Oxford users' guide to mathematics:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English German |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
2004
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XXII, 1284 S. graph. Darst. |
| ISBN: | 0198507631 9780199686926 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV017870543 | ||
| 003 | DE-604 | ||
| 005 | 20131216 | ||
| 007 | t | ||
| 008 | 040219s2004 xxkd||| |||| 00||| eng d | ||
| 016 | 7 | |a 973607602 |2 DE-101 | |
| 020 | |a 0198507631 |9 0-19-850763-1 | ||
| 020 | |a 9780199686926 |9 978-0-19-968692-6 | ||
| 020 | |z 978198507635 |9 978-19-850763-5 | ||
| 035 | |a (OCoLC)53393406 | ||
| 035 | |a (DE-599)BVBBV017870543 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 1 | |a eng |h ger | |
| 044 | |a xxk |c XA-GB | ||
| 049 | |a DE-355 |a DE-1050 |a DE-91G |a DE-521 |a DE-11 | ||
| 050 | 0 | |a QA40.T4813 2004 | |
| 082 | 0 | |a 510 |2 22 | |
| 082 | 0 | |a 510 22 | |
| 084 | |a SH 500 |0 (DE-625)143075: |2 rvk | ||
| 084 | |a MAT 001k |2 stub | ||
| 084 | |a 510 |2 sdnb | ||
| 130 | 0 | |a Teubner-Taschenbuch der Mathematik, Bd. 1 | |
| 245 | 1 | 0 | |a Oxford users' guide to mathematics |c ed. by Eberhard Zeidler |
| 246 | 1 | 3 | |a Users' guide to mathematics |
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2004 | |
| 300 | |a XXII, 1284 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Mathématiques - Guides, manuels, etc | |
| 650 | 7 | |a Wiskunde |2 gtt | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics |v Handbooks, manuals, etc | |
| 650 | 0 | 7 | |a Geometrie |0 (DE-588)4020236-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebra |0 (DE-588)4001156-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Physik |0 (DE-588)4037952-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Analysis |0 (DE-588)4001865-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Infinitesimalrechnung |0 (DE-588)4072798-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Optimierung |0 (DE-588)4043664-0 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4155008-0 |a Formelsammlung |2 gnd-content | |
| 689 | 0 | 0 | |a Mathematische Physik |0 (DE-588)4037952-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 1 | 1 | |a Analysis |0 (DE-588)4001865-9 |D s |
| 689 | 1 | 2 | |a Algebra |0 (DE-588)4001156-2 |D s |
| 689 | 1 | 3 | |a Geometrie |0 (DE-588)4020236-7 |D s |
| 689 | 1 | 4 | |a Infinitesimalrechnung |0 (DE-588)4072798-1 |D s |
| 689 | 1 | 5 | |a Optimierung |0 (DE-588)4043664-0 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Zeidler, Eberhard |d 1940-2016 |e Sonstige |0 (DE-588)121295869 |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=010721341&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-010721341 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804130543457009664 |
|---|---|
| adam_text | Titel: Oxford users guide to mathematics
Autor: Zeidler, Eberhard
Jahr: 2004
Contents
Introduction i
0. Formulas, Graphs and Tables 3
0.1 Basic formulas of elementary mathematics.................. 3
0.1.1 Mathematical constants........................ 3
0.1.2 Measuring angles............................ 5
0.1.3 Area and circumference of plane figures............... 7
0.1.4 Volume and surface area of solids................... 10
0.1.5 Volumes and surface areas of regular polyhedra........... 13
0.1.6 Volume and surface area of n-dimensional balls........... 15
0.1.7 Basic formulas for analytic geometry in the plane.......... 16
0.1.8 Basic formulas of analytic geometry of space............ 25
0.1.9 Powers, roots and logarithms..................... 26
0.1.10 Elementary algebraic formulas.................... 28
0.1.11 Important inequalities......................... 36
0.1.12 Application to the motion of the planets............... 41
0.2 Elementary functions and graphs....................... 45
0.2.1 Transformation of functions...................... 47
0.2.2 Linear functions............................ 48
0.2.3 Quadratic functions.......................... 49
0.2.4 The power function .......................... 50
0.2.5 The Euler e-function.......................... 50
0.2.6 The logarithm............................. 52
0.2.7 The general exponential function................... 53
0.2.8 Sine and cosine......................-...... 53
0.2.9 Tangent and cotangent......................... 59
0.2.10 The hyperlJoUc functions stahï and cosh z ............. 63
0.2.11 The hyperbolic functions tanhr and cothx............. 64
0.2.12 The inverse trigonometric function» ................. 66
0.2.13 The inverse hyperbolic functions . . ................. 68
0.2.14 Polynomials............................... 70
0.2.15 Rational functions........................... 71
Contents
0.3 Mathematics and computers - a revolution in mathematics........74
