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 موضوع: كتاب Advanced Engineering Mathematics 7ed الأربعاء 16 فبراير 2022, 3:06 pm  

أخواني في الله أحضرت لكم كتاب Advanced Engineering Mathematics 7ed Dennis G. Zill
و المحتوى كما يلي :
Contents Preface Ordinary Differential Equations Introduction to Differential Equations Definitions and Terminology InitialValue Problems Differential Equations as Mathematical Models Chapter in Review FirstOrder Differential Equations Solution Curves Without a Solution Direction Fields Autonomous FirstOrder DEs Separable Equations Linear Equations Exact Equations Solutions by Substitutions A Numerical Method Linear Models Nonlinear Models Modeling with Systems of FirstOrder DEs Chapter in Review HigherOrder Differential Equations Theory of Linear Equations InitialValue and BoundaryValue Problems Homogeneous Equations Nonhomogeneous Equations Reduction of Order Linear Equations with Constant Coefficients Undetermined Coefficients Variation of Parameters Cauchy–Euler Equations Nonlinear Equations Linear Models: InitialValue Problems Spring/Mass Systems: Free Undamped Motion Spring/Mass Systems: Free Damped Motion Spring/Mass Systems: Driven Motion Series Circuit Analogue Linear Models: BoundaryValue Problems Green’s Functions InitialValue Problems BoundaryValue Problems Nonlinear Models Solving Systems of Linear DEs Chapter in Review The Laplace Transform Definition of the Laplace Transform Inverse Transforms and Transforms of Derivatives Inverse Transforms Transforms of Derivatives Translation Theorems Translation on the saxis Translation on the taxis Additional Operational Properties Derivatives of Transforms Transforms of Integrals Transform of a Periodic Function Dirac Delta Function Systems of Linear Differential Equations Chapter in Review Series Solutions of Linear Equations Solutions about Ordinary Points Review of Power Series Power Series Solutions Solutions about Singular Points Special Functions Bessel Functions Legendre Functions Chapter in Review Numerical Solutions of Ordinary Differential Equations Euler Methods and Error Analysis Runge–Kutta Methods Multistep Methods HigherOrder Equations and Systems SecondOrder BoundaryValue Problems Chapter in ReviewPART Vectors, Matrices, and Vector Calculus Vectors Vectors in Space Vectors in Space Dot Product Cross Product Lines and Planes in Space Vector Spaces Gram–Schmidt Orthogonalization Process Chapter in Review Matrices Matrix Algebra Systems of Linear Equations Rank of a Matrix Determinants Properties of Determinants Inverse of a Matrix Finding the Inverse Using the Inverse to Solve Systems Cramer’s Rule Eigenvalue Problem Powers of Matrices Orthogonal Matrices Approximation of Eigenvalues Diagonalization LUFactorization Cryptography ErrorCorrecting Code Method of Least Squares Discrete Compartmental Models Chapter in Review Vector Calculus Vector Functions Motion on a Curve Curvature Partial Derivatives Directional Derivative Tangent Planes and Normal Lines Curl and Divergence Line Integrals Independence of Path Double Integrals Double Integrals in Polar Coordinates Green’s Theorem PART Surface Integrals Stokes’ Theorem Triple Integrals Divergence Theorem Change of Variables in Multiple Integrals Chapter in Review Systems of Differential Equations Systems of Linear Differential Equations Theory of Linear Systems Homogeneous Linear Systems Distinct Real Eigenvalues Repeated Eigenvalues Complex Eigenvalues Solution by Diagonalization Nonhomogeneous Linear Systems Undetermined Coefficients Variation of Parameters Diagonalization Matrix Exponential Chapter in Review Systems of Nonlinear Differential Equations Autonomous Systems Stability of Linear Systems Linearization and Local Stability Autonomous Systems as Mathematical Models Periodic Solutions, Limit Cycles, and Global Stability Chapter in Review Partial Differential Equations Fourier Series Orthogonal Functions Fourier Series Fourier Cosine and Sine Series Complex Fourier Series Sturm–Liouville Problem Bessel and Legendre Series Fourier–Bessel Series Fourier–Legendre Series Chapter in Review BoundaryValue Problems in Rectangular Coordinates Separable Partial Differential Equations Classical PDEs and BoundaryValue Problems Heat Equation Wave Equation PART Laplace’s Equation Nonhomogeneous BoundaryValue Problems Orthogonal Series Expansions HigherDimensional Problems Chapter in Review BoundaryValue Problems in Other Coordinate Systems Polar Coordinates Cylindrical Coordinates Spherical Coordinates Chapter in Review Integral Transforms Error Function Laplace Transform Fourier Integral Fourier Transforms Finite Fourier Transforms Fast Fourier Transform Chapter in Review Numerical Solutions of Partial Differential Equations