The vector analysis problem solver:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
New York
Research and Education Assoc.
1985
|
| Ausgabe: | Rev. print. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 1263 S. graph. Darst. |
| ISBN: | 0878915540 |
Internformat
MARC
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| 245 | 1 | 0 | |a The vector analysis problem solver |c Emil G. Milewski, chief ed. |
| 250 | |a Rev. print. | ||
| 264 | 1 | |a New York |b Research and Education Assoc. |c 1985 | |
| 300 | |a XVI, 1263 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Vector analysis |v Problems, exercises, etc | |
| 650 | 0 | 7 | |a Vektoranalysis |0 (DE-588)4191992-0 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4143389-0 |a Aufgabensammlung |2 gnd-content | |
| 689 | 0 | 0 | |a Vektoranalysis |0 (DE-588)4191992-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Milewski, Emil G. |e Sonstige |4 oth | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006130117&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006130117 | ||
Datensatz im Suchindex
| _version_ | 1804123663097659392 |
|---|---|
| adam_text | CONTENTS
Chapter No. Page No.
1 VECTORS AND SCALARS l
Basic Definitions; Graphical and Component
Representation of Vectors 2
Graphical Operations and Scalar Multiplication 10
Analytical Operations on Vectors 21
Applications in Geometry and Physics 26
2 MAGNITUDE, LINEAR DEPENDENCE AND
BASE VECTORS 34
Magnitude of a Vector 36
Applications in Geometry and Physics 42
Linear Combination, Linear Dependence of
Vectors 46
Representation of Vectors in Terms of Base
Vectors 55
(3) THE SCALAR PRODUCT AND THE VECTOR
PRODUCT 64
Definitions and Properties of the Scalar Product 66
Applications in Geometry and Physics 71
ix
Geometrical Definition of Vector Product 81
Component Definition of Vector Product 85
Scalar Triple Product and Vector Triple Product 92
Identities and Reciprocal Vectors 97
Vectors Equations of Lines, Planes, Spheres and the
Moment of a Vector 102
4 ORDINARY DERIVATIVES OF VECTORS 112
Vector Functions and Parametric Equations of a
Curve 113
Limits, Continuity and the Derivative of a Vector
Function 121
Graphical Representation of the Derivative, Tangent
Vector and Basic Properties 132
Vector Solutions to Differential Equations 141
5 APPLICATIONS OF ORDINARY DERIVATIVES
OF VECTORS IN DIFFERENTIAL GEOMETRY
AND MECHANICS 146
Space Curves, Frenet Formulas, Characteristic
Vectors and Plane Curves 147
Identities Involving Characteristic Vectors 171
Position Vector, Velocity, Angular Velocity and
Acceleration 177
Tangential and Normal Components of
Acceleration 188
Newton s Laws, Moment Vector, Angular Momentum
and Center of Mass 195
Trajectories and Collisions of Particles 205
Rigid Body Mechanics, Coordinate Systems and
Inertial Systems 210
6 DIFFERENTIAL CALCULUS OF FUNCTIONS
OF SEVERAL VARIABLES 220
Continuous Functions, Partial Derivatives and Total
Differential 222
Derivatives and Differentials of Composite Functions,
Scalar Fields and Vector Fields 233
x
Gradient of a Scalar Field 244
Properties of the Gradient Operator 247
Tangent Plane, Directional Derivative and Laplacian
Operator 252
7^ PARTIAL DIFFERENTIATION OF VECTORS,
GRADIENT AND DIVERGENCE 268
Partial Differentiation of Vectors 269
Gradient of a Scalar Field and Functionally Related
Functions 282
The Divergence and Laplacian Operators 290
Identities Involving Gradient and Divergence,
Solenoidal Vectors 297
8 CURL OF A VECTOR FIELD 308
Definition, Properties and Identities of the Curl
Operator 309
Irrotational (Conservative) Vector Fields, Solenoidal
Vector Fields 319
Laplacian Operator and Combined Operations 326
Complex Indentities Involving Curl, Divergence, and
Gradient Operators 332
Scalar Potential, Other Differential Operators and
Dyadics 341
9 ELEMENTS OF LINEAR ALGEBRA 356
Mappings, Binary Operations, Groves, Rings and
Fields 358
Vector Spaces and Span Sets 364