0.4 Tables of mathematical statistics.......................75
0.4.1 Empirical data for sequences of measurements (trials).......75
0.4.2 The theoretical distribution function.................77
0.4.3 Checking for a normal distribution..................79
0.4.4 The statistical evaluation of a sequence of measurements......80
0.4.5 The statistical comparison of two sequences of measurements ... 80
0.4.6 Tables of mathematical statistics...................83
0.5 Tables of values of special functions......................98
0.5.1 The gamma functions T(x) and 1/T(a;)................98
0.5.2 Cylinder functions (also known as Bessel functions).........99
0.5.3 Spherical functions (Legendre polynomials).............lu3
0.5.4 Elliptic integrals............................104
0.5.5 Integral trigonometric and exponential functions..........106
0.5.6 Fresnel integrals............................1°8
0.5.7 The function / V d*.........................1°8
0.5.8 Changing from degrees to radians...................!°9
0.6 table of prime numbers 4000........................110
0.7 Formulas for series and products.......................m
0.7.1 Special series..............................HI
0.7.2 Power series...............................H4
0.7.3 Asymptotic series............................124
0.7.4 Fourier series..............................127
0.7.5 Infinite products............................132
0.8 Tables for differentiation of functions.....................I33
0.8.1 Differentiation of elementary functions................I33
0.8.2 Rules for differentiation of functions of one variable ........I35
0.8.3 Rules for differentiating functions of several variables........I36
0.9 Tables of integrals...............................138
0.9.1 Integration of elementary functions..................I38
0.9.2 Rules for integration..........................I40
0.9.3 Integration of rational functions ...................*44
0.9.4 Important substitutions........................I45
0.9.5 Tables of indefinite integrals......................I49
0.9.6 Tables of definite intégrais.......................I86
0.10 Tables on integral transformations......................192
0.10.1 Fourier transformation.........................192
0.10.2 Laplace transformation ........................205
Contenta xiii
1. Analysis 221
1.1 Elementary analysis..............................222
1.1.1 Real numbers..............................222
1.1.2 Complex numbers...........................228
1.1.3 Applications to oscillations......................233
1.1.4 Calculations with equalities......................234
1.1.5 Calculations with inequalities.....................236
1.2 Limits of sequences...............................238
1.2.1 Basic ideas...............................238
1.2.2 The Hilbert axioms for the real numbers...............239
1.2.3 Sequences of real numbers.......................242
1.2.4 Criteria for convergence of sequences.................245
1.3 Limits of functions...............................249
1.3.1 Functions of a real variable......................249
1.3.2 Metric spaces and point sets......................254
1.3.3 Functions of several variables.....................259
1.4 Differentiation of functions of a real variable.................262
1.4.1 The derivative .............................262
1.4.2 The chain rule.............................264
1.4.3 Increasing and decreasing functions..................265
1.4.4 Inverse functions............................266
1.4.5 Taylor s theorem and the local behavior of functions........268
1.4.6 Complex valued functions.......................277
1.5 Derivatives of functions of several real variables...............278
1.5.1 Partial derivatives...........................278
1.5.2 The Fréchet derivative.........................279
1.5.3 The chain rule.............................282
1.5.4 Applications to the transformation of differential operators . . . .285
1.5.5 Application to the dependency of functions.............287
1.5.6 The theorem on implicit functions..................288
1.5.7 Inverse mappings............................290
1.5.8 The nih variation and Taylor s theorem...............292
1.5.9 Applications to estimation of errors.................293
1.5.10 The Fréchet differential........................295
1.6 Integration of functions of a real variable...................306
1.6.1 Basic ideas...............................307
1.6.2 Existence of the integral........................310
1.6.3 The fundamental theorem of calculus.................312
1.6.4 Integration by parts..........................313
1.6.5 Substitution...............................314
Contents
1.6.6 Integration on unbounded intervals..................317
1.6.7 Integration of unbounded functions..................318
1.6.8 The Cauchy principal value......................318
