Verfügbarkeit: Handbook of geometrical methods for scientists and engineers

Handbook of geometrical methods for scientists and engineers:

Gespeichert in:

Bibliographische Detailangaben
Hauptverfasser:	Ivancevic, Vladimir G. (VerfasserIn), Ivancevic, Tijana T. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	New York Nova Science Publ. 2010
Schlagworte:	Geometric analysis Geometrical models Ingenieurwissenschaften Geometrische Methode
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Includes bibliographical references and index
Beschreibung:	XIII, 630 S. Ill., graph. Darst.
ISBN:	9781607417699

Internformat

MARC


LEADER	00000nam a2200000zc 4500
001	BV036446417
003	DE-604
005	20130125
007	t
008	100510s2010 xxuad\|\| \|\|\|\| 00\|\|\| eng d
010			\|a 2009018844
020			\|a 9781607417699 \|c hardcover \|9 978-1-60741-769-9
035			\|a (OCoLC)705500810
035			\|a (DE-599)BVBBV036446417
040			\|a DE-604 \|b ger \|e aacr
041	0		\|a eng
044			\|a xxu \|c US
049			\|a DE-703 \|a DE-19
050		0	\|a QA300
082	0		\|a 516
084			\|a SK 950 \|0 (DE-625)143273: \|2 rvk
100	1		\|a Ivancevic, Vladimir G. \|e Verfasser \|4 aut
245	1	0	\|a Handbook of geometrical methods for scientists and engineers \|c Vladimir G. Ivancevic and Tijana Ivancevic
264		1	\|a New York \|b Nova Science Publ. \|c 2010
300			\|a XIII, 630 S. \|b Ill., graph. Darst.
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
500			\|a Includes bibliographical references and index
650		4	\|a Geometric analysis
650		4	\|a Geometrical models
650	0	7	\|a Ingenieurwissenschaften \|0 (DE-588)4137304-2 \|2 gnd \|9 rswk-swf
650	0	7	\|a Geometrische Methode \|0 (DE-588)4156715-8 \|2 gnd \|9 rswk-swf
689	0	0	\|a Ingenieurwissenschaften \|0 (DE-588)4137304-2 \|D s
689	0	1	\|a Geometrische Methode \|0 (DE-588)4156715-8 \|D s
689	0		\|5 DE-604
700	1		\|a Ivancevic, Tijana T. \|e Verfasser \|4 aut
856	4	2	\|m Digitalisierung UB Bayreuth \|q application/pdf \|u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020318667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA \|3 Inhaltsverzeichnis
999			\|a oai:aleph.bib-bvb.de:BVB01-020318667

