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Mathematics Handbook

for Science and Engineering
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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 metods wi...

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. This sixth edition is a thoroughly updated version of the book and every chapter has been revised and the layout of the entire book has been modernized. In particular, the chapters on numerical analysis, probability and statistics have gone through major updates. Teachers and researchers from Gothenburg University, Chalmers University of Technology, KTH Royal Institute of Technology and Lund University have contributed.

    • 9
      Preface
      • 1
        13
        Fundamentals Discrete Mathematics
        • 1.1
          13
          Logic
        • 1.2
          17
          Set Theory
        • 1.3
          19
          Binary Relations and Functions
        • 1.4
          23
          Algebraic Structures
        • 1.5
          34
          Graph Theory
        • 1.6
          38
          Codes
      • 2
        45
        Algebra
        • 2.1
          45
          Basic Algebra of Real Numbers
        • 2.2
          51
          Number Theory
        • 2.3
          61
          Complex Numbers
        • 2.4
          63
          Algebraic Equations
      • 3
        67
        Geometry and Trigonometry
        • 3.1
          67
          Plane Figures
        • 3.2
          72
          Solids
        • 3.3
          76
          Spherical Trigonometry
        • 3.4
          77
          Geometrical Vectors
        • 3.5
          79
          Plane Analytic Geometry
        • 3.6
          83
          Analytic Geometry in Space
        • 3.7
          87
          Fractals
      • 4
        91
        Linear Algebra
        • 4.1
          91
          Matrices
        • 4.2
          93
          Determinants
        • 4.3
          95
          Systems of Linear Equations
        • 4.4
          97
          Linear Coordinate Transformations
        • 4.5
          99
          Eigenvalues Diagonalization
        • 4.6
          103
          Quadratic Forms
        • 4.7
          105
          Linear Spaces
        • 4.8
          108
          Linear Mappings
        • 4.9
          114
          Tensors
        • 4.10
          115
          Complex matrices
      • 5
        119
        The Elementary Functions
        • 5.1
          119
          A Survey of the Elementary Functions
        • 5.2
          120
          Polynomials and Rational Functions
        • 5.3
          122
          Logarithmic, Exponential, Power and Hyperbolic Functions
        • 5.4
          125
          Trigonometric and Inverse Trigonometric Functions
      • 6
        133
        Differential Calculus (one variable)
        • 6.1
          133
          Basic concepts
        • 6.2
          134
          Limits and continuity
        • 6.3
          137
          Derivatives
        • 6.4
          140
          Monotonicity. Extrema of functions
      • 7
        143
        Integral Calculus
        • 7.1
          143
          Indefinite Integrals
        • 7.2
          147
          Definite Integrals
        • 7.3
          149
          Applications of Differential and Integral Calculus
        • 7.4
          154
          Tables of Indefinite Integrals
        • 7.5
          175
          Tables of Definite Integrals
      • 8
        179
        Sequences and Series
        • 8.1
          179
          Sequences of Numbers
        • 8.2
          180
          Sequences of Functions
        • 8.3
          181
          Series of Constant Terms
        • 8.4
          183
          Series of Functions
        • 8.5
          185
          Taylor Series
        • 8.6
          188
          Special Sums and Series
      • 9
        197
        Ordinary Differential Equations
        • 9.1
          197
          Differential Equations of the First Order
        • 9.2
          199
          Differential Equations of the Second Order
        • 9.3
          201
          Linear Differential Equations
        • 9.4
          211
          Autonomous systems
        • 9.5
          214
          General Concepts and Results
        • 9.6
          217
          Linear Difference Equations
      • 10
        221
        Multidimensional Calculus
        • 10.1
          221
          The Space Rn
        • 10.2
          223
          Surfaces Tangent Planes
        • 10.3
          224
          Limits and Continuity
        • 10.4
          224
          Partial Derivatives
        • 10.5
          228
          Extrema of Functions
        • 10.6
          230
          Functions f ∶ Rn → Rm (Rn → Rn)
        • 10.7
          233
          Double Integrals
        • 10.8
          236
          Triple Integrals
        • 10.9
          240
          Partial Differential Equations