1.6.9 Application to arc length.......................319
1.6.10 A standard argument from physics..................320
1.7 Integration of functions of several real variables...............321
1.7.1 Basic ideas...............................321
1.7.2 Existence of the integral........................329
1.7.3 Calculations with integrals ......................332
1.7.4 The principle of Cavalieri (iterated integration)...........333
1.7.5 Substitution...............................335
1.7.6 The fundamental theorem of calculus (theorem of Gauss-Stokes) . 335
1.7.7 The Riemannian surface measure...................341
1.7.8 Integration by parts..........................343
1.7.9 Curvilinear coordinates........................344
1.7.10 Applications to the center of mass and center of inertia......348
1.7.11 Integrals depending on parameters..................350
1.8 Vector algebra.................................351
1.8.1 Linear combinations of vectors....................351
1.8.2 Coordinate systems ..........................353
1.8.3 Multiplication of vectors........................354
1.9 Vector analysis and physical fields ......................357
1.9.1 Velocity and acceleration.......................357
1.9.2 Gradient, divergence and curl.....................359
1.9.3 Applications to deformations.....................361
1.9.4 Calculus with the nabla operator...................363
1.9.5 Work, potential energy and integral curves .............366
1.9.6 Applications to conservation laws in mechanics...........368
1.9.7 Flows, conservation laws and the integral theorem of Gauss . . . • 370
1.9.8 The integral theorem of Stokes....................372
1.9.9 Main theorem of vector analysis ...................373
1.9.10 Application to Maxwell s equations in electromagnetism......374
1.9.11 Cartan s differential calculus.....................376
1.10 Infinite series..................................376
1.10.1 Criteria for convergence........................3
1.10.2 Calculations with infinite series....................380
1.10.3 Power series...............................382
1.10.4 Fourier series..............................385
1.10.5 Summation of divergent series:....................*^
1.10.6 Infinite products:............................3s9
Contenta xv
1.11 Integral transformations............................391
1.11.1 The Laplace transformation......................393
1.11.2 The Fourier transformation......................398
1.11.3 The ^-transformation.........................403
1.12 Ordinary differential equations........................407
1.12.1 Introductory examples.........................407
1.12.2 Basic notions..............................415
1.12.3 The classification of differential equations..............424
1.12.4 Elementary methods of solution....................434
1.12.5 Applications ..............................450
1.12.6 Systems of linear differential equations and the propagator .... 454
1.12.7 Stability.................................457
1.12.8 Boundary value problems and Green s functions ..........459
1.12.9 General theory.............................464
1.13 Partial differential equations..........................468
1.13.1 Equations of first order of mathematical physics..........469
1.13.2 Equations of mathematical physics of the second order.......496
1.13.3 The role of characteristics.......................511
1.13.4 General principles for uniqueness...................521
1.13.5 General existence results........................522
1.14 Complex function theory............................532
1.14.1 Basic ideas...............................533
1.14.2 Sequences of complex numbers....................534
1.14.3 Differentiation.............................535
1.14.4 Integration...............................537
1.14.5 The language of differential forms ..................541
1.14.6 Representations of functions......................543
1.14.7 The calculus of residues and the calculation of integrals......549
1.14.8 The mapping degree..........................551
1.14.9 Applications to the fundamental theorem of algebra........552
1.14.10 Biholomorphic maps and the Riemann mapping theorem.....554
1.14.11 Examples of conformai maps.....................555
1.14.12 Applications to harmonic functions..................563
1.14.13 Applications to hydrodynamics....................566
1.14.14 Applications in electrostatics and magnetostatics..........568
1.14.15Analytic continuation and the identity principle...........569
1.14.16Applications to the Euler gamma function..............572
1.14.17Elliptic functions and elliptic integrals................574
1.14.18Modular forms and the inversion problem for the p-function . . . 581
1.14.19Elliptic integrals............................584
svi Contents
592
1.14.2ÖSingular differential equations.....................