Datensatz im Suchindex

_version_	1804142931269910528
adam_text	Contents Preface xiii Acknowledgments xv I Geometrical Preliminaries 1 1 Classical Local Calculation Tools 3 1.1 Elements of Vector Analysis ....................... 3 1.1.1 The Hamilton V—operator ................... 4 1.1.2 The Laplace Δ— operator and the Fundamental PDEs .... 6 1.1.3 Integrals of Vector-Fields over Paths and Surfaces ...... 7 1.1.4 Integral Theorems of Vector Analysis .............. 9 1.1.5 Some More Dynamical PDEs .................. 11 1.1.6 Euler Rigid Body Equations ................... 12 1.2 Transformation of Coordinates and Elementary Tensors ....... 14 1.2.1 Transformation of Coordinates ................. 14 1.2.2 Scalar Invariants ......................... 16 1.2.3 Vectors and Covectors ...................... 16 1.2.4 Second-Order Tensors ...................... 17 1.2.5 Higher-Order Tensors ...................... 19 1.2.6 Tensor Symmetry ......................... 20 1.3 Euclidean Tensors ............................ 21 1.3.1 Basis Vectors and the Metric Tensor in K .......... 21 1.3.2 Tensor Products in W1 ...................... 22 1.4 Covariant Differentiation ......................... 23 1.4.1 Christoffeľs Symbols ....................... 23 1.4.2 Geodesies ............................. 23 1.4.3 Covariant Derivative ....................... 24 1.4.4 Covariant Form of Vector Differential Operators ....... 25 1.4.5 Absolute Derivative ....................... 26 1.4.6 3D Curve Geometry: Frenet-Serret Formulae ......... 27 VI Contents 1.4.7 Mechanical Acceleration and Force ............... 27 1.5 Euler-Lagrangian vs. Hamiltonian Dynamics ............. 29 1.6 Kirchhoff s and Newton-Euler s Rigid Body Equations ........ 31 1.7 Covariant Mechanics ........................... 33 1.8 Covariant Fluid Dynamics ........................ 37 1.8.1 Continuity Equation ....................... 37 1.8.2 Forces Acting on a Fluid ..................... 39 1.8.3 Constitutive and Dynamical Equations ............. 40 1.8.4 Navier-Stokes Equations ..................... 41 1.9 Riemannian Curvature Tensor ...................... 42 1.10 Various PDEs with Their Lagrangians ................. 43 1.11 Exterior Differential Forms ....................... 43 1.11.1 From Green to Stokes ...................... 44 1.11.2 Exterior Derivative ........................ 46 1.11.3 Exterior p-Forms in R4 ..................... 46 1.11.4 Stokes Theorem in M4 ...................... 48 1.11.5 Hodge Star Operator ....................... 48 1.11.6 Topological Duality of p—Forms and p—Chains ........ 49 1.11.7 De Rham Cochain Complex ................... 49 1.11.8 De Rham Cohomology of a Smooth Manifold ......... 50 1.12 The Covariant Force Law ........................ 50 1.13 Basic Neurodynamics ........................... 52 Modern Global Algebraic Framework 55 2.1 Sets .................................... 55 2.2 Maps .................................... 56 2.2.1 Algebra of Maps ......................... 57 2.2.2 Compositions of Maps ...................... 57 2.2.3 η -tuple Chain Rule ....................... 58 2.2.4 n—tuple Integration and Change of Variables ......... 58 2.3 General Topology ............................. 59 2.4 Homotopy ................................. 50 2.4.1 Commutative Diagrams ..................... 62 2.5 Groups ................................... 53 2.6 Group-Related Algebraic Structures .................. 65 2.7 Categories ................................. 57 2.8 Functors . ........................... 59 2.9 Natural Transformations ........................ 72 2.9.1 Compositions of Natural Transformations ........... 72 2.9.2 Dinatural Transformations ................... 73 2.10 Limits and Colimits .......................... 74 2.11 Adjunction ......................... 74 Contents vii 2.12 Application: Physiological Sensory-Motor Adjunction ........ 76 2.13 те— Categories ............................... 76 2.13.1 From Small Categories to Big те— Categories ........ 76 2.13.2 Topological Structure of n—Categories ............. 80 Brief Review of Tools from Modern Analysis and Geometry 87 3.1 Banah and Hubert Spaces ........................ 87 3.1.1 Topological Space ........................ 