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Mathematics Handbook for Science and Engineering - Lennart Rade

Mathematics Handbook for Science and Engineering

Hardcover

Published: 16th March 2004
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Mathematics Handbook for Science and Engineering is a comprehensive handbook for scientists, engineers, teachers and students at universities. The book presents in a lucid and accessible form classical areas of mathematics like algebra, geometry and analysis and also areas of current interest like discrete mathematics, probability, statistics, optimization and numerical analysis. It concentrates on definitions, results, formulas, graphs and tables and emphasizes concepts and methods with applications in technology and science.For the fifth edition the chapter on Optimization has been enlarged and the chapters on Probability Theory and Statstics have been carefully revised.

From the reviews of the fifth edition:

"This student handbook covers the basic areas of mathematics, numerical analysis, probability ... . It concentrates on definitions, results ... emphasising the concepts and methods with applications in technology and science. ... This new edition has new sections on optimisation and fractals." (Book News on the Internet, January, 2005)

"The principal aim of this book is to provide useful information in a lucid and accessible form on some basic topics of mathematics, such as numerical analysis ... . Thus, the book will be of interest to students and teachers of mathematics, science and engineering ... . This is an excellent book being very carefully prepared and presented. The reviewer warmly recommends it to all those interested in the study of mathematics and to apply it for solving modern practical problems." (Ioan Pop, Journal of Applied Statistics, Vol. 32 (1), 2004)

"This well-known and very useful handbook presents in a very accessible form classical areas of mathematics ... and also areas of current interest ... . A `must' not only for libraries but also for scientists, engineers, teachers and students at universities." (Olaf Ninnemann, Zentralblatt MATH, Vol. 1094 (20), 2006)

"As usual from Springer, this is a beautifully produced book, sturdily bound in their usual blue and yellow and nicely printed, sitting comfortably in the hand and opening neatly to any page. ... Leafing through the book made me itch to get a pencil and paper and start playing with the mathematics. Above all useful, but also comforting, exciting and challenging, this is a book I wholeheartedly recommend to anyone with a penchant for applicable mathematics." (Peter Macgregor, The Mathematical Gazette, Vol. 89 (516), 2005)

"This is the fifth edition of this mathematics handbook, a book which covers all the basic areas of mathematics, numerical analysis, probability and statistics, and their various applications. ... this volume may be of interest to undergraduate students or those research scientists or engineers who are allergic to modern computerized methods of doing mathematics. ... The book is well produced ... and will surely withstand use over many years - and the price seems reasonable for such a large book." (Andre Hautot, Physicalia Magazine, Vol. 28 (1), 2006)