Laplace’s Equation Heat Equation Wave Equation Chapter in Review Complex Analysis Functions of a Complex Variable Complex Numbers Powers and Roots Sets in the Complex Plane Functions of a Complex Variable Cauchy–Riemann Equations Exponential and Logarithmic Functions Trigonometric and Hyperbolic Functions Inverse Trigonometric and Hyperbolic Functions Chapter in Review Integration in the Complex Plane Contour Integrals Cauchy–Goursat Theorem Independence of Path Cauchy’s Integral Formulas Chapter in Review Series and Residues Sequences and Series Taylor Series . A B C D Laurent Series Zeros and Poles Residue Theorem Evaluation of Real Integrals Chapter in Review Conformal Mappings Complex Functions as Mappings Conformal Mappings Linear Fractional Transformations Schwarz–Christoffel Transformations Poisson Integral Formulas Applications Chapter in Review Appendices IntegralDefined Functions Derivative and Integral Formulas Laplace Transforms Conformal Mappings Answers to Selected OddNumbered Problems Index A Absolute convergence: of a complex series, definition of, of a power series, , Absolute error, Absolute value of a complex number, Absolutely integrable, , Acceleration: centripetal, due to gravity, , normal component of, tangential component of, as a vector function, Adams, John Couch, Adams–Bashforth–Moulton method, Adams–Bashforth predictor, Adams–Moulton corrector, Adaptive numerical method, Addition: of matrices, of power series, – of vectors, – , Adjoint matrix: definition of, use in finding an inverse, – Age of a fossil, – Aging spring, , Aging spring equation, solution of, Agnew, Ralph Palmer, , Air resistance: linear, , , nonlinear, , , projectile motion with, , projectile motion with no, , proportional to square of velocity, , , proportional to velocity, , , – Airy, Sir George Biddell, Airy functions of the first and second kind, APP Airy’s differential equation: definition of, , solution as power series, – solution in terms of Bessel functions, various forms of, – Allee, Warder Clyde, Allee effect, Aliasing, – Alternative form of second translation theorem, – Ambient temperature, , Amperes (A), Amplitude: damped, of free vibrations, time varying, , Analytic function: criterion for, definition of, derivatives of, Analytic part of a Laurent series, Analyticity, vector fields and, Analyticity and path independence, Analyticity at a point: criterion for, definition of, , Angers suspension bridge, Angle between two vectors, Angle preserving mappings, Anharmonic overtones, Annular domain, Annulus in the complex plane, Anticommute, Antiderivative:of a complex function, definition of, existence of, Applications of differential equations: aging springs, , air exchange, air resistance, , , , – , , – Allee effect, bacterial growth, ballistic pendulum, bending of a circular plate, – buckling of a tapered column, buckling of a thin vertical column, – , – cantilever beam, – carbondating, catenary, caught pendulum, chemical reactions, – , – column bending under its own weight, competing species of animals, – , continuous compound interest, , cooling fin, cooling/warming, , – , coupled spring/mass system, – , – cycloid, damped motion, deflection of a beam, – , double pendulum, double spring systems, draining a tank, , electrical networks, – , , , electrical series circuits, , , , – emigration, evaporating raindrop, , evaporation, falling bodies with air resistance, , , , – falling bodies with no air resistance, – , falling chain, – floating barrel, fluctuating population, forgetfulness, growth of microorganisms in a chemostat, hanging chain, hard spring, harvesting, heart pacemaker, , hitting bottom, hole drilled through the Earth, immigr ation, , infus io n of a drug, le aking tanks, linear spring, lifting a heavy rope, lo gistic population growth, – marine toads, invasion of, – memorization, mixtures, , , networks, – nonlinear springs, – nonlinear pendulum, , , – orthogonal families of curves, – oscillating chain, Ötzi (the Iceman), – Paris guns, – pendulum of varying length, population dynamics, potassium–argon dating, , potassium decay, predator–prey, – , – projectile motion, , – , – pulsating sphere, pursuit curves, radioactive decay, , – , – , – , – reflecting surface, restocking, rocket motion, , , rope pulled upward by a constant force, , – rotating fluid, shape of a, rotating pendulum, – rotating rod, sliding bead on a, rotating shaft, rotating string, – , sawing wood, series circuit, , – Shroud of Turin, sinking in water, skydiving, sliding bead, , sliding box on an inclined plane, snowplow problem, soft spring, solar collector, spread of a disease, spring coupled pendulums, spring/mass systems, , – , – , – spring pendulum, streamlines, suspended cables and telephone