87 3.1.2 Metric Space ........................... 88 3.1.3 Banah Space ........................... 89 3.1.4 Hubert Space ........................... 89 3.2 Manifolds, Bundles and Jets ....................... 92 3.2.1 Manifolds ............................. 92 3.2.2 Bundles .............................. 93 3.2.3 Jets ................................ 94 II Basic Geometrical Methods 99 4 Smooth Manifolds and (Co)Tangent Bundles 101 4.1 Smooth Manifolds ............................ 101 4.1.1 Introduction to Smooth Manifolds ............... 101 4.1.2 Formal Definition of a Smooth Manifold ............ 105 4.1.3 Smooth Maps Between Smooth Manifolds ........... 106 4.2 (Co)Tangent Bundles of Smooth Manifolds .............. 107 4.2.1 Tangent Bundle and Lagrangian Dynamics .......... 107 4.2.2 Cotangent Bundle and Hamiltonian Dynamics ........ 109 4.2.3 Introducing Fibre-, Tensor-, and Jet-Bundles ......... 110 4.2.4 Example: Command/Control in Human-Robot Interactions . Ill 4.3 Tensor Fields on Smooth Manifolds ................... 114 4.3.1 Tensor Bundle .......................... 114 4.3.2 Differential Forms on Smooth Manifolds ......... . . . 122 4.3.3 Exterior Derivative and (Co)Homology ............. 126 4.3.4 The Paradigm of Dynamical Modelling ............. 138 5 Lie Derivatives and Lie Groups 141 5.1 Lie Derivatives on Smooth Manifolds .................. 141 5.1.1 Lie Derivative Operating on Functions ............. 141 5.1.2 Lie Derivative of Vector Fields ................. 143 5.1.3 Time Derivative of the Evolution Operator .......... 145 5.1.4 Lie Derivative of Differential Forms ............... 146 5.1.5 Lie Derivative of Various Tensor Fields ............. 147 5.1.6 Example: Lie-Derivative Neurodynamics ........... 149 viii Contents 5.1.7 Lie Algebras ........................... 149 5.2 Nonlinear Control ............................ 150 5.2.1 Feedback Linearization ...................... 151 5.2.2 Controllability .......................... 15 5.3 Lie Groups ................................ 161 5.3.1 Definition of a Lie Group .................... 162 5.3.2 Actions of Lie Groups on Smooth Manifolds .......... 165 5.3.3 Basic Dynamical Lie Groups .................. 167 5.3.4 Lie Groups in Human/Humanoid Biodynamics ........ 169 5.3.5 Euclidean Groups of Rigid Body Motion ............ 173 5.3.6 Basic Mechanical Examples ................... 176 5.3.7 Summary on Newton-Euler SE(S)—Dynamics ........ 178 5.3.8 Symplectic Group in Hamiltonian Mechanics ......... 182 5.3.9 Group Structure of a Biodynamical Manifold ......... 183 5.4 Biomedical Application: Brain Injury Mechanics ........... 187 5.4.1 Introduction to Traumatic Brain Injury ............ 187 5.4.2 SE(3)-jolt: the Cause of TBI ................. 189 Riemann—Finsler and Symplectic Geometry 197 6.1 Riemannian Manifolds .......................... 197 6.1.1 Local Riemannian Geometry .................. 197 6.1.2 Global Riemannian Geometry .................. 206 6.1.3 Ricci Flow ............................. 209 6.1.4 Structure Equations ....................... 210 6.1.5 Example: Autonomous Lagrangian Dynamics ......... 212 6.1.6 Basics of Morse and (Co)Bordism Theories .......... 214 6.2 Soft Introduction to De Rham-Hodge Theory ............. 218 6.2.1 Exact and Closed Forms and Chains .............. 218 6.2.2 De Rham Duality of Forms and Chains ............ 219 6.2.3 De Rham Cochain and Chain Complex ............ 219 6.2.4 De Rham Cohomology versus Chain Homology ........ 220 6.2.5 Hodge Star Operator ....................... 222 6.2.6 Hodge Inner Product ....................... 223 6.2.7 Hodge Codifferential Operator ................. 223 6.2.8 Hodge Laplacian Operator .................... 224 6.2.9 Hodge Adjoints and Self-Adjoints ............... 226 6.2.10 The Hodge Decomposition Theorem .............. 226 6.3 Ricci Flow and Reaction-Diffusion Processes ............. 227 6.3.1 Bio-Reaction-Diffusion Systems ................ 230 6.3.2 Reactive Neurodynamics ..................... 241 6.3.3 Dissipative Evolution under the Ricci Flow .......... 249 6.4 Finsler Manifolds ............................. 260 Contents ix 6.4.1 Definition of a Finsler Manifold ................. 