EBOOK

Concise Handbook of Mathematics and Physics

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Mai 1997

Beschreibung

Beschreibung

Concise Handbook of Mathematics and Physics presents a unified and coherent treatment of all the major aspects of modern elementary physics and mathematics. This complete text/reference includes definitions of fundamental notations and physical and mathematical quantities, formulas that express the laws of physics, axioms and theorems of mathematics, and more. The information is organized logically (instead of alphabetically) for better comprehension and quick, convenient access. The book contains extensive cross-referencing between the mathematical and physical sections. reflecting the considerable overlap between these two areas of study and increasing the usefulness of this handbook. Fundamental concepts, theorems, and laws are demonstrated through numerous practical examples and tasks to help build problem-solving skills. TOC:Mathematics: Basic Notations, Formulas, and Concepts. - Sets. Real Numbers. - Functions. - Equations and Systems of Equations. - Inequalities. Trigonometry. - Elements of Calculus. Combinatorics. - Complex Numbers. - Vectors. - Coordinates. - Symmetries. - Geometry. - Stereometry. - Numerical Analysis. - Probability Theory. - Physics: Physical Quantities and Systems of Units. - Mechanics. - Molecular Physics and Thermodynamics. - Electricity and Magnetism. - Oscillations and Waves. Optics. - Relativistic and Quantum Physics. - Appendix: Fundamental Physical Constants. - Physical Quantities and Their SI Units. - Conversion of Gaussian Units into SI Units. - Conversion of Non-System Units into SI Units. - Main Formulas of Electrodynamics in Gaussian Units and in SI Units. - Atomic Elements and their Masses. - Table of Elementary Particles. - Decimal Multiples to be Used with SI Units. - Relations between Fundamental Constants (in Gaussian System of Units). - Table of Mathematical Symbols. - Index.