wires, – , telephone wires, temperature in an annular cooling fin, temperature in a circular cylinder, – temperature in a circular plate, temperature between concentric cylinders, temperature between concentric spheres, , temperature in a quartercircular plate, temperature in a ring, temperature in a semiannular plate, temperature in a semicircular plate, temperature in a sphere, , , temperature in a wedgeshaped plate, terminal velocity, , , time of death, tractrix, tsunami, variable mass, – , vibrating beam, , vibrating string, – water clock, – Aquatic food chain, Arc, Arc length as a parameter, Archimedes of Syracuse, Archimedes’ principle, Area: of a parallelogram, of a surface, of a triangle, Area as a double integral, , , Argument of a complex number: definition of, principal, properties of, Arithmetic modulo , Arithmetic of power series, Associated homogeneous equation, Associated homogeneous system, Associated Legendre differential equation, Associated Legendre functions, Associative laws: of complex numbers, of matrix addition, of matrix multiplication, Asymptotically stable critical point, , , Attractor, , , Augmented matrix:definition of, elementary row operations on, – in reduced rowechelon form, in rowechelon form, row equivalent, Autonomous differential equation: critical points for, definition of, , direction field for, firstorder, secondorder, , translation property for, Autonomous system of differential equations: column vector form of, definition of, row vector form of, Auxiliary equation: for a Cauchy–Euler equation, for a linear equation with constant coefficients, , rational roots of, repeated complex roots of, roots of, , – Axis of symmetry of a beam, B Back substitution, Backward difference, Bacterial growth, Balancing chemical equations, – Ballistic pendulum, Banded matrix, Bandlimited signals, Bashforth, Francis, Basis of a vector space: definition of, standard, – BC, Beams: axis of symmetry, cantilever, clamped, deflection curve of, elastic curve of, embedded, free, flexural rigidity of, simply supported, static deflection of a homogeneous beam, – , – use of the Laplace transform, – Beats, Bell curve, Bending of a circular plate, Bending of a thin column, , Bendixson negative criterion, Bernoulli, Jacob, Bernoulli’s differential equation: definition of, solution of, Bessel, Friedrich Wilhelm, Bessel function(s): aging spring and, differential equations solvable in terms of, – differential recurrence relations for, of the first kind, graphs of, , , , of halfintegral order, – modified of the first kind, modified of the second kind, numerical values of, of order c, of order ½, – of order –½, orthogonal set of, properties of, recurrence relation for, of the second kind, spherical, – zeros of, Bessel series, Bessel’s differential equation: general solution of, , modified of order ν, of order ν, parametric form of, parametric form of modified equation, series solution of, – Beta function: definition of, APP expressed in terms of the gamma function, APP Biharmonic function, Binary string of length n, Binormal, Bits, Boundary conditions (BC): homogeneous, , mixed, nonhomogeneous, for an ordinary differential equation, , , , for a partial differential equation, – periodic, separated, time dependent, – time independent, – Boundary points, , Boundary of a set, Boundaryvalue problem (BVP): in cylindrical coordinates, deflection of a beam, – eigenfunctions for, – , , eigenvalues for, – , the Euler load, homogeneous, nonhomogeneous, , , nontrivial solutions of, numerical methods for ODEs, – numerical methods for PDEs, , , for an ordinary differential equation, , – , for a partial differential equation, , – , – , , , , , – , – with periodic boundary conditions, , , in polar coordinates, in rectangular coordinates, regular, rotating string, – secondorder, , singular, in spherical coordinates, – two point, Bounding theorem for contour integrals, – Branch of the complex logarithm, Branch cut, Branch point, Branch point of an electrical network, , Broughton suspension bridge, Buckling modes, Buckling of a tapered column, Buckling of a thin vertical column, , – Buoyant force, BVP, C Calculation of order hn, Cambridge halflife of C , Cantilever beam, Capacitance, Carbon dating, – Carrying capacity, Cartesian coordinates, – Cartesian equation of a plane, Catenary, Cauchy, AugustinLouis, Cauchy–Euler differential equation: auxiliary equation for, definition of, general solutions of, – generalization of, method of solution, – reduction to constant coefficients, regular singular point of, Cauchy–Goursat theorem, Cauchy–Goursat theorem for multiply connected domains, Cauchy principal value of an integral, Cauchy–Riemann equations, Cauchy–Schwarz inequality, Cauchy’s inequality, Cauchy’s