1.14.21 The Gaussian hypergeometric differential equation.........593
1.14.22 Application to the Bessel differential equation............593
1.14.23 Functions of several complex variables................
L 599
2. Algebra m
2.1 Elementary algebra..............................
599
2.1.1 Combinatorics.............................
2.1.2 Determinants..............................
2.1.3 Matrices.................................
.610
2.1.4 Systems of linear equations...................
615
2.1.5 Calculations with polynomials ....................
2.1.6 The fundamental theorem of algebra according to Gauss......618
624
2.1.7 Partial fraction decomposition ....................
2.2 Matrices.....................................626
ROfi
2.2.1 The spectrum of a matrix.......................
COSI
2.2.2 Normal forms for matrices.......................
2.2.3 Matrix functions............................635
2.3 Linear algebra..................................637
2.3.1 Basic ideas...............................637
2.3.2 Linear spaces..............................638
2.3.3 Linear operators............................
2.3.4 Calculating with linear spaces.....................
2.3.5 Duality.................................^48
2.4 Multilinear algebra...............................650
2.4.1 Algebras.................................650
eel
2.4.2 Calculations with multilinear forms..................
2.4.3 Universal products...........................657
2.4.4 Lie algebras...............................^1
2.4.5 Superalgebras..............................^2
2.5 Algebraic structures..............................^*^
2.5.1 Groups .................................m
2.5.2 Rings..................................^9
2.5.3 Fields..................................672
2.6 Galois theory and algebraic equations....................
675
2.6.1 The three famous ancient problems..................
2.6.2 The main theorem of Galois theory..................675
678
2.6.3 The generalized fundamental theorem of algebra..........°
679
2.6.4 Classification of field extensions....................
2.6.5 The main theorem on equations which can be solved by radical« •«8U
Contents xvü
2.6.6 Constructions with a ruler and a compass..............682
2.7 Number theory.................................685
2.7.1 Basic ideas...............................686
2.7.2 The Euclidean algorithm .......................687
2.7.3 The distribution of prime numbers..................690
2.7.4 Additive decompositions........................696
2.7.5 The approximation of irrational numbers by rational numbers and
continued fractions...........................699
2.7.6 Transcendental numbers........................705
2.7.7 Applications to the number n.....................708
2.7.8 Gaussian congruences.........................712
2.7.9 Minkowski s geometry of numbers..................715
2.7.10 The fundamental local-global principle in number theory.....715
2.7.11 Ideals and the theory of divisors...................717
2.7.12 Applications to quadratic number fields...............719
2.7.13 The analytic class number formula..................721
2.7.14 Hubert s class field theory for general number fields ........722
3. Geometry 725
3.1 The basic idea of geometry epitomized by Klein s Erlanger Program . . . 725
3.2 Elementary geometry..............................726
3.2.1 Plane trigonometry...........................726
3.2.2 Applications to geodesy........................733
3.2.3 Spherical geometry...........................736
3.2.4 Applications to sea and air travel...................741
3.2.5 The Hilbert axioms of geometry ...................742
3.2.6 The parallel axiom of Euclid .....................745
3.2.7 The non-Euclidean elliptic geometry.................746
3.2.8 The non-Euclidean hyperbolic geometry •...............747
3.3 Applications of vector algebra in analytic geometry.............749
3.3.1 Lines in the plane ...........................750
3.3.2 Lines and planes in space.......................751
3.3.3 Volumes.................................752
3.4 Euclidean geometry (geometry of motion)..................753
3.4.1 The group of Euclidean motions...................753
3.4.2 Conic sections .............................754
3.4.3 Quadratic surfaces...........................755
3.5 Projective geometry..............................760
3.5.1 Basic ideas...............................760
3.5.2 Projective maps............................762
3.5.3 The ri-dimetisjonal real projective space...............763
xviii Contents
(TCP
3 54 The n-dimensional complex projective space.............