      • 11
        247
        Vector Calculus
        • 11.1
          247
          Curves
        • 11.2
          249
          Vector Fields
        • 11.3
          254
          Line Integrals
        • 11.4
          256
          Surface Integrals
      • 12
        261
        Orthogonal Series and Special Functions
        • 12.1
          261
          Orthogonal Systems
        • 12.2
          265
          Orthogonal Polynomials
        • 12.3
          272
          Bernoulli and Euler Polynomials
        • 12.4
          273
          Bessel Functions
        • 12.5
          289
          Functions Defined by Transcendental Integrals
        • 12.6
          298
          Step and Impulse Functions
        • 12.7
          299
          Functional Analysis
        • 12.8
          305
          Lebesgue Integrals
        • 12.9
          307
          Some function spaces in Rn
        • 12.10
          310
          Generalized functions (Distributions)*
      • 13
        313
        Transforms
        • 13.1
          313
          Fourier Series
        • 13.2
          318
          Fourier Transforms
        • 13.3
          326
          Discrete Fourier Transforms
        • 13.4
          328
          The z-transform
        • 13.5
          330
          Laplace Transforms
        • 13.6
          337
          Dynamical Systems (Filters)
        • 13.7
          339
          Hankel and Hilbert transforms
        • 13.8
          342
          Wavelets
      • 14
        347
        Complex Analysis
        • 14.1
          347
          Functions of a Complex Variable
        • 14.2
          349
          Complex Integration
        • 14.3
          351
          Power Series Expansions
        • 14.4
          352
          Residues
        • 14.5
          354
          Zeros and Singularities
        • 14.6
          355
          Conformal Mappings
      • 15
        363
        Optimization
        • 15.1
          363
          Calculus of Variations
        • 15.2
          369
          Linear Optimization
        • 15.3
          376
          Integer and Combinatorial Optimization
        • 15.4
          380
          Nonlinear Optimization
        • 15.5
          385
          Dynamic Optimization
      • 16
        389
        Numerical Analysis
        • 16.1
          389
          Approximation, Errors and Convergence
        • 16.2
          390
          Approximation of Functions
        • 16.3
          395
          Numerical Summation
        • 16.4
          398
          Numerical Differentiation
        • 16.5
          403
          Numerical Integration (Quadrature)
        • 16.6
          409
          Numerical Solution of Linear Equations
        • 16.7
          416
          Numerical Solution of Eigenvalue Problems
        • 16.8
          417
          Numerical Solution of Nonlinear Equations
        • 16.9
          419
          Numerical Solution of ODE
        • 16.10
          424
          Numerical Solution of PDE
      • 17
        437
        Probability Theory
        • 17.1
          437
          Basic Probability Theory
        • 17.2
          448
          Probability Distributions
        • 17.3
          453
          Stochastic Processes
        • 17.4
          459
          Simulation
        • 17.5
          462
          Queueing Systems
        • 17.6
          464
          Tables
      • 18
        477
        Statistics
        • 18.1
          477
          Descriptive Statistics
        • 18.2
          478
          Point Estimation
        • 18.3
          482
          Confidence Intervals
        • 18.4
          487
          Tests of Significance
        • 18.5
          492
          Linear Models
        • 18.6
          498
          Distribution-free Methods
        • 18.7
          503
          Factorial Experiments
      • 19
        507
        Miscellaneous
        • 19.1
          507
          The Greek alphabet
        • 19.2
          507
          Physical constants
    • 511
      Glossaries
      • 511
        Glossary of functions
      • 512
        Glossary of symbols
    • 515
      Index

Information

Redaktörer:
Frank Wikström
Författare:
Lennart Råde Bertil Westergren
Språk:
Engelska
ISBN:
9789144128436
Utgivningsår:
1988
Revisionsår:
2019
Artikelnummer:
2505-06
Upplaga:
Sjätte
Sidantal:
530

Författare

Lennart Råde

Lennart Råde var docent i matematisk statistik vid Chalmers Tekniska Högskola i Göteborg, där han undervisade i detta ämne under ca 40 år. Han var ...

Bertil Westergren

Bertil Westergren worked formerly at the Mathematics Department of Chalmers University of Technology and the University of Gothenburg, Sweden.

Frank Wikström

Frank Wikström är docent i matematik vid Lunds universitet. Han har tidigare även undervisat vid Umeå universitet och Mittuniversitetet och arbetat...

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