integral formula, Cauchy’s integral formula for derivatives, Cauchy’s residue theorem, Cauchy’s theorem, Caught pendulum, Cavalieri, Bonaventura, Cayley, Arthur, , Cayley–Hamilton theorem, Center: as a critical point, of curvature, of mass, , of a power series, Central difference: approximation for derivatives, , , , definition of, Central force, Centripetal acceleration, Centroid, Chain Rule, , APP Chain Rule of partial derivatives, Chain Rule for vector functions, Change of scale theorem, Change of variables: in a definite integral, – in a double integral, , , – in a triple integral, Characteristic equation of a matrix, Characteristic values of a matrix, Characteristic vectors of a matrix, Chebyshev, Pafnuty, Chebyshev polynomials, Chebyshev’s differential equation, , Chemical equations, balancing of, – Chemical messages, – Chemical reactions: firstorder, – secondorder, , , , – Chemostat, Cholesky, AndréLouis, Cholesky’s method, Christoffel, Elwin Bruno, Circle: in complex plane, of convergence, of curvature, Circlepreserving property, Circuits, differential equations of, , , – , , Circular helix, Circulation, Circulation of a vector field, Clamped end conditions of a beam, Classification of differential equations: by linearity, by order, – by type, Classification of linear partial differential equations by type, Classifying critical points, , – , Clepsydra, Clockwise (negative) direction on a simple closed curve, Closed curve, , Closed disk, Closed region in the complex plane, Closure axioms of a vector space, Cn[a, b] vector space, Code, Code word, Coefficient matrix, Coefficients of variables in a linear system, Cofactor(s): definition of, – expansion of a determinant by, – a property of, Coil spring, Column bending under its own weight, Column vector, , Column vector form of an autonomous system, Commutative laws of complex numbers, Commutator, Compartmental analysis, Compartmental models, Compatibility condition, Competition models, – , , Competitive interaction, Complementary error function: definition of, , , APP graph of, Complementary function: for a linear differential equation, for a system of linear differential equations, , Complete set of functions, Completing the square, Complex conjugate, Complex eigenvalues of a matrix, Complex form of Fourier integral, Complex form of Fourier series, Complex function: analytic, , , , continuous, , definition of, derivative of, differentiable, – domain of, entire, , , exponential, fundamental region, hyperbolic, inve rse hyperbolic, inve rse trigonometric, limit of, lo garithmic, as a mapping, , periodic, , polynomial, power, range of, rational, as a source of harmonic functions, as a transformation, trigonometric, as a twodimensional fluid flow, Complex impedance, Complex integral, Complex line integrals: definition of, evaluation of, , , properties of, – Complex number(s): absolute value of, addition of, argument of, associative laws for, commutative laws for, complex powers of, conjugate of a, , definition of, , distributive law for, division of, , equality of, geometric interpretation of, ima ginary part of, ima ginary unit, int eger powers of, lo garithm of, magnitude of, modulus of, multiplication of, , polar form of, – principal argument of, principal nth root of, pure imaginary, real part of, roots of a, – subtraction of, triangle inequality for, vector interpretation, Complex plane: definition of, ima ginary axis of, real axis of, sets in, – Complex potential, Complex powers: of a complex number, principal value of, Complex sequence, Complex series, – Complex vector space, Complex velocity potential, Component of a vector on another vector, Components of a vector, , , Conformal mapping, Conformal mapping and the Dirichlet problem, Conformal mappings, table of, APP Conjugate of a complex number, , Conjugate complex roots, , – , , Connected region, , Conservation of energy, Conservative force field, Conservative vector field: definition of, , potential function for, , , test for, , , Consistent system of linear equations, Constant rules of differentiation, , APP Constants of a linear system, Constructing an orthogonal basis: for R , for R , for R , Continuing numerical method, Continuity of a complex function, Continuity equation, – Continuity of a vector function, Continuous compound interest, nContour: definition of, ind ented, Contour integral: bounding theorem for, – definition of, evaluation of, – , , fundamental theorem for, ind ependent of the path, – , for the inverse Laplace transform, properties of, Contourplot, Convergence: of a complex geometric series, of a complex sequence, of a complex series, – of a Fourier integral, of a Fourier series, of a Fourier–Bessel series, of a Fourier–Legendre series, of