260 6.4.2 Energy Functional, Variations and Extrema.......... 261 6.4.3 Example: Finsler-Lagrangian Field Theory .......... 264 6.5 Symplectic Manifolds ........................... 265 6.5.1 Symplectic Algebra ........................ 265 6.5.2 Symplectic Geometry ...................... 266 6.6 Autonomous Hamiltonian Dynamics .................. 268 6.6.1 Basics of Hamiltonian Dynamics ................ 268 6.6.2 Real 1 DOF Hamiltonian Dynamics ............... 270 6.6.3 Complex 1 DOF Hamiltonian Dynamics ............ 276 6.6.4 Library of Basic Hamiltonian Systems ............. 279 6.6.5 Hamilton-Poisson Mechanics .................. 286 6.6.6 Completely Integrable Hamiltonian Systems .......... 288 6.6.7 Momentum Map and Symplectic Reduction .......... 294 6.7 Example: Human versus Humanoid-Robot Biodynamics ....... 296 6.7.1 Idealistic Configuration Manifold of Humanoid-Robot Motion 296 6.7.2 Realistic Configuration Manifold of Human Motion ...... 296 6.7.3 Generalized Lagrangian and Hamiltonian Biodynamics .... 297 7 Path-Integral and Quantum Fields 301 7.1 Soft Introduction to Quantum Field Theory .............. 301 7.1.1 Basics of Non-Relativistic Quantum Mechanics ........ 301 7.1.2 Transition to Quantum Fields .................. 313 7.2 Feynman s Sum-Over Histories ..................... 322 7.2.1 Intuition Behind a Path Integral ................ 322 7.2.2 Basic Path-Integral Calculations ................ 332 7.2.3 Path-Integral Quantization ................... 338 7.2.4 Statistical Mechanics via Path Integrals ............ 345 7.2.5 Path Integrals and Green s Functions ............. 347 7.2.6 Monte Carlo Simulation of the Path Integral ......... 352 7.2.7 Feynman s Action-Amplitude Formalism in QFT ....... 357 7.2.8 Path-Integral TQFT ....................... 363 7.2.9 Non-Abelian Gauge Theories .................. 368 III Advanced Geometrical Methods 381 8 Kahler and Conformai Geometry 383 8.1 Complex and Kahler Manifolds ..................... 383 8.1.1 Hermitian and Kahler Metrics ................. 385 8.1.2 Kähler-Ricci Flow ........................ 389 8.1.3 Kahler Orbifolds......................... 392 8.1.4 Kähler-Ricci Flow on Kähler-Einstein Orbifolds ....... 394 Contents 8.1.5 Induced Evolution Equations .................. 395 8.1.6 Calabi-Yau Manifolds ...................... 395 8.2 Conformai Killing-Riemannian Geometry ............... 396 8.2.1 Conformai Killing Vector-Fields and Forms .......... 396 8.2.2 Conformai Killing Tensors and Laplacian Symmetry ..... 397 8.3 Gauges and Monopoles .......................... 399 8.3.1 Gauge Theories .......................... 399 8.3.2 Monopoles ............................ 406 8.4 Monge-Ampère Equations ........................ 413 8.4.1 Monge-Ampère Equations and Hitchin Pairs ......... 415 8.4.2 The Ђ- Operator ......................... 419 9 Geometry and Topology of Fibre Bundles 425 9.1 Fibre Bundles ............................... 425 9.1.1 Definition of a Fibre Bundle ................... 425 9.2 Vector and Affine Bundles ........................ 429 9.2.1 Vertical Tangent and Cotangent Bundles ........... 434 9.2.2 Distributions and Foliations on Manifolds ........... 436 9.2.3 Principal Bundles ........................ 437 9.3 Multivector-Fields and Tangent-Valued Forms ............ 439 9.4 Semi-Riemannian Dynamics ....................... 446 9.4.1 Vector-Fields and Connections ................. 446 9.4.2 Hamiltonian Structures on a Tangent Bundle ......... 448 9.5 A -Theory ................................ 451 9.5.1 Topological K-Theory ..................... 451 9.5.2 Algebraic A -Theory ....................... 452 9.5.3 Chern Classes and Chern Character .............. 453 9.5.4 Atiyah s View on AT-Theory .................. 456 9.5.5 Atiyah-Singer Index Theorem .................. 458 9.5.6 The Infinite-Order Case ..................... 460 10 Jet Geometry and Non- Autonomous Dynamics 463 10.1 Definition of a 1-Jet Manifold ...................... 463 10.2 Connections as 1-Jet Fields ....................... 467 10.3 Definition of a 2-Jet Manifold ...................... 472 10.4 Jets and Non-Autonomous Dynamics ................. 475 10.4.1 Geodesies ............................. 