Състояние: Много добро
Забележка: Почти отлична.
Издателство: Вега 74
Град на издаване: София
Наличност: singular
Корици: Меки

The main purpose of the book Mathematical Handbook is to present school Students, applying to Mathematical Colleges and Universities, candidates for SAT I and SAT II, Students of Mathematics, Computer sciences, Economics, Engineering, Physics and other sciences full information on mathematics concepts, formulas, graphs, axioms, theorems and tables.

Moreover, this book is helpful to those Students who go to mathematics exams and competitions, where they can easily express their own ideas and thoughts by solving mathematical problems. Mathematical handbook is written according to the newest educational programs and textbooks of this subject all over the world.

We would like to thank of the reviewer Prof. Dr Sci Jordan Tabov and publisher - graduate engineer Stoyan Beev for their professional help and valuable advice.

Съдържание:

Preface
Measures - transform factors
Mathematical symbols. Greek alphabet. Important constants
Discrete Mathematics
Mathematical logic. Boolean operations
Sets
Systems of numeration
Algorithms
Combinatory
Graph theory
Coding theory
Algebra
Arithmetic
Number sets
Set of natural numbers N
Division of natural numbers
Common fractions
Decimal fractions. Percent and ratio
Set of real numbers R
Number intervals
Absolute value (module) of a real number
Powers and roots of real numbers
Algebraic expressions - formulas for abbreviated multiplication and factorization of a polynomial to factors
Logarithmic and antilogarithmic transformation of real numbers
Number sequences
Progressions
Some numerical inequalities
Set of complex numbers C
Linear algebra
Determinants
Matrices
Systems of linear equations
Linear programming
Linear programming in two dimensions geometric approach
Simplex method
Transportation problem
Types of functions of one independent variable, equations, inequalities and simultaneous equations and inequalities
Linear function, equation, inequalitie and simultaneous equations and inequalities
Fractional-linear function, fractional-linear equations and inequalities
Quadratic function, quadratic equations and inequalities
Functions consisting of modules, module equations and inequalities
Cubic function, cubic equations and inequalities
Integer rational function of fourth power, equations and inequalities
Fraction-rational function, fraction-rational equations and inequalities
Power function, power equations and inequalities of integer degree
Irrational function, irrational equations and inequalities
Exponential function, exponential equations and inequalities
Logarithmic function, logarithmic equations and inequalities
Trigonometric functions, identities, equations and inequalities
Inverse trigonometric functions and identities
Hyperbolic functions and identities
Inverse hyperbolic functions and identities
Differential calculus of a function of one independent variable
Properties of a numerical function
Some non-elementary functions of one independent variable
Some elementary functions of one independent variable - domains and ranges
Limit of function
Function continuity
Derivative of a function
Some higher order derivatives of functions
Function analysis
Differential calculus of two and more independent variables. Implicit functions
Functions of two or more independent variables
Partial derivatives
Implicit functions
Integral calculus
Indefinite integrals
Definite (Riemann’s) integrals
Improper integrals
Applications of definite integrals
Integrals depending on a parameter
Vector analysis
Multiple integration
Double integrals
Triple integrals
Application of double and triple integrals in geometry
Curvilinear integrals
Surface integrals
Infinite series
Number series
Infinite series of functions
Complex analysis
Operational calculus
Laplace’s transforms
Fourier’s transforms
Differential equations
Ordinary differential equations
Partial differential equations
Numerical analysis
Numerical solution of equations
Numerical differentiation
Numerical integration
Special functions and orthogonal polynomials
Exponential integral functions
Euler’s integrals
Error function, Frenel integrals, Zeta function
Bessel functions
Hypergeometric functions
Elliptic functions
Orthogonal polynomials
Probability theory
Statistics
Number characteristic of average
Measuring the dispersion of data around a mean
Number characteristic of a random variable
Estimating the mean - confidence integral
Test of hypotheses
Linear regression and correlation
Mathematics of finance
Simple and compound interest
Discount and annuity
Capital public securities - bonds and stocks
Geometry
Plane geometry
Axioms of the plane geometry
Angle. Proportional line segments
Vectors
Some loci in the plane
Congruence. Criteria for congruence of triangles
Homothety. Criteria for homothety of triangles
Triangle
Quadrilateral
Polygon
Circle
Solid geometry
Axioms of the solid geometry
Parallel and perpendicularity
Parallel and orthogonal projection. Angles in the space
Geometric solid
Edgy solids (polyhedrons)
Circular solids
Spherical trigonometry
Areas of surfaces and volumes of edged and circular solids
Area of a sphere, volume of a sphere and its segments
Plane analytical geometry
Coordinate systems in the plane
Transformation of the coordinate system
Vector - operations
Division of a segment in a given ratio
Equations of a straight line
Conic sections
General equation of second degree curves
Some plane curves
Solid analytical geometry
Coordinate systems in the space
Vector - operations
Equations of a plane and a straight line
Surfaces
Differential geometry
Applications