an improper integral, of a power series, , Convergent improper integral, Convolution, properties of, – Convolution integral, , , – Convolution theorem: for the Fourier transform, , – inve rse form, for the Laplace transform, Cooling of a cake, , Cooling fin, temperature in a, Cooling and warming, Newton’s law of, , Coordinate planes, Coordinates of a midpoint, Coordinates of a vector relative to a basis, Coordinates of a vector relative to an orthonormal basis, Coplanar vectors, Coplanar vectors, criterion for, Cosine integral function, APP Cosine series, Cosine series in two variables, Coulomb (C), Coulomb’s law, Counterclockwise (positive) direction on a simple closed curve, Coupled pendulums, Coupled spring/mass system, – Coupled systems, Coverup method, Cramer, Gabriel, Cramer’s rule, Crank, John, Crank–Nicolson method, – Criterion for an exact differential, Critical loads, Critical points of an autonomous firstorder differential equation: asymptotically stable, attractor, definition of, is olated, repeller, semistable, unstable, Critical points for autonomous linear systems: attractor, center, classifying, definition of, degenerate stable node, – degenerate unstable node, – lo cally stable, repeller, saddle point, stable node, stable spiral point, stability criteria for, unstable, unstable node, unstable spiral point, Critical points for plane autonomous systems: asymptotically stable, classifying, stability criteria for, stable, unstable, Critical speeds, – Critically damped electrical circuit, Critically damped spring/mass system, Cross product: alternative form of, component form of, as a determinant, magnitude of, properties of, – test for parallel vectors, Crossratio, Crout, Preston D., Crout’s method, Cryptography, Curl of a vector field: definition of, as a matrix product, physical interpretation of, , – Curvature, , Curve integral, Curves: closed, defined by an explicit function, great circles, of intersection, parallel, parametric, piecewise smooth, positive direction on, simple closed, smooth, Curvilinear motion in the plane, Cycle of a plane autonomous system, Cycloid, Cylinder functions, Cylindrical coordinates: conversion to rectangular coordinates, definition of, Laplacian in, triple integrals in, Cylindrical wedge, D D’Alembert, JeanBaptiste le Rond, D’Alembert’s solution, Da Vinci, Leonardo, Damped amplitude, Damped motion, , – Damping, linear, Damping constant, Damping factor, Daphnia, Daughter isotope, DE, De Moivre, Abraham, De Moivre’s formula, Decay, radioactive, Decay constant, Decoding a message, – Definite integral, definition of, Deflation, method of, Deflection of a cantilever beam, Deflection curve of a beam, Deflection of a vertical column, Deformation of contours, Degenerate nodes: stable, – unstable, – Del operator, – Densitydependent hypothesis, Dependent variables, Derivative of a complex function: of complex exponential function, of complex hyperbolic functions, of complex inverse hyperbolic functions, of complex inverse trigonometric functions, of the complex logarithm function, of complex trigonometric functions, definition of, of integer powers of z, rules for, Derivative of a definite integral, , Derivative of an integral defined function, APP , APP Derivative and integral formulas, APP , APP Derivative of a Laplace transform, Derivative of real function, notation for, Derivative of a sum of functions, APP Derivative of vector function, definition of, Descartes, René, Determinant(s): of a × matrix, of a × matrix, cofactors of, – definition of, evaluating by row reduction, – expansion by cofactors, – , of a matrix product, minor of, of order n, as a product of eigenvalues, properties of, – of a transpose, of a triangular matrix, with two identical rows, Diagonal matrix, , Diagonalizability: criterion for, , sufficient condition for, , Diagonalizable matrix: definition of, orthogonally, Diagonalization, solution of a linear system of DEs by, – Difference equation replacement: for heat equation, – for Laplace’s equation, for a secondorder ODE, – for wave equation, – Difference quotients, Differentiable at a point, Differential: of arc length, , exact, form of a firstorder ODE, of a function of several variables, nthorder operator, operator, recurrence relation, of surface area, Differential equation (ordinary): Airy’s, , , , associated Legendre’s, autonomous, , , – Bernoulli’s, Bessel’s, Cauchy–Euler, Chebyshev’s, with constant coefficients, , , definitions and terminology, differential form of, Duffing’s, exact, explicit solution of, families of solutions of, firstorder, , firstorder with homogeneous coefficients, general form of, general solution of, , , , , – , – Gompertz, Hermite’s, , higherorder, , homogeneous, , – , , , imp licit