. 765
35 5 The classification of plane geometries.................
......769
3.6 Differential geometry......................
.....770
3.6.1 Plane curves........................
.....775
3.6.2 Space curves........................
3.6.3 The Gaussian local theory of surfaces................
788
3.6.4 Gauss global theory of surfaces....................
, , , .....788
3.7 Examples of plane curves.....................
3.7.1 Envelopes and caustics.........................
, .... 789
3.7.2 Evolutes............................
. 790
3.7.3 Involutes...............................
790
3.7.4 Huygens tractrix and the catenary curve..............
3.7.5 The lemniscate of Jakob Bernoulli and Cassini s oval........791
793
3.7.6 Lissajou figures.............................
793
3.7.7 Spirals..................................
794
3.7.8 Ray curves (chonchoids)........................
3.7.9 Wheel curves..............................
799
3.8 Algebraic geometry...............................
799
3.8.1 Basic ideas...............................
808
3.8.2 Examples of plane curves.......................
813
3.8.3 Applications to the calculation of integrals..............
814
3.8.4 The projective complex form of a plane algebraic curve ......°
818
3.8.5 The genus of a curve..........................
822
3.8.6 Diophantine Geometry.........................
oog
3.8.7 Analytic sets and the Weieratrass preparation theorem.......
829
3.8.8 The resolution of singularities.....................
831
3.8.9 The algebraization of modern algebraic geometry..........
837
3.9 Geometries of modern physics.........................
3.9.1 Basic ideas...............................^7
• i 840
3.9.2 Unitary geometry, Hilbert spaces and elementary particles.....
847
3.9.3 Pseudo-unitary geometry.......................
850
3.9.4 Minkowski geometry..........................
854
3.9.5 Applications to the special theory of relativity ...........
860
3.9.6 Spin geometry and fermions......................
868
3.9.7 Almost complex structures......................
3.9.8 Symplectic geometry
813
L Foundations of Mathematics
873
4.1 The language of mathematics.........................
873
4.1.1 True and fabe statements.......................
Contents xix
4.1.2 Implications...............................874
4.1.3 Tautological and logical laws.....................876
4.2 Methods of proof................................878
4.2.1 Indirect proofs.............................878
4.2.2 Induction proofs............................878
4.2.3 Uniqueness proofs...........................879
4.2.4 Proofs of existence...........................879
4.2.5 The necessity of proofs in the age of computers...........881
4.2.6 Incorrect proofs.............................882
4.3 Naive set theory................................884
4.3.1 Basic ideas...............................884
4.3.2 Calculations with sets.........................886
4.3.3 Maps ..................................889
4.3.4 Cardinality of sets...........................891
4.3.5 Relations................................892
4.3.6 Systems of sets.............................895
4.4 Mathematical logic...............................895
4.4.1 Prepositional calculus.........................896
4.4.2 Predicate logic.............................899
4.4.3 The axioms of set theory .......................900
4.4.4 Cantor s structure at infinity.....................901
4.5 The history of the axiomatic method.....................905
5. Calculus of Variations and Optimization 909
5.1 Calculus of variations - one variable.....................910
5.1.1 The Euler Lagrange equations....................910
5.1.2 Applications ..............................913
5.1.3 Hamilton s equations..........................919
5.1.4 Applications ..............................925
5.1.5 Sufficient conditions for a local minimum..............927
5.1.6 Problems with constraints and Lagrange multipliers........930
5.1.7 Applications ..............................931
5.1.8 Natural boundary conditions.....................934
5.2 Calculus of variations - several variables...................935
5.2.1 The Euler-Lagrange equations....................935
5.2.2 Applications ..............................936
5.2.3 Problems with constraints and Lagrange multipliers........939
5.3 Control problems................................940
5.3.1 Bellman dynamical optimization...................941
5.3.2 Applications ..............................942
Contents
5 3 3 The Pontryagin maximum principle.................
