reflection, Projection, and Rotation -- 8.2 Practice -- 8.2.1 Example Code -- 8.2.2 Example Output -- Reference -- Chapter 9 Bicomplex Numbers -- 9.1 Theory -- 9.1.1 Conjugate -- 9.1.2 Magnitude -- 9.1.3 Inverse -- 9.1.4 Reflection, Projection, and Rotation -- 9.2 Practice -- 9.2.1 Example Code -- 9.2.2 Example Output -- Reference -- Chapter 10 Electromagnetic Fields -- 10.1 Theory -- 10.1.1 Time and Frequency -- 10.1.2 Electromagnetic Entities -- 10.1.3 Dirac Operators -- 10.1.4 Maxwell's Equations -- 10.1.5 Simplified Notation -- 10.1.6 Magnitude -- 10.1.7 Inverse -- 10.1.8 Reflection -- 10.1.9 Projection -- 10.1.10 Rotation -- 10.2 Practice -- 10.2.1 Example Code -- 10.2.2 Example Output -- 10.3 Field Arithmetic -- 10.3.1 Extensions Based on Quaternions -- 10.3.2 Inverses -- 10.3.3 Example Code -- 10.3.4 Example Output -- References -- Chapter 11 Arrays of Clifford Numbers -- 11.1 Theory -- 11.2 Practice -- 11.2.1 Example Code -- 11.2.2 Example Output -- Reference -- Chapter 12 Power Series -- 12.1 Theory -- 12.1.1 User Defined -- 12.1.2 Predefined -- 12.1.3 Convergence -- 12.1.4 Factorisation -- 12.1.5 Squaring -- 12.2 Practice -- 12.2.1 User Defined -- 12.2.2 Predefined -- 12.2.2.1 Standard Convergence -- 12.2.2.2 Extended Convergence -- 12.2.2.3 Doubly Extended Convergence -- References -- Chapter 13 Matrices of Clifford Numbers -- 13.1 Background -- 13.2 Inversion -- 13.3 Practice -- 13.3.1 Example Code -- 13.3.2 Example Output -- Reference -- Part II Customisation -- Chapter 14 Memory -- 14.1 Memory Usage -- 14.2 Examples -- 14.2.1 Memory Tree Sparsity -- 14.2.2 Memory Expansion -- 14.2.3 Memory Recycling. 14.2.3.1 Explicit and Implicit -- 14.2.3.2 Implicit and Nested -- Reference -- Chapter 15 Errors -- 15.1 User Errors -- 15.1.1 Syntax Errors and Messages -- 15.2 System Errors -- 15.3 Recovery -- 15.4 Beneficial Usage -- Reference -- Chapter 16 Extension -- 16.1 Accumulation -- 16.2 Multiplication -- 16.3 Transformation -- 16.4 Filtration -- Part III Application -- Chapter 17 Verification -- 17.1 Identities -- 17.2 Tests -- 17.2.1 Example Code -- 17.2.2 Example Output -- Reference -- Chapter 18 Lines Not Parallel -- 18.1 Theory -- 18.1.1 Common Plane -- 18.1.1.1 Inner Product -- 18.1.1.2 Outer Product -- 18.1.1.3 Geometrical Interpretation -- 18.1.2 No Plane in Common -- 18.1.2.1 Inner Product -- 18.1.2.2 Solution -- 18.2 Practice -- 18.2.1 Example Code -- 18.2.2 Example Output -- Reference -- Chapter 19 Perspective Projection -- 19.1 Theory -- 19.2 Practice -- 19.2.1 Example Code -- 19.2.2 Example Output -- Reference -- Chapter 20 Linear Systems -- 20.1 Theory -- 20.2 Practice -- 20.2.1 Example Code -- 20.2.2 Example Output -- References -- Chapter 21 Fast Fourier Transform -- 21.1 Theory -- 21.2 Practice -- 21.2.1 Example Code -- 21.2.2 Example Output -- References -- Chapter 22 Hertzian Dipole -- 22.1 Theory -- 22.2 Practice -- 22.2.1 Example Code -- 22.2.2 Example Output -- Reference -- Chapter 23 Finite Difference Time Domain -- 23.1 Theory -- 23.1.1 Analytical Solution -- 23.1.2 Series Solution -- 23.1.3 Analytical Example -- 23.1.4 Numerical Derivatives -- 23.2 Practice -- 23.2.1 Example Code -- 23.2.2 Example Output -- References -- Chapter 24 Cauchy Extension -- 24.1 Background -- 24.2 Theory -- 24.2.1 Two Dimensions -- 24.2.2 Three Dimensions -- 24.2.3 Singularity -- 24.2.4 The Taming Function -- 24.2.5 Construction -- 24.3 Practice -- 24.3.1 Example Code -- 24.3.2 Example Output -- References -- Chapter 25 Electromagnetic Scattering. 25.1 Background -- 25.2 Theory -- 25.3 Practice -- 25.3.1 Example Code -- 25.3.2 Example Output -- References -- Part IV Programming -- Chapter 26 Interfaces -- 26.1 Configuration and Observation -- 26.1.1 Management -- 26.1.2 Printing -- 26.2 Simple Entities -- 26.2.1 Units -- 26.2.2 Components -- 26.2.3 Numbers -- 26.2.3.1 Establishing and Recovering Values -- 26.2.3.2 Functions -- 26.2.3.3 Addition and Subtraction -- 26.2.3.4 Multiplication -- 26.2.3.5 Geometric -- 26.2.3.6 Filtering -- 26.3 Higher Entities -- 26.3.1 Vectors -- 26.3.2 Bicomplex Numbers -- 26.3.3 Quaternions -- 26.3.4 Pauli Matrices -- 26.3.5 Electromagnetic Fields -- 26.4 Multiple Entities -- 26.4.1 Arrays -- 26.4.2 Fast Fourier Transforms -- 26.4.3 Series -- 26.4.4 Matrices -- Reference -- Chapter 27 Descriptions -- 27.1 Arguments -- 27.2 Data types -- 27.3 Formats -- 27.4 Manual Pages -- 27.4.1 A-E -- 27.4.2 F-J -- 27.4.3 K-O -- 27.4.4 P-T -- 27.4.5 U-Z -- 27.5 Quick Reference -- Reference -- A Key to Example Code and Results -- Index -- EULA. |
| Record Nr. | UNINA-9910830173803321 |
|
Seagar Andrew
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| Hoboken, NJ : , : Wiley, , [2023] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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