Mathematics Handbook - for Science and Engineering [Hardcover] by Lennart Råde (Author), Bertil Westergren (Author) Hardcover: 562 pages Publisher: Studentlitteratur AB; 5 edition (28 Nov. 2003) Language: English ISBN-10: 9144031092 ISBN-13: 978-9144031095 16cm X 22.5cm
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 metods with applications in technology and science.
Preface ---------------------------------------------------7 1Fundamentals. Discrete Mathematics---------------9 1.1Logic-------------------------------------------------9 1.2Set Theory------------------------------------------14 1.3Binary Relations and Functions------------------17 1.4Algebraic Structures-------------------------------21 1.5Graph Theory--------------------------------------33 1.6Codes------------------------------------------------37 2Algebra--------------------------------------------------43 2.1Basic Algebra of Real Numbers-----------------43 2.2Number Theory------------------------------------49 2.3Complex Numbers---------------------------------61 2.4Algebraic Equations-------------------------------63 3Geometry and Trigonometry-------------------------66 3.1Plane Figures---------------------------------------66 3.2Solids------------------------------------------------71 3.3Spherical Trigonometry---------------------------75 3.4Geometrical Vectors-------------------------------77 3.5Plane Analytic Geometry-------------------------79 3.6Analytic Geometry in Space----------------------83 3.7Fractals----------------------------------------------87 4Linear Algebra------------------------------------------90 4.1Matrices---------------------------------------------90 4.2Determinants---------------------------------------93 4.3Systems of Linear Equations---------------------95 4.4Linear Coordinate Transformations-------------97 4.5Eigenvalues. Diagonalization---------------------98 4.6Quadratic Forms----------------------------------103 4.7Linear Spaces-------------------------------------106 4.8Linear Mappings----------------------------------108 4.9Tensors--------------------------------------------114 4.10Complex matrices-------------------------------114 5The Elementary Functions--------------------------118 5.1A Survey of the Elementary Functions--------118 5.2Polynomials and Rational Functions-----------119 5.3Logarithmic, Exponential, Power and Hyperbolic Functions------------121 5.4Trigonometric and Inverse Trigonometric Functions------------125 6Differential Calculus (one variable)----------------132 6.1Some Basic Concepts----------------------------132 6.2Limits and Continuity----------------------------133 6.3Derivatives-----------------------------------------136 6.4Monotonicity. Extremes of Functions----------139 7Integral Calculus--------------------------------------141 7.1Indefinite Integrals--------------------------------141 7.2Definite Integrals----------------------------------146 7.3Applications of Differential and Integral Calculus-------148 7.4Table of Indefinite Integral----------------------153 7.5Tables of Definite Integrals----------------------178 8Sequences and Series--------------------------------183 8.1Sequences of Numbers--------------------------183 8.2Sequences of Functions-------------------------184 8.3Series of Constant Terms-----------------------185 8.4Series of Functions-------------------------------187 8.5Taylor Series--------------------------------------189 8.6Special Sums and Series-------------------------192 9Ordinary Differential Equations (ODE)------------200 9.1Differential Equations of the First Order-------200 9.2Differential Equations of the Second Order-------202 9.3Linear Differential Equations--------------------205 9.4Autonomous systems-----------------------------213 9.5General Concepts and Results-------------------216 9.6Linear Difference Equations---------------------218 10Multidimensional Calculus--------------------------221 10.1The Space Rn------------------------------------221 10.2Surfaces. Tangent Planes-----------------------222 10.3Limits and Continuity---------------------------223 10.4Partial Derivatives-------------------------------224 10.5Extremes of Functions--------------------------227 10.6Functions f: Rn Æ Rm (Rn ÆRn)-------------229 10.7Double Integrals---------------------------------231 10.8Triple Integrals----------------------------------234 10.9Partial Differential Equations------------------239 11Vector Analysis--------------------------------------246 11.1Curves--------------------------------------------246 11.2Vector Fields-------------------------------------248 11.3Line Integrals------------------------------------253 11.4Surface Integrals--------------------------------256 12Orthogonal Series and Special Functions--------259 12.1Orthogonal Systems----------------------------259 12.2Orthogonal Polynomials-----------------------263 12.3Bernoulli and Euler Polynomials--------------269 12.4Bessel Functions--------------------------------270 12.5Functions Defined by Transcendental Integrals---------287 12.6Step and Impulse Functions-------------------297 12.7Functional Analysis-----------------------------298 12.8Lebesgue Integrals------------------------------303 12.9Generalized functions (Distributions)--------308 13Transforms------------------------------------------310 13.1Trigonometric Fourier Series------------------310 13.2Fourier Transforms-----------------------------315 13.3Discrete Fourier Transforms------------------325 13.4The z-transform---------------------------------327 13.5Laplace Transforms----------------------------330 13.6Dynamical Systems (Filters)------------------338 13.7Hankel and Hilbert transforms----------------341 13.8Wavelets-----------------------------------------344 14Complex Analysis-----------------------------------349 14.1Functions of a Complex Variable-------------349 14.2Complex Integration----------------------------352 14.3Power Series Expansions----------------------354 14.4Zeros and Singularities-------------------------355 14.5Conformal Mappings---------------------------356 15Optimization-----------------------------------------365 15.1Calculus of Variations--------------------------365 15.2Linear Optimization-----------------------------371 15.3Integer and Combinatorial Optimization--------379 15.4Nonlinear Optimization-------------------------383 15.5Dynamic Optimization-------------------------389 16Numerical Analysis---------------------------------391 16.1Approximations and Errors--------------------391 16.2Numerical Solution of Equations-------------392 16.3Perturbation analysis---------------------------397 16.4Interpolation-------------------------------------398 16.5Numerical Integration and Differentiation---------404 16.6Numerical Solutions of Differential Equations--------412 16.7Numerical summation--------------------------421 17Probability Theory---------------------------------424 17.1Basic Probability Theory----------------------424 17.2Probability Distributions-----------------------434 17.3Stochastic Processes---------------------------439 17.4Algorithms for Calculation of Probability Distributions--------443 17.5Simulation---------------------------------------445 17.6Queueing Systems------------------------------449 17.7Reliability----------------------------------------452 17.8Tables--------------------------------------------459 18Statistics---------------------------------------------479 18.1Descriptive Statistics---------------------------479 18.2Point Estimation--------------------------------488 18.3Confidence Intervals---------------------------491 18.4Tables for Confidence Intervals--------------495 18.5Tests of Significance---------------------------501 18.6Linear Models-----------------------------------507 18.7Distribution-free Methods---------------------512 18.8Statistical Quality Control---------------------518 18.9Factorial Experiments--------------------------522 18.10Analysis of life time (failure time) data--------525 18.11Statistical glossary-----------------------------526 19Miscellaneous---------------------------------------530 Glossary of functions---------------------------------544 Glossary of symbols----------------------------------545 Index----------------------------------------------------547
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