Riassunto
BETA Mathematics Handbook is a comprehensive, accessible reference compilation of all basic facts and information for pure and applied mathematics, probability and statistics, and numerical analysis and basic applications. It offers a unique blend of classical areas of mathematics such as algebra, geometry, and analysis with new, modern topics. As a result, the book is up to date with all the latest math information used frequently in science and engineering. Modern topics covered include:
Discrete math, including graph theory
Analytic geometry in space
Transforms, including FFT and dynamical systems (filters)
Optimization, including dynamic optimization
Modern probability, including stochastic processes, simulation, and queuing systems
Lebesgue integrals
Each topic is given its own section for a more logical presentation and easier reference. For example, one variable and multivariable calculus appear in separate chapters. Separate chapters are devoted to vector analysis, probability, and statistics as well.
The book also makes extensive use of summary charts, grids, and tables to succinctly convey information. These include:
Methods of proof
Survey of algebraic structures
Summary of integral calculus functions
Summary of methods of deriving Taylor series
Summary table of power series expansions
Differential geometry by concepts summary
Summary chart of special Fourier series
Special conformal mappings grid
The wealth of special features and unique format make BETA Mathematics Handbook, Second Edition an essential reference for all students and professionals working in mathematics, science, engineering, and technology disciplines.
Contenuti
FUNDAMENTALS. DISCRETE MATHEMATICS. Logic. Set Theory. Binary Relations and Functions. Algebraic Structures. Graph Theory. Codes. ALGEBRA. Basic Algebra of Real Numbers. Number Theory. Complex Numbers. Algebraic Equations. GEOMETRY AND TRIGONOMETRY. Plane Figures. Solids. Spherical Trigonometry. Geometrical Vectors. Plane Analytic Geometry. Analytic Geometry in Space. LINEAR ALGEBRA. Matrices. Determinants. Systems of Linear Equations. Linear Coordinate Transformations. Eigenvalue. Diagonalization. Quadratic Forms. Linear Spaces. Linear Mappings. Tensors. Complex Matrices. THE ELEMENTARY FUNCTIONS. A Survey of the Elementary Functions. Polynomials and Rational Functions. Logarithmic, Exponential, Power and Hyperbolic Functions. Trigonometric and Inverse Trigonometric Functions. DIFFERENTIAL CALCULUS (ONE VARIABLE). Some Basic Concepts. Limits and Continuity. Derivatives. Monotonicity. Extremes of Functions. INTEGRAL CALCULUS. Indefinite Integrals. Definite Integrals. Applications of Differential and Integral Calculus. Tables of Indefinite Integrals. Tables of Definite Integrals. SEQUENCES AND SERIES. Sequences of Numbers. Sequences of Functions. Series of Constant Terms. Series of Functions. Taylor Series. Special Sums and Series. ORDINARY DIFFERENTIAL EQUATIONS (ODE). Differential Equations of the First Order. Differential Equations of the Second Order. Linear Differential Equations. General Concepts and Results. Linear Difference Equations. MULTIDIMENSIONAL CALCULUS. The Space Rn. Surfaces. Tangent Planes. Limits and Continuity. Partial Derivatives. Extremes of Functions. Functions f: RnĘRm(RnĘRn). Double Integrals. Triple Integrals. Partial Differential Equations. VECTOR ANALYSIS. Curves. Vector Fields. Line Integrals. Surface Integrals. ORTHOGONAL SERIES AND SPECIAL FUNCTIONS. Orthogonal Systems. Orthogonal Polynomials. Bernoulli and Euler Polynomials. Bessel Functions. Functions Defined by Transcendental Integrals. Step and Impulse Functions. Functional Analysis. Lebesgue Integrals. Generalized Functions (Distributions). TRANSFORMS. Trigonometric Fourier Series. Fourier Transforms. Discrete Fourier Transforms. The z-Transform. Laplace Transforms. Dynamical Systems (Filters). Hankel and Hilbert Transforms. COMPLEX ANALYSIS. Functions of a Complex Variable. Complex Integration. Power Series Expansions. Zeros and Singularities. Conformal Mappings. OPTIMIZATION. Calculus of Variations. Linear Optimization. Non-Linear Optimization. Dynamic Optimization. NUMERICAL ANALYSIS AND PROGRAMMING. Approximations and Errors. Numerical Solution of Equations. Interpolation. Numerical Integration and Differentiation. Numerical Solutions of Differential Equations. Numerical Summation. Programming. PROBABILITY THEORY. Basic Probability Theory. Probability Distributions. Stochastic Processes. Algorithms for Calculation of Probability Distributions. Simulation. Queueing Systems. Reliability. Tables. STATISTICS. Descriptive Statistics. Point Estimation. Confidence Intervals. Tables for Confidence Intervals. Tests of Significance. Linear Models. Distribution-Free Methods. Statistical Quality Control. Factorial Experiments. Statistical Glossary. MISCELLANEOUS. Glossary of Functions. Glossary of Symbols. INDEX.
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