479 10.4.2 Quadratic Dynamical Equations ................ 480 10.4.3 Equation of Free-Motion .................... 481 10.4.4 Quadratic Lagrangian and Newtonian Systems ........ 481 10.4.5 Jacobi Fields ........................... 482 10.4.6 Constraints ............................ 484 10.4.7 Time-Dependent Lagrangian Dynamics ............ 487 Contents xi 10.4.8 Time-Dependent Hamiltonian Dynamics............ 488 10.4.9 Time-Dependent Constraints .................. 491 10.4.10 Lagrangian Constraints ..................... 493 10.4.11 Quadratic Degenerate Lagrangian Systems .......... 494 10.4.12 Time-Dependent Integrable Hamiltonian Systems ...... 497 10.4.13 Time-Dependent Action-Angle Coordinates .......... 499 10.4.14 Lyapunov Stability ........................ 500 10.4.15 First-Order Dynamical Equations ............... 501 10.4.16 Lyapunov Tensor and Stability ................. 502 10.4.17 Multi-Time Rheonomic Dynamics ............... 506 10.5 Jets and Action Principles ........................ 508 10.6 Jets and Lagrangian Field Theory ................... 512 10.6.1 Lagrangian Conservation Laws ................. 516 10.6.2 General Covariance Condition .................. 520 10.7 Jets and Hamiltonian Field Theory ................... 523 10.7.1 Covariant Hamiltonian Field Systems ............. 524 10.7.2 Associated Lagrangian and Hamiltonian Systems ....... 526 10.7.3 Evolution Operator ........................ 528 10.7.4 Quadratic Degenerate Systems ................. 532 11 Advanced Path-Integral Methods 535 11.1 Sum over Geometries and Topologies .................. 535 11.1.1 Simplicial Quantum Geometry ................. 536 11.1.2 Discrete Gravitational Path Integrals .............. 537 11.1.3 Regge Calculus .......................... 539 11.1.4 Lorentzian Path Integral ..................... 541 11.1.5 Non-Perturbative Quantum Gravity .............. 545 11.2 Cerebellum as an oo—Dimensional Recurrent Neural Network .... 565 11.2.1 Spinal Reflex Control of Biodynamics ............. 567 11.2.2 Local Muscle-Joint Mechanics ................. 567 11.2.3 Cerebellum: Adaptive Path-Integral Comparator ....... 570 11.3 Quantum Geometrical Psychodynamics ................ 574 11.3.1 Classical versus Quantum Probability ............. 577 11.3.2 The Life Space Foam ....................... 581 11.3.3 Geometric Chaos and Topological Phase Transitions ..... 587 11.3.4 Joint Action of Several Agents ................. 592 11.3.5 Chaos and Bernstein-Brooks Adaptation ........... 594 11.4 Geometrical Model for Crowd Behavioral Dynamics ......... 596 11.4.1 Cognition and Crowd Behavior ................. 597 11.4.2 Generic Three-Step Crowd Behavioral Dynamics ....... 598 11.4.3 Formal Individual, Aggregate and Crowd dynamics ...... 600 11.4.4 Crowd Entropy, Chaos and Phase Transitions ......... 610 xii Contents 11.4.5 Crowd Ricci Flow and Perelinan Entropy ........... 610 11.4.6 Chaotic Inter-Phase in Crowd Dynamics ............ 613 11.4.7 Crowd Phase Transitions .................... 614 Index 617
any_adam_object	1
author	Ivancevic, Vladimir G. Ivancevic, Tijana T.
author_facet	Ivancevic, Vladimir G. Ivancevic, Tijana T.
author_role	aut aut
author_sort	Ivancevic, Vladimir G.
author_variant	v g i vg vgi t t i tt tti
building	Verbundindex
bvnumber	BV036446417
callnumber-first	Q - Science
callnumber-label	QA300
callnumber-raw	QA300
callnumber-search	QA300
callnumber-sort	QA 3300
callnumber-subject	QA - Mathematics
classification_rvk	SK 950
ctrlnum	(OCoLC)705500810 (DE-599)BVBBV036446417
dewey-full	516
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	516 - Geometry
dewey-raw	516
dewey-search	516
dewey-sort	3516
dewey-tens	510 - Mathematics
discipline	Mathematik
