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polinomi polinomio in forma normale grado di un polinomio polinomio omogeno addizione di polinomi sottrazione di polinomi moltiplicazione di polinomi interpretazione geometrica del prodotto di polinomi prodotti notevoli prodotto somma differenza quadrato del binomio somma quadrato del binomio differenza quadrato del trinomio cubo del binomio somma cubo del binomio differenza potenza del binomio triangolo di Tartaglia le funzioni polinomiali zeri di un polinomio identità di polinomi divisione di polinomi divisibilità tra polinomi divisione con resto di polinomi regola di Ruffini teorema del resto teorema di Ruffini scomposizione di differenza di due quadrati scomposizione di differenza di due cubi scomposizione di somma di due cubi polynomials polynomial in normal form degree of a polynomial homogeneous polynomial addition of polynomials subtraction of polynomials multiplication of polynomials geometric interpretation of the polynomial product remarkable products product sum difference square of the sum binomial square of the difference binomial square of the trinomial cube of the sum binomial cube of the difference binomial power of the binomial Tartaglia triangle the polynomial functions zeros of a polynomial identity of polynomials division of polynomials divisibility between polynomials division with rest of polynomials Ruffini's rule Theorem of the rest Ruffini's theorem decomposition of difference of two squares difference decomposition of two cubes sum decomposition of two cubes
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inequalities Fractional inequalities Set of solutions of inequalities Whole inequalities Literal inequalities Parametric inequalities Equivalent inequalities Open range Closed interval Unlimited interval Limited range Equivalence principles for inequalities First degree inequalities Second degree inequalities Second degree inequalities Degree of inequality Model of the parable Resolution of a second degree inequality A sign of a second degree trinity Whole inequalities higher than the second Monomestic inequalities Binomial inequalities Trinomial inequalities Fractional inequalities System of inequalities Irrational inequalities Irrational equation Irrational inequalities absolute value Equation with absolute values Inequalities with absolute values report controimmagine An analytic expression of a function functions Actual real variable functions Image set Image element codomain domain Algebraic functions Field of existence of a function Fractional functions Full functions Irrational functions Rational functions Transcendent functions Definition set Dependent variable Independent variable An analytic expression of a function Graph of a function Sign function Equal functions Sign of a function Zero of a function Odd functions Equal functions Functions growing in the broad sense Decreasing functions in the broad sense Strictly growing functions Slightly decreasing functions Injective functions Monotonous functions Surice functions Biophysical functions Reverse functions Invertible functions Algebra of functions Composite functions Restriction of a function succession General term of a succession Graph of a succession Succession in recursive form Sequence defined for listing Succession defined recursively Graph of a succession Monotony of successions Monotony property of a succession Arithmetic progression reason Sum of the first terms of an arithmetic progression The general term of an arithmetic progression Geometric progression reason General term of a geometric progression Sum of the first terms of a geometric progression abscissa Axis of ascites Axis of the ordinates Biunivocal correspondence tidy origin Cartesian plan Reference system Dimeric reference system Monometric reference system clock face Distance between two points The middle point of a segment Center of gravity of a triangle carriers Components of a carrier Equality between vectors Operations between vectors Parallelism of vectors Linear functions Angular coefficient Ordered at the origin Slope of a straight line Linear functions at times Equation of the straight line Functions with absolute value Parallel lines Straight lines parallel to the axes Bisectors of the dials Straight line equation Equation of the straight line in implicit form General equation of the straight line Reciprocal position of two straight lines Parallel lines Perpendicular lines Straight line for a point Straight through two points Axis of a segment Distance of a point from a straight line bisectors Bundle of improper lines Bundle of straight lines Straight beam Straight line bundle generated by two straight lines Method of straight line bundles demiplane segment ray angle polygon strip