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Oxford Users' Guide to Mathematics
     

Oxford Users' Guide to Mathematics

by Eberhard Zeidler
 

ISBN-10: 0198507631

ISBN-13: 9780198507635

Pub. Date: 11/04/2004

Publisher: Oxford University Press

Recognizing the importance of mathematics in research and commerce, the many instances in which different aspects of mathematics are coming to inform each other, and the prevalence of the personal computer, Zeidler (Max Planck Institute for Mathematics in the Sciences) and contributors offer a basic overview of mathematics for students, practitioners, and teachers.

Overview

Recognizing the importance of mathematics in research and commerce, the many instances in which different aspects of mathematics are coming to inform each other, and the prevalence of the personal computer, Zeidler (Max Planck Institute for Mathematics in the Sciences) and contributors offer a basic overview of mathematics for students, practitioners, and teachers. They begin by explaining basic formulas, graphs and tables, then describe analysis (including vector analysis, differential equations, and complex function theory), algebra (including linear algebra, Galois theory, and number theory), geometry (including Euclidean, projective, differential and algebraic), calculus of variations and optimization, statistical calculus and the mathematics of chance, and numerical mathematics and scientific computing. They include a sketch of the history of mathematics, a list of mathematical symbols, and tables of physical constants. This is a translation of Teubner-Taschenbuch der Mathematik Vol. 1 published by G. G. Teubner in 1996. Annotation ©2004 Book News, Inc., Portland, OR

Product Details

ISBN-13:
9780198507635
Publisher:
Oxford University Press
Publication date:
11/04/2004
Pages:
1308
Product dimensions:
8.60(w) x 5.70(h) x 1.80(d)

Table of Contents

Introduction1
0Formulas, Graphs and Tables3
0.1Basic formulas of elementary mathematics3
0.2Elementary functions and graphs45
0.3Mathematics and computers - a revolution in mathematics74
0.4Tables of mathematical statistics75
0.5Tables of values of special functions98
0.6Table of prime numbers [less than or equal] 4000110
0.7Formulas for series and products111
0.8Tables for differentiation of functions133
0.9Tables of integrals138
0.10Tables on integral transformations192
1Analysis221
1.1Elementary analysis222
1.2Limits of sequences238
1.3Limits of functions249
1.4Differentiation of functions of a real variable262
1.5Derivatives of functions of several real variables278
1.6Integration of functions of a real variable306
1.7Integration of functions of several real variables321
1.8Vector algebra351
1.9Vector analysis and physical fields357
1.10Infinite series376
1.11Integral transformations391
1.12Ordinary differential equations407
1.13Partial differential equations468
1.14Complex function theory532
2Algebra599
2.1Elementary algebra599
2.2Matrices626
2.3Linear algebra637
2.4Multilinear algebra650
2.5Algebraic structures663
2.6Galois theory and algebraic equations675
2.7Number theory685
3Geometry725
3.1The basic idea of geometry epitomized by Klein's Erlanger Program725
3.2Elementary geometry726
3.3Applications of vector algebra in analytic geometry749
3.4Euclidean geometry (geometry of motion)753
3.5Projective geometry760
3.6Differential geometry769
3.7Examples of plane curves788
3.8Algebraic geometry799
3.9Geometries of modern physics837
4Foundations of Mathematics873
4.1The language of mathematics873
4.2Methods of proof878
4.3Naive set theory884
4.4Mathematical logic895
4.5The history of the axiomatic method905
5Calculus of Variations and Optimization909
5.1Calculus of variations - one variable910
5.2Calculus of variations - several variables935
5.3Control problems940
5.4Classical non-linear optimization946
5.5Linear optimization952
5.6Applications of linear optimization963
6Stochastic Calculus - Mathematics of Chance975
6.1Elementary stochastics976
6.2Kolmogorov's axiomatic foundation of probability theory989
6.3Mathematical statistics1015
6.4Stochastic processes1031
7Numerical Mathematics and Scientific Computing1049
7.1Numerical computation and error analysis1050
7.2Linear algebra1055
7.3Interpolation1075
7.4Non-linear problems1093
7.5Approximation1102
7.6Ordinary differential equations1109
7.7Partial differential equations1121
Sketch of the history of mathematics1179
Bibliography1203
List of Names1231
Index1235
Mathematical symbols1275
Dimensions of physical quantities1279
Tables of physical constants1281

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