solution of, Laguerre’s, , Legendre’s, , linear firstorder, , linear secondorder, as a mathematical model, – modified Bessel’s, – nonhomogeneous, , , nonlinear, , , – , – with nonpolynomial coefficients, normal form of, notation for, order of, ordinary, ordinary point of, parametric Bessel, parametric modified Bessel, particular solution of, , , piecewise linear, with polynomial coefficients, – , Riccati’s, secondorder, , , – , – , – selfadjoint form of, – separable, – singular points of, , singular solution of, solution of, – standard form of a linear, , , substitutions in, superposition principles for linear, , system of, , , – , – Van der Pol’s, , with variable coefficients, , , , , – , written as a firstorder system, – Differential equation (partial): classification of linear secondorder, definition of, diffusion, , heat, – , – , homogeneous linear secondorder, Laplace’s, , , – , – linear secondorder, nonhomogeneous linear secondorder, order of, Poisson’s, separable, – solution of, superposition principle for homogeneous linear, time dependent, time independent, wave, , , – , Differential form, , Differential operator:linearity property of, nth order, Differential recurrence relation, Differentiation of vector functions, rules of, Diffusion equation, , – Dimension of a vector space, , Dirac, Paul Adrien Maurice, Dirac delta function: definition of, , Laplace transform of, Direction angles, Direction cosines, Direction field, , Direction numbers of a line, Direction vector of a line, Directional derivative: computing, definition of, for functions of three variables, for functions of two variables, – maximum values of, – Dirichlet, Johann Peter Gustav Lejeune, Dirichlet condition, Dirichlet problem: for a circular plate, for a cylinder, – , definition of, – , , exterior, harmonic functions and, for a planar region, for a rectangular region, , , for a semicircular plate, – solving using conformal mapping, for a sphere, superposition principle for, – Disconnected region, Discontinuous coefficients, Discrete compartmental models, – Discrete Fourier transform, – Discrete signal, Discretization error, Distance formula, Distance from a point to a line, Distributions, theory of, Distributive law: for complex numbers, for matrices, Divergence theorem, Divergence of a vector field: definition of, physical interpretation of, , Divergent improper integral, Division of two complex numbers, , Domain: of a complex function, in the complex plane, of a function, of a function of two variables, of a solution of an ODE, – Dominant eigenvalue, – Dominant eigenvector, Doolittle, Myrick H., Doolittle’s method, – Dot notation for differentiation, Dot product: component form of, definition of, , properties of, in terms of matrices, as work, Double cosine series, Double eigenvalues, Double integral: as area of a region, , as area of a surface, change of variables, definition of, evaluation of, – as an iterated integral, in polar coordinates, properties of, reversing the order of integration in, as volume, Double pendulum, Double sine series, Double spring systems, Doubly connected domain, Downward orientation of a surface, Drag, Drag coefficient, , Drag force, , Draining a tank, , Driven motion: with damping, – without damping, Driving function, , Drosophila, Drug dissemination, model for, Drug infusion, DSolve command, Duffing, Georg, Duffing’s differential equation, Dulac negative criterion, Dynamical system: definition of, , response of, state of, E Ecosystem, states of, , Effective spring constant, Effective weight, Eigenfunctions: of a boundaryvalue problem, of a Sturm–Liouville problem, – Eigenvalues of a boundaryvalue problem, , – Eigenvalues of a matrix: approximation of, complex, , definition of, , – of a diagonal matrix, distinctreal, dominant, – of an inverse matrix, of multiplicity m, of multiplicity three, of multiplicity two, repeated, of a singular matrix, of a symmetric matrix, , of a triangular matrix, Eigenvector(s) of a matrix: complex, – definition of, , dominant, of an inverse matrix, orthogonal, Elastic curve, Electrical circuits, , , , – , – , – Electrical networks, , , Electrical vibrations: critically damped, forced, free, overdamped, simple harmonic, underdamped, Elementary functions, Elementary matrix, Elementary operations for solving linear systems, Elementary row operations on a matrix: definition of, – notation for, Elimination method(s): for a system of algebraic equations, – , – for a system of ordinary differential equations, – Elliptic partial differential equation, Elliptical helix, Embedded end conditions of a beam, , Empirical laws of heat conduction, Encoding a message, Encoding a message in the Hamming ( , ) code, Entire function, Entries in a