Inhaltsverzeichnis

MATHEMATICS Basic Notations, Formulas, and Concepts General Rules
Some Notations
The Rules to Remove Brackets
Short Methods of Multiplication
Fractions
The Rules of Handling with Fractions
Fractional Expressions
Proportions
Percentage Decimal Fractions
Introduction
Handling with Decimal Fractions
Normalized Form of Numbers
Repeating Decimals Rounding Off Numbers. Approximate Numbers
Rounding Off
Approximate Numbers The Mathematical Induction Method Sets. Real Numbers. Functions. Sets
Concept of a Set
Subsets
Intervals Real Numbers
Natural Numbers
Rational Numbers
Irrational Numbers
Properties of Arithmetic Operations Functions
Concept of a Function
Variables
Graph Basic Characteristics of Functions
Monotonicity
Periodicity
Evenness and Oddness
Boundedness Inverse Functions
Definition
Inverse Function for a Monotonic One
Graph of the Inverse Function Linear and Quadratic Functions. Modulus
Linear Function
Quadratic Function
Modulus Degree Function Exponential and Logarithmic Functions
Exponential Function
Hyperbolic Functions
Logarithmic Function Equations and Systems of Equations. Inequalities General Concepts
Concept of the Equation
Multiplicity of a Root
Equivalent Equations
Extraneous Roots Linear and Quadratic Equations
Linear Equation
Quadratic Equation
Biquadratic Equation Polynomials
Definitions
Horner's Method
Polynomial Algebra
Factorization of a Polynomial Algebraic Equations
Roots of an Algebraic Equation
On General Formulas for the Roots
Reduction of the Degree of a Polynomial
Binomial Algebraic Equation
Rational Equations Irrational and Modulus Equations
Irrational Equations
Modulus Equations Systems of Equations
Linear System, Two Equations
Linear System, Three Equations
Nonlinear System Inequalities
Definitions
Basic Properties of Inequalities
Problems Related with Inequalities
Domain of Definition
Algebraic Inequalities
Irrational Inequalities
Transcendental Inequalities
Inequalities with Modulus Symbol Trigonometry Trigonometric Functions
Trigonometric Functions of an Acute Angle
Trigonometric Functions of Arbitrary Values of Argument
Properties of the Trigonomic Functions Formulas of Trigonometry
Reduction Formulas
The Basic Formulas of Trigonometry Inverse Trigonomic Functions
Arcsine
Arccosine
Arctangent
Arccotangent
Formulas for Inverse Trigonomic Functions Trigonometric Equations and Inequalities
Simplest Trigonomic Equations
Equation Reducible to the Simplest One
Equation a sin x + b cos x = c
Trigonometric Inequalities Elements of Calculus Sequences
Concept of a Sequence
Limit of a Sequence
Monotonic and Bounded Sequences. Infinitesimal Sequences
Infinite Limit
Arithmetic Progression and Series
Geometric Progression and Series
Infinitely Decreasing Geometric Progression
The Number "e" Limit of Function
Definition and Theorems
One-Side Limits
Infinite Limit
Limit at Infinity
Rules to Calculate the Limits of Functions Continuity of Function. Discontinuities
Continuity
Discontinuities Derivative. Differentiation Rules
Derivative
Derivatives of Higher Order
Application of Derivatives
Inflection
Differentiation Rules Some Differential Equations
Introduction
Some Simple Differential Equations
Some Problems Related to Differential Equations Antiderivative. Indefinite Integral
Antiderivative
Indefinite Integral Definite Integral and its Applications
Definition
Properties of the Definite Integral
Improper Integrals: Infinite Interval
Improper Integrals: Discontinuous Function
Some Applications of the Definite Integral Some Information about Series
Convergence of a Series
Tests for Convergence of Series
Series Whose Members are of Arbitrary Sign
Power Series Combinatorics Permutations. Arrangements. Combinations
Permutations
Factorial
Stirling Formula
Semi-Factorial
Arrangements
Combinations Binomial Formula and Applications
Binomial Formula
Properties of the Binomial Coefficients
Pascal Triangle
Sum of Natural Numbers in a Certain Power Complex Numbers Basic Concepts
Notations
Rules to Operate with Complex Numbers
Conjugate Numbers Algebraic Form of Complex Number Trigonometric and Exponential Forms
Vector Interpretation
Modulus and Argument of a Complex Number
Trigonometric Form
Exponential Form
Euler Formulas
De Moivre Formula
Roots of Complex Numbers Logarithms of Complex Numbers Complex Roots of Equations Vectors. Coordinates. Symmetries Vectors. Projections
Vectors
Projections
Expansion in Unit Vectors Scalar and Vector Products
Scalar Product
Vector Product Coordinate Systems
Coordinate Axis
Coordinate System in a Plane
Coordinate Systems in Space
Polar Coordinates Displacement. Symmetry. Similarity
Displacement
Symmetry
Spatial Symmetry