Linear inequalities in two unknowns Mixed systems Analytical method Synthetic method isometry Central symmetry Equations of a central symmetry Symmetry center Axial symmetry translation expansion Composite transformation simile dilation Properties of dilation Transformations and function graphs circumference Equation in normal form Reciprocal position between straight and circumference Straight tangent to a circumference Doubling formulas Polar straight Reciprocal position of two circumferences Radical axis Bundle of circumferences Radical axis Base points Method of circumference bundles semicircle parabola Axis of a parable Director of a parable Fire of a parable Summit of a parabola Opening a parabola Concavity of a parabola Equation associated with a parabola Straight and parabolic position Tangent straight to a parabola Parabolic segment Archimedes theorem Bundle of parables Base points Method of parabola bundles Parabola and functions ellipse Center of an ellipse Focal distance of an ellipse Fires of an ellipse The largest axis of an ellipse Axis smaller than an ellipse Equation in the normal shape of an ellipse Fires of an ellipse Vertices of an ellipse Eccentricity of an ellipse Dilatations of an ellipse Reciprocal position between straight and ellipse Straight tangent to an ellipse Ellipse translated Ellipses and functions hyperbole Axis of symmetry of a hyperbola Symmetry center of a hyperbola Fires of a hyperbole Focal distance of a hyperbole Equation in normal shape of a hyperbole Asymptotic of a hyperbole Non-transverse axis of a hyperbole Transverse axis of a hyperbole Fires of a hyperbole Halfper of a hyperbole Tops of a hyperbole Eccentricity of a hyperbole Equilibrium Equation of a Hyperbole Hyperbole related to its axes Hyperboles related to their asymptotes Homogeneous function Symmetry center of a hyperbola Reciprocal position between straight and hyperbole Tangent lines to a hyperbole Doubling formulas Transverse hyperbola Hyperbole and functions conical Cone degenerate Flap of a conic Generator of a conic Conical surface Summit of a conic conical General equation of a conic Eccentricity of a conic Fire of a conic Intersections between conics Reciprocal position of two cones Tangency between conics Geometric place Cartesian equation of a geometric place Parametric Equation of a Geometric Location Second degree inequations in two unknowns Mixed parametric systems angle radiant Goniometric functions cosine otherwise tangent Triangles rectangles The first rectangular triangle theorem According to the rectangular triangle theorem Associated angles Graph of the goniometric functions Functions and transformations Sinusoidal functions pulsation phase displacement Periodic functions Inverse goniometric functions cosecant cotangent secant Statistical character Qualitative statistical character Statistically quantifiable character data Statistical mode Statistical population statistics Statistical unit Frequency distribution Continuous variable Discrete variable Statistical class Position indexes Indices of variability average median fashion standard deviation variance Joint distribution Marginal distribution Statistical distribution Conditioning distribution Statistical dependence Statistical independence Chi-square index correlation covariance Linear correlation Regression line Set of real numbers Set of real numbers: Addition properties Set of real numbers: properties of multiplication Irrational numbers Contiguous classes completeness Set of real numbers: order properties Separate sets Indefinite sets Approximate by default Approximation for excess Power to irrational exponent power Exponential function Exponential function: base Exponential function: domain Exponential function: graph Number of Nepero Number e Exponential equations Elementary exponential equations Exponential inequalities Inequality: algebraic resolution Inequality: graphic resolution Elemental inequalities Algebraic numbers Transcendent numbers logarithm Logarithm: argument Logarithm: base Logarithmic function Logarithmic function: graph Decimal logarithm Natural logarithm Logarithm neperian Property of logarithms Logarithm: basic change Logarithmic equations Exponential equations solvable by logarithms Logarithmic equations that can be solved graphically Logarithmic inequalities Elementary logarithmic inequalities Exponential growth Growth models Exponential decline Decay models Cosine: definition Goniometric functions Sinus: Definition Tangent: definition of Associated angles Associated angles that differ from a flat angle Complementary angles Angles associated with the opposite Additional associated angles Goniometric functions: application to rectangular triangles cosine arcoseno arctangent Addition and subtraction formulas