Prefacep. 7
Fundamentals. Discrete Mathematicsp. 9
Logicp. 9
Set Theoryp. 14
Binary Relations and Functionsp. 17
Algebraic Structuresp. 21
Graph Theoryp. 33
Codesp. 37
Algebrap. 43
Basic Algebra of Real Numbersp. 43
Number Theoryp. 49
Complex Numbersp. 61
Algebraic Equationsp. 63
Geometry and Trigonometryp. 66
Plane Figuresp. 66
Solidsp. 71
Spherical Trigonometryp. 75
Geometrical Vectorsp. 77
Plane Analytic Geometryp. 79
Analytic Geometry in Spacep. 83
Linear Algebrap. 87
Matricesp. 87
Determinantsp. 90
Systems of Linear Equationsp. 92
Linear Coordinate Transformationsp. 94
Eigenvalues. Diagonalizationp. 95
Quadratic Formsp. 100
Linear Spacesp. 103
Linear Mappingsp. 105
Tensorsp. 110
Complex matricesp. 111
The Elementary Functionsp. 115
A Survey of the Elementary Functionsp. 115
Polynomials and Rational Functionsp. 116
Logarithmic, Exponential, Power and Hyperbolic Functionsp. 118
Trigonometric and Inverse Trigonometric Functionsp. 122
Differential Calculus (one variable)p. 129
Some Basic Conceptsp. 129
Limits and Continuityp. 130
Derivativesp. 132
Monotonicity. Extremes of Functionsp. 135
Integral Calculusp. 137
Indefinite Integralsp. 137
Definite Integralsp. 142
Applications of Differential and Integral Calculusp. 144
Tables of Indefinite Integralsp. 149
Tables of Definite Integralsp. 174
Sequences and Seriesp. 179
Sequences of Numbersp. 179
Sequences of Functionsp. 180
Series of Constant Termsp. 181
Series of Functionsp. 183
Taylor Seriesp. 185
Special Sums and Seriesp. 188
Ordinary Differential Equations (ODE)p. 196
Differential Equations of the First Orderp. 196
Differential Equations of the Second Orderp. 198
Linear Differential Equationsp. 201
Autonomous systemsp. 209
General Concepts and Resultsp. 212
Linear Difference Equationsp. 214
Multidimensional Calculusp. 217
The Space Rnp. 217
Surfaces. Tangent Planesp. 218
Limits and Continuityp. 219
Partial Derivativesp. 220
Extremes of Functionsp. 223
Functions f: Rn → Rm (Rn → Rn)p. 225
Double Integralsp. 227
Triple Integralsp. 230
Partial Differential Equationsp. 235
Vector Analysisp. 242
Curvesp. 242
Vector Fieldsp. 244
Line Integralsp. 249
Surface Integralsp. 252
Orthogonal Series and Special Functionsp. 255
Orthogonal Systemsp. 255
Orthogonal Polynomialsp. 259
Bernoulli and Euler Polynomialsp. 265
Bessel Functionsp. 266
Functions Defined by Transcendental Integralsp. 283
Step and Impulse Functionsp. 293
Functional Analysisp. 294
Lebesgue Integralsp. 299
Generalized functions (Distributions)p. 304
Transformsp. 306
Trigonometric Fourier Seriesp. 306
Fourier Transformsp. 311
Discrete Fourier Transformsp. 320
The z-transformp. 322
Laplace Transformsp. 325
Dynamical Systems (Filters)p. 333
Hankel and Hilbert transformsp. 336
Waveletsp. 339
Complex Analysisp. 344
Functions of a Complex Variablep. 344
Complex Integrationp. 347
Power Series Expansionsp. 349
Zeros and Singularitiesp. 350
Conformal Mappingsp. 351
Optimizationp. 360
Calculus of Variationsp. 360
Linear Optimizationp. 366
Non-linear Optimizationp. 370
Dynamic Optimizationp. 372
Numerical Analysis and Programmingp. 374
Approximations and Errorsp. 374
Numerical Solution of Equationsp. 375
Interpolationp. 381
Numerical Integration and Differentiationp. 387
Numerical Solutions of Differential Equationsp. 395
Numerical summationp. 404
Probability Theoryp. 407
Basic Probability Theoryp. 407
Probability Distributionsp. 417
Stochastic Processesp. 422
Algorithms for Calculation of Probability Distributionsp. 426
Simulationp. 428
Queueing Systemsp. 432
Reliabilityp. 435
Tablesp. 442
Statisticsp. 462
Descriptive Statisticsp. 462
Point Estimationp. 471
Confidence Intervalsp. 474
Tables for Confidence Intervalsp. 478
Tests of Significancep. 484
Linear Modelsp. 490
Distribution-free Methodsp. 495
Statistical Quality Controlp. 501
Factorial Experimentsp. 505
Analysis of life time (failure time) datap. 508
Statistical glossaryp. 509
Miscellaneousp. 513
Glossary of functionsp. 527
Glossary of symbolsp. 528
Indexp. 531
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540211419
ISBN-10: 3540211411
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 562
Published: 16th March 2004
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 3.81
Weight (kg): 1.08
Edition Number: 5
Edition Type: Revised