Position Vectors, Transformations, Invariants,
Linear Combinations and Rotation 373
Linear Transformations 385
Linearly Independent Vectors and The Fundamental
Theorem of Linear Algebra 401
Transformation of Cartesian Coordinate Systems,
Determinants and Inverse Transformations 405
xi
10 TENSOR NOTATION 413
Systems of Order Zero, One, Two , Kronecker
Delta and Summation Convention 415
Basic Operations and Contraction of Systems,
Symmetric and Sken Symmetric Systems,
e System 420
Determinants, Cofactors, Systems of Linear Equations
and Quadratic Forms 428
Scalar and Vector Product, Differentiation, Gradient,
Divergence, Rotation and The Laplacian in Tensor
Notation 435
1 1 APPLICATIONS OF GRADIENT, DIVERGENCE
AND CURL IN PHYSICS 445
Graphical Representation of Vector Fields 445
Gravitation, Harmonic Functions, Reflection of Light,
Ridgid Body Rotation, Surface Tension and
Elasticity 450
Concepts in Fluid Dynamics 461
Concepts in Heat Flow 481
Concepts in Electromagnetics, Maxwell s
Equations 485
12 ORDINARY INTEGRALS OF VECTORS
AND LINE INTEGRALS 504
Ordinary Vector Integration, Integral of Scalar and
Vector Product of Vectors 506
Kinematics, Central Force, Angular Momentum,
Aerial Velocity and Kepler s Laws 512
Parametric Representation, Orientation and Length
of Curves 520
Line Integrals, Work Done in a Force Field 527
Integration of Tangential and Normal Components of
a Vector, Kinetic and Potential Energy, Regions and
Domains 546
Conservative Vector Fields, Scalar Potential 554
Curl of a Conservative Field 562
Exact Differentials, Particle in the Conservative
Field and Vector Potential 572
xii
13 DOUBLE INTEGRALS 582
Smooth Surfaces, Orientation and Vectors Normal to
a Surface 583
Definition of Double Integral, Iterated Integrals 593
Double Integrals Representing Area 606
Double Integrals Representing Volume 612
Center of Mass and Moments of Inertia 616
Transformation of Coordinates 628
14 SURFACE INTEGRALS OF VECTORS, FLUX 635
Surfaces, Unit Normal Vector, and Parametric
Representation of a Surface 636
Surfaces Given by Z=f(x,y) 645
Flux of a Vector Field 657
Special Cases of Vector Integration, Cartesian Form
of Surface Integrals 675
15 SURFACE INTEGRALS AND FLUX
IN PHYSICAL APPLICATIONS 683
Flux of a Fluid Flow 683
Heat Flow 687
Electric Field, Gauss Law and Electrostatic
Potential 694
16 VOLUME INTEGRALS 704
Definition of Triple Integral, Riemann Sums, Iterated
Integrals 705
Volume of a Region 716
Triple Integration in Cylindrical and Spherical
Coordinates 723
Multiple Integrals, Mass and Density, Center of
Gravity 732
Moment of Inertia 737
Volume Integrals of Vectors, Surface and Volume
Integral Relationship, Gauss Law and Electrostatic
Potential 746
xiii
17 GREEN S THEOREM IN THE PLANE 758
Green s Theorem, Applications and Verification of
Green s Theorem 759
Area Bounded by a Closed Curve, Polar
Coordinates 777
Green s Theorem (Extended Version) 786
Green s Theorem for Multiply Connected Regions and
its Applications 790
Green s Theorem in Vector Notation 802
Applications in Physics Force Field, Flow,
Circulation and Gauss Theorem 806
Cauchy Riemann Equations, Line Integrals
Independent of Path 815
Transformation of Coordinates 825
18 CONSERVATIVE VECTOR FIELDS 828
19 DIVERGENCE THEOREM 854
Divergence Theorem, Basic Applications 855
Verification of the Divergence Theorem 869
Basic Applications of the Divergence Theorem 876
Basic Identities, Green s First and Second
Identities 883
Applications of Green s Identities, Harmonic
Functions 888
Further Applications of the Divergence Theorem 895
Definition of Divergence, Gradient and Rotation 899
Gauss Theorem, Solid Angle, Divergence of
n dimensional Space 904
20 STOKES THEOREM 945
Del Operator, Rotation of a Vector Function 946
Stokes Theorem, Proof of Stokes Theorem 949
Applications of Stokes Theorem 965
Basic Identities Involving Stokes Theorem, Further
Applications 979
Stokes Theorem for Surfaces Given in Parametric
Form 992