for cosine Addiction and subtraction formulas for the sinus Goniometric functions: graphs Inverse goniometric functions Cosine of a difference Cosine of a sum sin of a difference sin of a sum Addition and subtraction formulas for the tangent Tangent to a difference Tangent of a sum Duplication formulas Bisection formulas Batch modulation formulas for tangent Parametric formulas Angle formed by two straight lines Parametric equations of the circumference and the ellipse Geometric place Linear function in cosine Normalizing factor Cosine cosine linear function: amplitude Cosine cosine linear function: graph Cosine cosine linear function: image Cosine cosine linear function: period Harmonic analysis Goniometric equations Goniometric equations of the type sin x = m Elemental goniometric equations Goniometric equations of the type cos x = m Goniometric equations of the type tan x = m Goniometric equations of the type sin f (x) = m Goniometric equations of the type cos f (x) = m Goniometric equations tan f (x) = m Goniometric equations of the type sin f (x) = sin g (x) Goniometric equations of the type cos f (x) = cos g (x) Goniometric equations of the type tan f (x) = tan g (x) Goniometric equations that can be traced back to elementary Linear goniometric equations in sin and cosine Parametric formulas Method of added angle Homogeneous goniometric equations of second degree in sin and cosine Goniometric inequalities Elemental goniometric inequalities Elemental goniometric inequalities Fractional goniometric inequalities Linear goniometric inequalities in sin and cosine Product inequalities Homogeneous gonometric inequalities of second degree in sin and cosine Theorems on rectangular triangles trigonometry Applications of theorems on rectangular triangles Area of a triangle Rope theorem sin theorem Cosine theorem Cosine theorem with vector calculation Resolution of a triangle Angle of rotation rotation Rotation with center in the origin of the axes Equation of a rotation with center in the origin Equation of the corresponding curve of a given rotation Reverse rotation Rotation: applications to the conic Rectangular term Conditions to recognize a conic affinity Direct affinity Equations of an affinity Reverse affinities expansion Invariant properties of affinities Affinity ratio Identification of an affinity United points of affinity Joined straight lines of affinity Geometric transformations Similarity report similitudes Similarities: equations Similarities: united elements Similarity: identification Similarities: invariant properties Gliss-symmetry isometries Isometrics: classification Isometrics: equations Axial symmetries Isometrics: united elements Isometrics: identification Isometrics: invariant properties Recognition of affinity Groups of transformations Erlangen program topology Set of complex numbers such as R expansion Complex numbers Imaginary unity Imaginary axis Real axis Conjugated complex numbers Complex numbers: algebraic form Complex opposing numbers Complex numbers: imaginary part Complex numbers: real part Complex numbers: equal Imaginary numbers Gauss Plan Complex numbers: module Complex numbers: geometric representation Geometric interpretation of addiction and subtraction between complex numbers Geometric interpretation of multiplication and division between complex numbers Complex numbers like vectors Operations in C vector Distance in the Gauss plane Parallelogram rule Complex conjugation property Building complex number complex numbers Polar axis Polar coordinates Polar coordinates: anomaly Polar coordinates: topic Polar coordinates: module Polar coordinates: passing to Cartesian coordinates pole Vector ray Polar coordinates: passing from Cartesian coordinates Complex numbers: trigonometric form Power of a complex number N-th roots of a complex number De Moivre theorem Equations in C Multiplicity of a solution Fundamental theorem of the algebra Complex numbers: exponential form Endless cardinality of sets Euler's formulas Planes in space Point in space Straight in space space Complanar lines Reciprocal positions of two straight lines Reciprocal positions of two floors Reciprocal positions of a straight line and a plan Figure in space Solid figures Congruent solid figures Planes in space Parallel planes Secantial planes Perpendicularity in space Perpendicularity between straight and flat Axial plane Perpendicularity between two straight lines Corner deer Perpendicularity between two floors Normal section of a dialect Amplitude of a dihedral angle Perpendicular planes Semipian bisector Parallelism in space Parallelism between lines in space Parallel lines Parallel between straight and flat Parallelism between floors Bundle of parallel planes Talete theorem Distance of one line from one floor