Similarity Geometry. Stereometry Points, Straight Lines, and Angles in a Plane
Points and Straight Lines
Segment
Angle
Degree
Radian
Intersection of Straight Lines Triangles. Polygons
Triangle
Elements of a Triangle
Equal Triangles
Similar Triangles
Formulas for a Triangle
Polygons
Parallelogram
Rhombus
Rectangle
Square
Trapezoid Circle, Ellipse, Hyperbola, Parabola
Circle
Ellipse
Hyperbola
Parabola
Curvature of a Curve Planes and Straight Lines in Space
Parallelism of Planes and Lines
Skew-Lines
Perpendicular
Angle Between Two Planes
Dihedral Angle
Projection of a Figure on a Plane Polyhedrons
Polyhedral Surface
Polyhedron
Prism
Parallelepiped
Pyramid
Frustum of a Pyramid
Regular Polyhedrons Bodies of Revolution
Surface of Revolution
Cylinder
Cone
Sphere
Spherical Segment
Spherical Sector
Spherical Layer
Torus Curvature of a Surface Numerical Analysis Rounding Off and Errors Approximation of Functions
Approximate Formulas
Function Given by a Table
Method of Least Squares Numerical Integration
Trapezoid Rule
Formula of Rectangles
Simpson's Formula
Taylor Approximation
Improper Integrals Approximate Solution of Equations
Bisection Method
Iteration Method
Newton's Method Approximate Solution of Differential Equations
Euler's Method
Runge-Kutta Method Probability Theory Random Events and Their Probabilities
Random Event
Probability
Bernoulli Formula
Large Numbers' Law Random Variables and Distribution
Random Variable
Mean Value and Dispersion PHYSICS Physical Quantities and Systems of Units Basic Concepts. Law of Physics
Physical Quantities and Measurements
Equations in Physics
Physical Models Systems of Units
Based and Derived Units
Dimensions of Physical Quantities
Standards of Base Units
Units of Magnetic Quantities in Gaussian System of Units
Units of Magnetic Quantities in SI
Relationship between SI and Gaussian Units The Method of Dimensional Analysis
Dimensionless and Dimensional Units
Example: Velocity in Free Fall
Example: Flight Range
Example: Viscous Flow
Example: Speed of Sound
Example: Velocity of Waves
Example: Microscopic Model of a Real Gas
Example: Time of Relaxation in a Gas
Example: Time of Relaxation in Plasma
Example: Temperature Dependence of Black-Body Radiation Mechanics Kinematics
Kinematics of a Particle
Example: Motion Along an Ellipse
Velocity and Acceleration
Tangential and Radial Acceleration
Rectilinear Motion
Circular Uniform Motion
Kinematics of a Rigid Body
Rotation About a Fixed Axis
Plane Motion of a Solid
Rotation About a Fixed Point Dynamics
Basic Concepts of Classical Dynamics
Momentum
Determination of Force on the Basis of Given Motion
Motion Caused by Given Forces
Restricted Motion Forces of Gravitation, Friction, and Elasticity
The Law of Gravitation
Friction and Elasticity Conservation Laws
Conservation of Momentum
The Center of Mass
The Law of Motion of the Center of Mass
Jet Propulsion
Work and Kinetic Energy
Potential Energy
Conservation of Mechanical Energy
Collisions Motion in a Central Gravitational Field
Kepler's Laws of Planetary Motion
Cosmic Velocities
Example: Elliptic Orbit of a Satellite Mechanical Equilibrium
Conditions of Equilibrium
Plane System of Forces
Example: Determination of Forces of Reaction
Statics and Energy Conservation
The Stability of Equilibrium Dynamics of a Solid
The Principal Laws
Moment of Inertia
Energy of Rotation
A Gyroscope Hydrostatics
Pressure in a Liquid
Hydrostatic Pressure
Archimedes' Principle and Buoyant Force
Measurement of Density
Floating on the Surface Hydrodynamics
Equation of Continuity
Bernoulli's Principle
Motion of a Viscous Fluid
Turbulent Flow of Viscous Fluid Molecular Physics and Thermodynamics Principles of Thermodynamics
Thermal Equilibrium
Parameters of the Equilibrium State
Equation of State for the Ideal Gas
Gas Thermometer
Components and Phases
Reversible and Irreversible Phases
Internal Energy
Heat Capacity
Isoprocesses in the Ideal Gas
Efficiency of a Heat Engine
The Second Law of Thermodynamics
A Refrigerator Machine
Thermodynamic Temperature
Enthropy The Principles of Statistical Mechanics
Thermal Motion
Molecular Interaction
Amount of Substance
Kinetic Theory of an Ideal Gas Statistical Distributions
Distributions of Different Quantities
Maxwell Distribution
Probabilities
Calculation of Mean Values
Boltzmann Distribution
Fluctuations
Physical Reasons of Irreversibility
Statistical Meaning of Enthropy Real Gases
Van der Vaals Equation
Experimental Isotherms and Phase Transitions
Phase Transitions
Humidity of Air
Equilibrium of Phases Liquids
Surface Tension
Capillary Phenomena Solids
Crystals and Amorphous Bodies
Elastic Deformations
Thermal Expansion Heat Exchange. Phase Transitions