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01668nam a2200433zc 4500</leader><controlfield tag="001">BV036446417</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20130125 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">100510s2010 xxuad\|\| \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2009018844</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781607417699</subfield><subfield code="c">hardcover</subfield><subfield code="9">978-1-60741-769-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)705500810</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV036446417</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA300</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ivancevic, Vladimir G.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Handbook of geometrical methods for scientists and engineers</subfield><subfield code="c">Vladimir G. Ivancevic and Tijana Ivancevic</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York</subfield><subfield code="b">Nova Science Publ.</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 630 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometric analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometrical models</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Ingenieurwissenschaften</subfield><subfield code="0">(DE-588)4137304-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geometrische Methode</subfield><subfield code="0">(DE-588)4156715-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Ingenieurwissenschaften</subfield><subfield code="0">(DE-588)4137304-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Geometrische Methode</subfield><subfield code="0">(DE-588)4156715-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ivancevic, Tijana T.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020318667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-020318667</subfield></datafield></record></collection>
id	DE-604.BV036446417
illustrated	Illustrated
indexdate	2024-07-09T22:39:36Z
institution	BVB
isbn	9781607417699
language	English
lccn	2009018844
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-020318667
oclc_num	705500810
open_access_boolean
owner	DE-703 DE-19 DE-BY-UBM
owner_facet	DE-703 DE-19 DE-BY-UBM
physical	XIII, 630 S. Ill., graph. Darst.
publishDate	2010
publishDateSearch	2010
publishDateSort	2010
publisher	Nova Science Publ.
record_format	marc
spelling	Ivancevic, Vladimir G. Verfasser aut Handbook of geometrical methods for scientists and engineers Vladimir G. Ivancevic and Tijana Ivancevic New York Nova Science Publ. 2010 XIII, 630 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Geometric analysis Geometrical models Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Geometrische Methode (DE-588)4156715-8 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 s Geometrische Methode (DE-588)4156715-8 s DE-604 Ivancevic, Tijana T. Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020318667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Ivancevic, Vladimir G. Ivancevic, Tijana T. Handbook of geometrical methods for scientists and engineers Geometric analysis Geometrical models Ingenieurwissenschaften (DE-588)4137304-2 gnd Geometrische Methode (DE-588)4156715-8 gnd
subject_GND	(DE-588)4137304-2 (DE-588)4156715-8
title	Handbook of geometrical methods for scientists and engineers
title_auth	Handbook of geometrical methods for scientists and engineers
title_exact_search	Handbook of geometrical methods for scientists and engineers
title_full	Handbook of geometrical methods for scientists and engineers Vladimir G. Ivancevic and Tijana Ivancevic
title_fullStr	Handbook of geometrical methods for scientists and engineers Vladimir G. Ivancevic and Tijana Ivancevic
title_full_unstemmed	Handbook of geometrical methods for scientists and engineers Vladimir G. Ivancevic and Tijana Ivancevic
title_short	Handbook of geometrical methods for scientists and engineers
title_sort	handbook of geometrical methods for scientists and engineers
topic	Geometric analysis Geometrical models Ingenieurwissenschaften (DE-588)4137304-2 gnd Geometrische Methode (DE-588)4156715-8 gnd
topic_facet	Geometric analysis Geometrical models Ingenieurwissenschaften Geometrische Methode
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020318667&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT ivancevicvladimirg handbookofgeometricalmethodsforscientistsandengineers AT ivancevictijanat handbookofgeometricalmethodsforscientistsandengineers

Verfügbarkeit

Es ist kein Print-Exemplar vorhanden.

Fernleihe Bestellen Achtung: Nicht im THWS-Bestand! Inhaltsverzeichnis

MARC

Datensatz im Suchindex

Es ist kein Print-Exemplar vorhanden.

Ähnliche Einträge