Distance of a point from one plane Distance between two parallel planes Angles in space Angle between two straight lines Corner between a straight and a floor Distance between two sheds prism Properties of the prism parallelepiped Property of the parallelepiped angoloide pyramid Straight pyramid apothem Regular pyramid cylinder Rotation solids cone truncated cone ball Spherical surface Spherical shell Spherical segment to a base Cast spherical Spherical segment Spherical segment with two bases Spherical sector Spherical sphere Spherical zone polyhedron Convex polyhedron Regular polyhedron Euler's relationship Polyhedron properties Pyramid trunk Isometrics: in space Space symmetries Geometric transformations in space translation Space rotation Space wrap Developable surface Principle of Knights Space wrap Pyramid: area Volume of a solid Volume of a parallelepiped Volume of a cube Volume of a prism Area of the pyramid trunk Pyramid: volume Volume of the pyramid trunk Cylinder area Volume of the cylinder Area of the cone Volume of the cone Area of the trunk of cone anticlessidra Volume of the cone trunk Sphere area Volume of the ball Analytical geometry in space quote Distance between two points in space Middle point in space Vectors in space Vectors in space: operations Equation of a plane in space Equation of a plane in space: Cartesian form A condition of parallelism and perpendicularity between floors Equation of a straight line in space Parametric equation of a straight line in space Plan your reciprocal position Vector direction Cartesian equation of a straight line in space Distance of a point from one plane Distance of a point from a straight line ball Spherical surface Combinatorial calculation Fundamental principle of combinatorial calculation Simple arrangements sorting permutations Provisions with repetition Permutations with repetition combination Binomial coefficient Combination with repetition N-th power of a binomial Newton's binomial Statistical event Sample space Sure event Elementary statistical event Impossible statistical event Operations between events Incompatible events Probability: classical definition chance Probability conditioning Independent events Disintegration theorem Bayes theorem Probability: frequentist definition Probability: subjective definition Law of great numbers Infinitesimal calculation optimization Snell's Law Tangent straight Method of indivisibility measure speed instantaneous speed average speed mathematical analysis Ordered field (R) Completeness of R Together R intervals Intervals: amplitude Open intervals Closed intervals Limited intervals Together inferiorly limited Limited set maggiorante Maximum of a set Minimum of a set minorante Lower extremity The lower extremity of a set Upper extremity of a set Upper extremity Unlimited intervals Expanded R system (R *) Circular around All around Right around Around less infinite Around more infinite Around a point Around the left around Collection point Derived set Isolated point Classification of functions codomain Function definition domain An analytic expression of a function function Actual real variable function Theorem of Bolzano-Weierstrass Equal functions Sign of a function Zeros of a function image The lower extremity of a function Top end of a function Function is limited Together superbly limited Maximum of a function Minimum of a function Tightly growing function Strictly decreasing function Growing function in the broad sense Decreasing function in the broad sense Monotone function Odd function Equal function Periodic function Period of a function Restriction of a function Composite function Introduction limits Right Limit Left limit Limits: general definition limits Limits: particular definitions Asynthos vertical Horizontal asymmetry Limit by default Excess limit Verification of a limit Comparison theorem Boundary existence theorem for monotone functions Sign permanence theorem Limit uniqueness theorem Continuity at one point Continuity of elementary functions Limitations of functions Constraints of elemental functions Limit algebra Forms of indecision Indeterminate forms Partial arithmetic of the infinite symbol Limit of composite functions Indeterminate forms: polynomial functions Limits of polynomial functions Indeterminate forms: fractious rational functions Limitations of fractious rational functions Indeterminate forms: irrational algebraic functions Limitations of irrational algebraic functions Change of variable in the calculation of the limits Indeterminate forms: transcendent functions Significant limits of goniometric functions Indeterminate forms: exponential functions Indeterminate forms: logarithmic functions Significant limits of exponential functions Significant limits of logarithmic functions