Another Definition of Rotation, Further
xiv
Applications 996
Applications in Electromagnetics 1003
Irrotational Fields 1006
Solenidal Fields 1011
21 CYLINDRICAL AND SPHERICAL
COORDINATES 1015
Polar Coordinates 1016
Coordinate Surfaces and Curves, Orthogonal
Systems 1020
The Unit Tangent Vectors of the Cylindrical
Coordinate System 1026
Element of Arc Length, Volume Element and Scale
Factors of the Cylindrical and Spherical Coordinate
Systems 1031
The Unit Tangent Vectors of the Spherical
Coordinate System 1040
Volume Element in Spherical, Cylindrical and
Curvilinear Coordinates 1048
The Gradient, Divergence, Curl, Laplacian and
Jacobian in Cylindrical and Spherical
Coordinates 1057
22 CURVILINEAR COORDINATES 1088
Coordinate Surfaces, Coordinate Curves, Orthogonal
Coordinate Systems 1089
Unit Tangent Vectors and Scale Factors 1093
Element of Arc Length, Volume Element 1099
The Gradient Divergence, Curl and Laplacian in
Orthogonal Coordinates 1102
Some Types of Orthogonal Coordinate Systems 1110
Transformation of Coordinates Orthogonal
Coordinate Systems 1116
Contravariant and Covariant Components of a
Vector, Metric Coefficients and the Jacobian of a
Transformation 1127
23 ADVANCED TOPICS 1142
MATRIX METHODS IN VECTOR ANALYSIS 1142
xv
LINEAR ORTHOGONAL TRANSFORMATIONS 1179
Transformation Matrix, Rotation, Orthogonal
Transformation 1179
Transformation of Scalar and Vector Fields,
Transformation of grad f, div F and Properties
of curl F 1184
TRANSPORT THEOREM 1191
Flux Through a Moving Surface 1191
Flux Transport Theorem 1193
Reynold s Transport Theorem, Euler s Expansion
Formula 1203
DIFFERENTIAL FORMS 1207
Differential One form, Exterior Product 1207
Differential Two form, Differential p forms, Addition
and Multiplication of Forms 1211
Properties of p forms, Integrals of One forms and
p forms 1219
EXTERIOR DERIVATIVE 1228
Exterior Differentiation, Basic Identities,
Conservative and Solenoida] Fields 1228
Green s Theorem, Stokes Theorem, Divergence
Theorem, Exact Differential Forms 1236
APPENDIX 1242
INDEX 1252
xvi
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| ctrlnum | (OCoLC)13720804 (DE-599)BVBBV009220388 |
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| id | DE-604.BV009220388 |
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| indexdate | 2024-07-09T17:33:21Z |
| institution | BVB |
| isbn | 0878915540 |
| language | English |
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| spelling | The vector analysis problem solver Emil G. Milewski, chief ed. Rev. print. New York Research and Education Assoc. 1985 XVI, 1263 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Vector analysis Problems, exercises, etc Vektoranalysis (DE-588)4191992-0 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Vektoranalysis (DE-588)4191992-0 s DE-604 Milewski, Emil G. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006130117&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The vector analysis problem solver Vector analysis Problems, exercises, etc Vektoranalysis (DE-588)4191992-0 gnd |
| subject_GND | (DE-588)4191992-0 (DE-588)4143389-0 |
| title | The vector analysis problem solver |
| title_auth | The vector analysis problem solver |
| title_exact_search | The vector analysis problem solver |
| title_full | The vector analysis problem solver Emil G. Milewski, chief ed. |
| title_fullStr | The vector analysis problem solver Emil G. Milewski, chief ed. |
| title_full_unstemmed | The vector analysis problem solver Emil G. Milewski, chief ed. |
| title_short | The vector analysis problem solver |
| title_sort | the vector analysis problem solver |
| topic | Vector analysis Problems, exercises, etc Vektoranalysis (DE-588)4191992-0 gnd |
| topic_facet | Vector analysis Problems, exercises, etc Vektoranalysis Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006130117&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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