Table of contents for Mathematics handbook for science and engineering / Lennart Råde, Bertil Westergren.


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F1 undamentals. Discrete Mathematics 9
LI    Logic 9
12    Set Theory 14
1.3   Binary Relations and Functions 17
1.4   Algebraic Structures 21
1.5   Graph Theory 33
16   Codes 37
2  Algebra 43
2.    Basic Algebra of Real Numbers 43
2.2   Number Theory 49
23    Complex Numbers 61
2.4   Algebraic Equations 63
3   Geometry and Trigonometry 66
31    Plane Figures 66
3.2   Solids 71
3.3   Spherical Trigonometry 75
3.4   Geometrical Vectors 77
3.5   Plane Analytic Geometry 79
16    Analytic Geometry in Space 83
337   Fractals 87
4   Linear Algebra 90
4.1   Matrices 90
4.2   Determinants 93
4.3   Systems of Linear Equations 95
4.4   Linear Coordinate Transformations 97
4 5   Eigenvalues. Diagonalization 98
4.6   Quadratic Forms 103
4.7   Linear Spaces 106
4.8   Linear Mappings 108
4.9   T ensors 114
4.10  Complex matrices 114
5   The Elementary Functions 118
5.1   A Survey of the Elementary Functions 118
5.2   Polynomials and Rational Functions 119
5.3   Logarithmic, Exponential, Power and Hyperbolic Functions 121
5.4   Trigonometric and Inverse Trigonometric Functions 125
6   Differential Calculus (one variable) 132
6.1   Some Basic Concepts 132
6.2   Limits and Continuity 133
6.3   Derivatives 136
6.4   Monotonicity. Extremes of Functions 139
7   Integral Calculus 141
7.1   Indefinite Integrals 141
7.2   Definite Integrals 146
7.3   Applications of Differential and Integral Calculus '148
7.4   Table of Indefinite Integral 153
7.5   Tables of Definite Integrals 178
8   Sequences and Series 183
8.1   Sequences of Numbers 183
8.2   Sequences of Functions 184
8,3   Series of Constant Terms 185
8.4   Series of Functions 187
8.5   Taylor Series 189
8.6   Special Sums and Series 192
9   Ordinary Differential Equations (ODE) 200
9.1   Differential Equations of the First Order 200
9.2   Differential Equations of the Second Order 202
9 3   Linear Differential Equations 205
9.4   Autonomous systems 2313
9.5   General Concepts and Results 216
9.6   Linear Difference Equations 218
10 Multidimensional Calculus 221
10.1  The Space Rn 221
1012  Surfaces. Tangent Planes 222
103   Limits and Continuity 223
10 4  Partial Derivatives 224
105   Extremes of Functions 227
10.6  Functions f: Rn -- Rm (R" -Rn) 229
10.7  Double Integrals 231
10.8  Triple Integrals 234
10.9  Partial Differential Equations 239
11 Vector Analysis 246
11.1  Curves 246
11.2  Vector Fields 248
11.3  Line Integrals 253
11.4  Surface Integrals 256
12 Orthogonal Series and Special Functions 259
12.1  Orthogonal Systems 259
12.2  Orthogonal Polynomials 263
12.3  Bernoulli and Euler Polynomials 269
12.4  Bessel Functions 270
12 5  Functions Defined by Transcendental Integrals 287
12.6  Step and Impulse Functions 297
12.7  Functional Analysis 298
12.8  Lebesgue Integrals 303
12.9  Generalized functions (Distributions) 308
13 Transforms 310
13 1  Trigonometric Fourier Series 310
13.2  Fourier Transforms 315
13.3  Discrete Fourier Transforms 325
13.4  The -transform  327
13.5  Laplace Transforms 330
13.6  Dynamical Systems (Filters) 338
i3,7  Hankel and Hilbert transforms 341
13.8  Wavelets 344
14 Complex Analysis 349
14.1  Functions of a Complex Variable 349
14.2  Complex Integration 352
4.3   Power Series Expansions 354
14.4  Zeros and Singularities 355
14.5  Conformal Mappings 356
15 Optimization 365
15.1  Calculus of Variations 365
15.2  Linear Optimization 371
15.3 Integer and Combinatorial Optimization 379
15.4  Nonlinear Optimization 383
15.5  Dynamic Optimization 389
16 Numerical Analysis 391
16.   Approximations and Errors 391
16.2  Numerical Solution of Equations 392
16.3  Perturbation analysis 397
16.4 ixterpolation 398
16.5  Numerical Integration and Differentiation 404
16.6  Numerical Solutions of Differential Equations 412
16.7  Numerical summation 421
17 Probability Theory 424
17.1  Basic Probability Theory 424
17.2 Probability Distributions 434
17.3  Stochastic Processes 439
17.4  Algorithms for Calculation of Probability Distributions 443
17.5  Simulation 445
17.6  Queueing Systems 449
17.7  Reliability 452
17.8  Tables 459
18 Statistics 479
1 8.1  Descriptive Statistics 479
18.2  Point Estimation 488
18.3  Confidence Intervals 491
18.4  Tables for Confidence Intervals 495
18.5  Tests of Significance 501
18.6  Linear Models 507
18.7  Distribution-free Methods 512
18.8  Statistical Quality Control 518
18.9  Factorial Experiments 522
18.10 Analysis of life time (failure time) data 525
18.11 Statistical glossary 526
19 Miscellaneous 530



Library of Congress subject headings for this publication: Mathematics Formulae, Mathematics Tables, Mathematics Handbooks, manuals, etc