Considerable limits Number e Infinitesimi (functions) Infinite (functions) Order of infinity Order of an infinite Comparison between infinitesimi Comparison of infinites Infinite hierarchy Asymptotic equivalence Asymptotic functions Function continues succession Succession: graph Succession: general term Succession defined recursively Limited succession Inferior succession below Limited succession in the upper Arithmetic progression Geometric progression Increasing succession Descending succession Monotone succession Tightly growing succession Closely decreasing succession The general term of an arithmetic progression General term of a geometric progression Sum of arithmetic progression Sum of a geometric progression Converging succession Divergent succession Character of a succession Limitations of sequences and function limits Indeterminate succession Irregular succession Oscillating succession Comparison theorem for successions The theorem of the sign for succession Limit existence theorem for monotone sequences Calculation of succession limits Succession limits Induction principle summation Paradox of Zenone Numeric series Convergent numeric series Divergent numeric series Irregular numerical series Numerical series: linearity Succession of partial sums Numerical series of Mengoli Telescopic numerical series Geometric numerical series Axioms of Peano Axiomatic method Continuity from the right Continuity from the left Continuity at one point continuity Continuity and algebraic operations between functions Continuity and composition of functions Continuity and inverse function Point of discontinuity Singular point singularity Continuous extension of a function Unique point of the first species Singular jump point Singular point of second species Unique point eliminable Zeros theorem Bisection method Weierstrass theorem Intermediate values theorem Right horizontal asymmetry Asynchronous horizontal left Horizontal asymmetry Right asymmetry Left vertical asymmetry Asynthos vertical Right asymmetry Oblique asymmetry Asymmetry left Curved asymptotic Probable graph of a function Incremental ratio First derivative derived Derivable function Notation of Leibniz Right derivative Left derivative Continuity and derivability Derivability and continuity Derivative function Derivative of the constant function Derivative of the identical function Order derivative n Second derivative Derivative of the power function Derivative of exponential function Derivative of the logarithmic function Derivative of cosine function Derivative of the sin function Derivative algebra Linearity of the derivative Derivative of the function product Derivative of the mutual function Derivative of the quotient of functions Derivative of the tangent function Derivative of the composite function Derivatives of elementary functions Derivative of the reverse function Calculation of the derivative cusp Angular point Vertical tangent flush point Limit of the derivative Geometric applications of the derivative Straight line Tangent straight Tangency between two curves acceleration Applications to the sciences of the derivative differential Relative maximum of a function Relative minimum of a function Relative point of reference Relative maximum point Relative minimum point Absolute maximum of a function Absolute minimum of a function Extreme point Absolute maximum point Minimum point Absolute minimum point Stationary points Fermat's theorem Rolle theorem Lagrange theorem Lagrange Point A monotony criterion for derivable functions Stationary point analysis Monotone intervals Stationary point test optimization Optimization issues critical points Maximum and minimum problems Concave function Convex function Concave and convexity inflection Point of flitting Ascending flush point Descending flush point Oblique flush point Horizontal flush point Necessary and sufficient condition point Cauchy Point Cauchy's theorem The de Hopital theorem De l'Hopital theorem applications Zero existence theorem Zeros theorem Limit of the derivative Function study Function study scheme Polynomial function study Fractional rational function study Irrational function study Exponential function study Logarithmic function study Goniometric function study Function study with absolute values Deductible graph graphic Number of solutions of an equation Function study and equations Discussion of parametric equations Newton method primitive Indefinite integer Immediate integrals Integration by decomposition Indefinite integrity linearity Almost instantaneous integral integration Integration of composite functions Integration for replacement Differential factor Finished factor Integration of fractional rational functions Simple brothers area Area calculation trapezoid Sum of Riemann Sign