matrix, Epidemics, , , Equality of complex numbers, Equality of matrices, Equality of vectors, , , Equation of continuity, – Equation of motion, – Equilibrium point, Equilibrium position of a spring/mass system, Equilibrium solution, , Equipotential curves, Error(s): absolute, discretization, formula, global truncation, lo cal truncation, percentage relative, relative, roundoff, sum of square, Error function: definition of, , , APP graph of, Errorcorrecting code, – Errordetecting code, , Escape velocity, Essential singularity, Euclidean inner product, Euler, Leonhard, , APP Euler load, Euler’s constant, Euler’s formula, Euler’s improved method, Euler’s method: error analysis of, , – for firstorder differential equations, , for secondorder differential equations, for systems of differential equations, , Evaluation of real integrals by residues, – Evaporating raindrop, , Evaporation, Even function: definition of, properties of, Exact differential: definition of, test for, Exact differential equation: definition of, solution of, Existence of Fourier transforms, Existence of Laplace transform, Existence of power series solutions, Existence of a unique solution, – , , Expansion of a function: in a complex Fourier series, in a cosine series, in a Fourier series, – in a Fourier–Bessel series, – in a Fourier–Legendre series, – halfrange, – in a Laurent series, – in a power series, – in a sine series, in terms of orthogonal functions, – Explicit finite difference method, Explicit solution, Exponential form of a Fourier integral, Exponential form of a Fourier series, Exponential function: definition of, derivative of, fundamental region of, period of, properties of, – Exponential integral function, APP Exponential order, Exponents of a singularity, Exterior Dirichlet problem, Exterior point, External force, Extreme displacement, F Factorial function, APP Falling bodies, mathematical models of, – , Falling chain, – Falling raindrops, , Family of solutions, Farads (f), Fast Fourier transform, Fast Fourier transform, computing with, Fehlberg, Erwin, Fibonacci, Fibonacci sequence, Fick, Adolf Eugen, Fick’s law of diffusion, Filtered signals, Finite difference approximations, – , , , Finite difference equation, Finite difference method: explicit, , imp licit, Finite differences, Finite dimensional vector space, Finite Fourier transforms: cosine, inve rse of, operational properties of, , sine, First buckling mode, First harmonic, First moments, First normal mode, First octant, Firstorder chemical reaction, Firstorder differential equations: applications of, – , solution of, , , , , – Firstorder initialvalue problem, Firstorder Runge–Kutta method, , Firstorder system, First shifting theorem, First standing wave, First translation theorem: form of, inve rse form of, Fivepoint approximation of the Laplacian, Flexural rigidity, Flow: of fluid around a corner, of fluid around a cylinder, of heat, steadystate fluid, Fluctuating population, Flux and Cauchy’s integral formula, Flux through a surface, Flux of a vector field, Folia of Descartes, , Forced electrical vibrations, Forced motion: with damping, without damping, Forcing function, , Forgetfulness, Formula error, Forward difference, Fossil, age of, Fourier, JeanBaptiste Joseph, Fourier coefficients, Fourier cosine transform: definition of, operational properties of, – Fourier integral: complex form, conditions for convergence, cosine form, definition of, exponential form, sine form, Fourier integrals, Fourier series: complex, – conditions for convergence, cosine, – definition of, generalized, sine, – in two variables, Fourier sine transform: definition of, operational properties of, – Fourier transform pairs, Fourier transforms: complex (exponential) form of, definitions of, existence of, finite, linearity of, operational properties of, – Fourier–Bessel series: conditions for convergence, definition of, , Fourier–Legendre series: conditions for convergence, definition of, – , Fourthorder partial differential equation, , Fourthorder Runge–Kutta methods: for firstorder differential equations, , , – for secondorder differential equations, for systems of differential equations, – Free electrical vibrations, Freeend conditions of a beam, , Free motion of a spring/mass system: damped, – undamped, Free vectors, Frequency of free vibrations, Frequency filtering, Frequency response curve, Frequency spectrum, Fresnel, AugustinJean, Fresnel cosine integral function, APP Fresnel sine integral function, , , APP Frobenius, Georg Ferdinand, Frobenius, method of, Frobenius’ theorem, Fubini, Guido, Fubini’s theorem, Fulcrum supported ends of a beam, Fullwave rectification of sine, Function(s): Airy, APP beta, APP complementary, complementary error, , APP of a complex