944
5.3.4 Applications ..............................
,. . .. .....946
5.4 Classical non-linear optimization..................
5.4.1 Local minimization problems.....................
5.4.2 Global minimization problems and convexity............9
5 4.3 Applications to Gauss method of least squares...........9
948
5.4.4 Applications to pseudo-inverses....................
5.4.5 Problems with constraints and Lagrange multipliers........948
5.4 S Applications to entropy........................
951
5.4.7 The subdifferential...........................*
951
5.4.8 Duality theory and saddle points...................
5.5 Linear optimization...............................
5.5.1 Basic ideas...............................
955
5.55 The general linear optimization problem...............
5.5.3 The normal form of an optimization problem and the minimal test 957
5.5.4 The simplex algorithm.........................
.............958
............961
.............962
...........963
...........963
.............963
..........964
..........964
..........965
. . .966
5.5.5 The minimal test.............
5.5.6 Obtaining the normal form.......
5.5.7 Duality in linear optimization.....
5.5.8 Modifications of the simplex algorithm
5.6 Applications of linear optimization......
5.6.1 Capacity utilization..........
5.6.2 Mixing problems............
5.6.3 Distributing resources or products . .
5.6.4 Design and shift planing........
5.6.5 Linear transportation problems ....
Q75
6. Stochastic Calculus - Mathematics of Chance
976
6.1 Elementary stochastics.............................
6.1.1 The classical probability model...........
6.1.2 The law of large numbers due to Jakob Bernoulli .
6.1.3 The limit theorem of de Moivre...........
6.1.4 The Gaussian normal distribution.........
6.1.5 The correlation coefficient..............
6.1.6 Applications to classical statistical physics.....
6.2 Kolmogorov s axiomatic foundation of probability theory .
6.2.1 Calculations with events and probabilities . . . .
6.2.2 Random variables.................
6.2.3 Random vectors..................
6.2.4 Limit theorems...................
977
.979
.980
.980
.983
.986
.989
.992
.995
.1001
.1006
Contents xxi
6.2.5 The BernoulU model for successive independent trials .......1007
6.3 Mathematical statistics ............................1015
6.3.1 Basic ideas...............................1016
6.3.2 Important estimators..........................1017
6.3.3 Investigating normally distributed measurements..........1018
6.3.4 The empirical distribution function..................1021
6.3.5 The maximal likelihood method ...................1027
6.3.6 Multivariate analysis..........................1029
6.4 Stochastic processes..............................1031
6.4.1 Time series...............................1033
6.4.2 Markov chains and stochastic matrices................1039
6.4.3 Poisson processes............................1041
6.4.4 Brownian motion and diffusion....................1042
6.4.5 The main theorem of Kolmogorov for general stochastic processes 1046
7. Numerical Mathematics and Scientific Computing 1049
7.1 Numerical computation and error analysis..................1050
7.1.1 The notion of algorithm........................1050
7.1.2 Representing numbers on computers.................1051
7.1.3 Sources of error, finding errors, condition and stability.......1052
7.2 Linear algebra..................................1055
7.2.1 Linear systems of equations - direct methods............1055
7.2.2 Iterative solutions of linear systems of equations..........1062
7.2.3 Eigenvalue problems..........................1065
7.2.4 Fitting and the method of least squares...............1069
7.3 Interpolation..................................1075
7.3.1 Interpolation polynomials.......................1075
7.3.2 Numerical differentiation .......................1084
7.3.3 Numerical integration.........................1085
7.4 Non-linear problems..............................1093
7.4.1 Non-linear equations..........................1093
7.4.2 Non-linear systems of equations....................1094
7.4.3 Determination of zeros of polynomials................1097
7.5 Approximation.................................1102
7.5.1 Approximation in quadratic means..................1102
7.5.2 Uniform approximation........................1106
7.5.3 Approximate uniform approximation.................1108
7.6 Ordinary differential equations........................1109