area Defined integral Linearity of the defined integer Integrity additivity defined Monotony of the defined integer The first fundamental theorem of integral calculus Change of variable in integral calculus Defined integer applications Area of the region limited by the function graph Area of the region limited by the graph of two functions Volume of a solid Rotation solids Method of cylindrical shells speed Work of a force Hooke's Law Average value theorem for integers Darboux theorem Average value of a function Generalized integral Improper integral Comparison theorem for integers Derivative of the integral function The first fundamental theorem of integral calculus Error function Gauss function Numerical integration Method of rectangles Trapezius method Parabolic method Simpson's method Errors: evaluation in numerical integration Differential equations: general integral Differential equations: particular integer Linear differential equations of the first order Differential equations General integral (differential equations) Integral whole Singular integral Order of a differential equation Solutions of a differential equation Integral curve Differential equations with separable variables Secondary differential equations of the second order Homogeneous differential equations Cauchy's problem Characteristic equation Growth models Decay models Equation of motion Logistics equation Bernoulli process Random variable Discrete random variables Probability density standard deviation Probability distribution of discrete random variable Average of a random variable Average squared deviation Math hope Expected value variance Fair play Bernoulli's experiment Bernoulli's test Binomial distribution Binomial random variable Poisson distribution Geometric distribution Poisson random variable Poisson process Continuous random variable Probability density standard deviation Breakdown function Uniform distribution Uniform random variable Distribution of exponential Absence of memory (exponential random variables) Time of life Normal distribution Normal random variable Typical ranges Mathematical models
MATHEMATICAL TOOLS FOR PHYSICS Equivalences between units of measurement Calculations with powers Proportions and percentages The equations: derive an unknown quantity from a formula Relationships between the sides of a triangle Trigonometric relations THE MEASURE IN PHYSICS What does physics study? The physical quantities Properties of powers of 10 Scientific notation Direct and indirect measurements in physics Making estimates: Fermi's problems DATA PROCESSING IN PHYSICS Measurement errors Estimate of the error The propagation of errors and significant figures The construction of a Cartesian graph Representations of experimental data Mathematical and graphical representation of physical laws SCALAR GREATNESS AND VECTOR GRANDEZES Moving into physics Difference between Displacement and path traveled Sum of vectors Sum of perpendicular vectors Scalars and vectors Vector operations Subtraction of vectors Breakdown of a vector Corners and Cartesian components of a vector Scalar product vector product FORCES AS VECTORS Forces Sum of forces The weight force Elastic force The binding forces The friction force THE SOLID BALANCE Balance in physics Moment of a force Moment of a force system The balance of a rigid body Center of gravity and stability of balance The simple machines: levers and pulleys THE PRESSURE AND THE BALANCE OF FLUIDS Fluids and pressure Pressure in liquids Atmospheric pressure The floating of the bodies THE UNIFORM MOTORCYCLE The description of the bike Speed in physics The space-time graph The uniform rectilinear motion THE UNIFORMLY ACCELERATED MOTORCYCLE acceleration The speed-time graph The uniformly accelerated motion The free fall in physics MOTIONS IN THE FLOOR HARMONIC MOTION The motions in the plane The motion of the projectiles The uniform circular motion Displacement and angular velocity The harmonic motion DYNAMICS (in physics) NEWTON From the description of the motion to its causes The first principle of dynamics The second principle of dynamics The third principle of dynamics The pendulum fall motions circular motion and laws of dynamics harmonic motion and laws of dynamics WORK AND ENERGY (physics) The work of a constant force The work of the weight force The work of a variable force The power Kinetic energy The potential gravitational energy Energy conservation TEMPERATURE AND HEAT Temperature and balance Thermal expansion Heat (physical) Heat as energy in transit The propagation of heat Aggregation states status changes GEOMETRIC OPTICS Light sources and light rays Reflection (optic) Refraction Total reflection Spherical mirrors The lenses (optical)
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