Thermal Capacity
Heat of Combustion
Latent Heat of Phase Transitions Electricity and Magnetism Electrostatics
Interaction of Electric Charges
Electrostatic Field
Electrostatic Field in Dielectrics
Electric Field Near Conductors
Capacitors
Connection of Capacitors
Energy of Electric Field Electric Current
Ohm's Law
Series and Parallel Connection of Resistors
Measurements in Direct Current Circuits
Circuit with a Source
Kirchhoff's Rules
The Work of Electric Current
A Power Source in a Circuit
Faraday's Laws of Electrolysis Magnetic Field
Induction of Magnetic Field
Ampere's Force and Lorentz' Force
Magnetic Field Energy
Magnetic Field in Substances Electromagnetic Induction
Faraday's Law
Inductance Alternating Electric Current (AC)
AC in Circuits with One Element
Series RLC-Circuit
Parallel RLC-Circuit
Impedance of a Circuit
Resonance of Voltages and Resonance of Currents
Power of Alternating Current
Transformer Electromagnetic Field
Relative Character of Electric and Magnetic Fields
Invariants of Electromagnetic Field
Maxwell's Equations Oscillations and Waves Classification of Oscillations Harmonic Oscillations
Kinematics of Simple Harmonic Motion
Vector Diagrams for Harmonic Oscillations Natural Oscillations of Simple Systems
Differential Equation of Harmonic Oscillator
Initial Conditions
Transformations of Energy in Oscillations
Nonlinear Free Oscillations
Damped Natural Oscillations
Damping by Dry Friction Forced Oscillations. Resonance
Steady-State Forced Oscillations
Resonance Curves of Linear Oscillator
Resonance of Velocity
Transformations of Energy in Forced Oscillations
Transient Processes
Non-Sinusoidal External Force Parametric Resonance. Self-Excited Oscillations
Parametric Excitation of Oscillations
Self-Excited Oscillations Oscillations of Complex Systems. Composition of Oscillations
Degenerate Oscillatory Systems
Normal Oscillations (Modes)
Coupled Pendulums
Forced Oscillations of Coupled Pendulums
Coupled Electromagnetic Circuits
Standing Waves as Normal Oscillations Waves
Waves of Different Physical Nature
Polarization of Waves
Kinematics of Wave Motion
The Speed of Waves
Energy Transferred by Waves
Plane, Spherical, and Cylindrical Waves
Reflection and Refraction of Waves
Interference of Waves
Standing Waves
Diffraction of Waves
Doppler Effect
Electromagnetic Waves
Waves on the Water
Speed of Wave Packets Optics Geometrical Optics
The Principal Laws
Plane Mirrors
Paraxial Approximation and Optical Images
Spherical Mirrors
Lenses Optical Instruments
Camera
Diascope
Magnifying Glass
Microscope
Telescope Interference of Light
Interference and Coherent Light
Interference Fringes
Young's Double-Slit Experiment
Localized Interference Patterns
Multiple-Ray Interference
The Enlightenment of Optical Systems Diffraction of Light
The Huygens-Fresnel Principle
Diffraction Spreading of a Parallel Light Beam
Fresnel Diffraction
Fraunhofer Diffraction
Diffraction Grating
Dispersion Spectrometer
Holography
Photometry Relativistic and Quantum Physics The Theory of Relativity Relativistic Kinematics
Galilean Transformation
Insufficiency of Classical Concepts
Main Principles of the Theory of Relativity
The Relativity of Simultaneity. Time Dilation and Lorentz Contraction
Lorentz Transformations
Relativistic Interval Relativistic Dynamics
Relativistic Momentum and Energy
Mass and Energy
Relativistic Kinetic Energy
Relativistic Transformation of Energy and Momentum
Example: Acceleration by
a Constant Force
Example: Relativistic Particle in Magnetic Field
Transmutations of Elementary Particles The Principles of Quantum Physics
Uncertainty Relations
Wave-Particle Duality
Range of Validity of Classical Theory
Quanta of Light-Photons
Photoelectric Effect
Light Pressure
Doppler Effect
Compton Effect The Structure of an Atom
Bohr's Model of the Hydrogen Atom
Electron Shells
Light Radiation of an Atom
Black-Body Radiation Atomic Nucleus
Composition of Atomic Nuclei
Radioactive Decay
Nuclear Reactions Elementary Particles APPENDIX Fundamental Physical Constants Physical Quantities and Their SI Units Conversion of Gaussian Units into SI Units Conversion of Non-System Units into SI Units Main Formulas of Electrodynamics in Gaussian Units and in SI Units Atomic Elements and Their Masses Table of Elementary Particles Decimal Multiples to be Used with SI Units Relations between Fundamental Constants (in Gaussian System of Units) Table of Mathematical Symbols Index
EAN: 9780849377457
ISBN: 0849377455
Untertitel: Sprache: Englisch.
Verlag: CRC PR INC
Erscheinungsdatum: Mai 1997
Seitenanzahl: 520 Seiten
Format: gebunden
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