7.6.1 Initial value problems.........................1109
7.6.2 Boundary value probJenis.......................1118
xxii Contents
7.7 Partial differential equations..........................1121
7.7.1 Basic ideas...............................1121
7.7.2 An overview of discretization procedures...............1122
7.7.3 Elliptic differential equations.....................1127
7.7.4 Parabolic differential equations....................1138
7.7.5 Hyperbolic differential equations...................1141
7.7.6 Adaptive discretization procedures..................1149
7.7.7 Iterative solutions of systems of equations..............1152
7.7.8 Boundary element methods......................1163
7.7.9 Harmonic analysis...........................1165
7.7.10 Inverse problems............................1176
Sketch of the history of mathematics 1179
Bibliography 1203
List of Names 1231
Index 1235
Mathematical symbols 1275
Dimensions of physical quantities 1279
Tables of physical constants 1281
|
| any_adam_object | 1 |
| author_GND | (DE-588)121295869 |
| building | Verbundindex |
| bvnumber | BV017870543 |
| callnumber-first | Q - Science |
| callnumber-label | QA40 |
| callnumber-raw | QA40.T4813 2004 |
| callnumber-search | QA40.T4813 2004 |
| callnumber-sort | QA 240 T4813 42004 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SH 500 |
| classification_tum | MAT 001k |
| ctrlnum | (OCoLC)53393406 (DE-599)BVBBV017870543 |
| dewey-full | 510 51022 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 510 22 |
| dewey-search | 510 510 22 |
| dewey-sort | 3510 |
| 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>02708nam a2200685 c 4500</leader><controlfield tag="001">BV017870543</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20131216 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">040219s2004 xxkd||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">973607602</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0198507631</subfield><subfield code="9">0-19-850763-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780199686926</subfield><subfield code="9">978-0-19-968692-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">978198507635</subfield><subfield code="9">978-19-850763-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)53393406</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV017870543</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">ger</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxk</subfield><subfield code="c">XA-GB</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-1050</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA40.T4813 2004</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">22</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510 22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SH 500</subfield><subfield code="0">(DE-625)143075:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 001k</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="130" ind1="0" ind2=" "><subfield code="a">Teubner-Taschenbuch der Mathematik, Bd. 1</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Oxford users' guide to mathematics</subfield><subfield code="c">ed. by Eberhard Zeidler</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">Users' guide to mathematics</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Oxford</subfield><subfield code="b">Oxford Univ. Press</subfield><subfield code="c">2004</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XXII, 1284 S.</subfield><subfield code="b">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">Hier auch später erschienene, unveränderte Nachdrucke</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathématiques - Guides, manuels, etc</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Wiskunde</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield><subfield code="v">Handbooks, manuals, etc</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geometrie</subfield><subfield code="0">(DE-588)4020236-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematische Physik</subfield><subfield code="0">(DE-588)4037952-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Infinitesimalrechnung</subfield><subfield code="0">(DE-588)4072798-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Optimierung</subfield><subfield code="0">(DE-588)4043664-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4155008-0</subfield><subfield code="a">Formelsammlung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mathematische Physik</subfield><subfield code="0">(DE-588)4037952-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="2"><subfield code="a">Algebra</subfield><subfield code="0">(DE-588)4001156-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="3"><subfield code="a">Geometrie</subfield><subfield code="0">(DE-588)4020236-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="4"><subfield code="a">Infinitesimalrechnung</subfield><subfield code="0">(DE-588)4072798-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="5"><subfield code="a">Optimierung</subfield><subfield code="0">(DE-588)4043664-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zeidler, Eberhard</subfield><subfield code="d">1940-2016</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)121295869</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</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=010721341&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:BVB01-010721341</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| genre | (DE-588)4155008-0 Formelsammlung gnd-content |
| genre_facet | Formelsammlung |
| id | DE-604.BV017870543 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:22:42Z |
| institution | BVB |
| isbn | 0198507631 9780199686926 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010721341 |
| oclc_num | 53393406 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-1050 DE-91G DE-BY-TUM DE-521 DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-1050 DE-91G DE-BY-TUM DE-521 DE-11 |
| physical | XXII, 1284 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Teubner-Taschenbuch der Mathematik, Bd. 1 Oxford users' guide to mathematics ed. by Eberhard Zeidler Users' guide to mathematics Oxford Oxford Univ. Press 2004 XXII, 1284 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Mathématiques - Guides, manuels, etc Wiskunde gtt Mathematik Mathematics Handbooks, manuals, etc Geometrie (DE-588)4020236-7 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf (DE-588)4155008-0 Formelsammlung gnd-content Mathematische Physik (DE-588)4037952-8 s DE-604 Mathematik (DE-588)4037944-9 s Analysis (DE-588)4001865-9 s Algebra (DE-588)4001156-2 s Geometrie (DE-588)4020236-7 s Infinitesimalrechnung (DE-588)4072798-1 s Optimierung (DE-588)4043664-0 s 1\p DE-604 Zeidler, Eberhard 1940-2016 Sonstige (DE-588)121295869 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010721341&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Oxford users' guide to mathematics Mathématiques - Guides, manuels, etc Wiskunde gtt Mathematik Mathematics Handbooks, manuals, etc Geometrie (DE-588)4020236-7 gnd Algebra (DE-588)4001156-2 gnd Mathematische Physik (DE-588)4037952-8 gnd Analysis (DE-588)4001865-9 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd Mathematik (DE-588)4037944-9 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4001156-2 (DE-588)4037952-8 (DE-588)4001865-9 (DE-588)4072798-1 (DE-588)4037944-9 (DE-588)4043664-0 (DE-588)4155008-0 |
| title | Oxford users' guide to mathematics |
| title_alt | Teubner-Taschenbuch der Mathematik, Bd. 1 Users' guide to mathematics |
| title_auth | Oxford users' guide to mathematics |
| title_exact_search | Oxford users' guide to mathematics |
| title_full | Oxford users' guide to mathematics ed. by Eberhard Zeidler |
| title_fullStr | Oxford users' guide to mathematics ed. by Eberhard Zeidler |
| title_full_unstemmed | Oxford users' guide to mathematics ed. by Eberhard Zeidler |
| title_short | Oxford users' guide to mathematics |
| title_sort | oxford users guide to mathematics |
| topic | Mathématiques - Guides, manuels, etc Wiskunde gtt Mathematik Mathematics Handbooks, manuals, etc Geometrie (DE-588)4020236-7 gnd Algebra (DE-588)4001156-2 gnd Mathematische Physik (DE-588)4037952-8 gnd Analysis (DE-588)4001865-9 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd Mathematik (DE-588)4037944-9 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Mathématiques - Guides, manuels, etc Wiskunde Mathematik Mathematics Handbooks, manuals, etc Geometrie Algebra Mathematische Physik Analysis Infinitesimalrechnung Optimierung Formelsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010721341&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | UT teubnertaschenbuchdermathematikbd1 AT zeidlereberhard oxfordusersguidetomathematics AT zeidlereberhard usersguidetomathematics |