variable, continuous, cosine integral, APP defined by an integral, , , APP differentiable, directional derivative of, – domain of, driving, , , error, , – , APP even, exponential, exponential integral, APP factorial, APP forcing, , , – Fresnel cosine integral, APP Fresnel sine integral, , APP gamma, , , APP generalized, generalized factorial, APP gradient of, graph of, harmonic, , – , hyperbolic, inne r product of, int egral defined, inp ut, , lo garithmic, lo garithmic integral, APP odd, orthogonal, output, , partial derivative of, – periodic, polynomial, potential, , power, , range of, rational, of a real variable, response, , sine integral, , , APP vs. solution, stream, of three variables, trigonometric, as a twodimensional flow, of two variables, vector, weight, Fundamental angular frequency, Fundamental critical speed, Fundamental frequency, Fundamental matrix: definition of, matrix exponential as a, Fundamental mode of vibration, Fundamental period, , Fundamental region of the complex exponential function, Fundamental set of solutions: definition of, , existence of, , Fundamental theorem: of algebra, – of calculus, , for contour integrals, for line integrals, G g, , Galileo Galilei, , Gamma function: asymptotes of graph, APP definition of, , APP graph of, APP recursion formula for, , APP Gauss, Johann Carl Friedrich, , APP Gauss’ law, , Gauss’ theorem, Gaussian elimination, Gauss–Jordan elimination, Gauss–Seidel iteration, , General form of a linear ordinary differential equation, General form of an ordinary differential equation, General solution: of Bessel’s equation, , definition of, , , , of a homogeneous linear differential equation, of a homogeneous secondorder linear differential equation, – of a homogeneous system of linear differential equations, of a linear firstorder equation, of linear higherorder equations, – of modified Bessel’s equation, – of a nonhomogeneous linear differential equation, of a nonhomogeneous system of linear differential equations, of parametric form of Bessel’s equation, of parametric form of modified Bessel’s equation, of a secondorder Cauchy–Euler equation, – Generalized factorial function, APP Generalized Fourier series, Generalized functions, Generalized length, Geometric series, Geometric vectors, George Washington monument, Gibbs, Josiah Willard, Gibbs phenomenon, Global truncation error, Globally stable critical point, Gompertz, Benjamin, Gompertz differential equation, Goursat, Edouard, Gradient: of a function of three variables, – of a function of two variables, – geometric interpretation of, – vector field, , Gram–Schmidt orthogonalization process, – , Graph(s): of the complementary error function, of the error function, of a function of two variables, of the gamma function, , , APP of level curves, of level surfaces, of a plane, Great circles, Green, George, , Green’s function: for a boundaryvalue problem, – for an initialvalue problem, for a secondorder differential equation, for a secondorder differential operator, Green’s identities, Green’s theorem in the plane, Green’s theorem in space, Growth and decay, – , – Growth constant, Growth rate, relative, H Halflife: of carbon , definition of, of a drug, of plutonium , of radium , of uranium , Halfplane, Halfrange expansions, – Halfwave rectification of sine, Hamilton, William Rowan, Hamming ( , ) code, Hamming ( , ) code, Hamming, Richard W., Hanging chain, Hard spring, Harmonic conjugate functions, Harmonic function, , – , Harmonic function, transformation theorem for, Harmonic functions and the Dirichlet problem, Harvesting, Hawking, Stephen, Hawking radiation, Heart pacemaker, model for, , Heat equation: derivation of onedimensional equation, – difference equation replacement for, – , – and discrete Fourier series, and discrete Fourier transform, – onedimensional, – in polar coordinates, solution of, twodimensional, Heaviside, Oliver, Heaviside function, Heaviside layer, Helmholtz, Hermann Ludwig Ferdinand von, Helmholtz’s partial differential equation, Helix: circular, elliptical, pitch of, Henrys (h), Hermite, Charles, Hermite polynomials, Hermite’s differential equation, , Higherorder ordinary differential equations, , , Hinged end of a beam, Hitting bottom, Hole through the Earth, Homogeneous boundary conditions, , , Homogeneous boundaryvalue problem, , Homogeneous firstorder differential equation: definition of, solution of, Homogeneous function, Homogeneous linear differential equation: ordinary, , partial, Homogeneous systems of linear algebraic equations: definition of, , matrix form of, nontrivial solutions of, properties of, trivial solution of, Homogeneous systems of linear differential equations: complex eigenvalues, – definition of, distinctreal eigenvalues, fundamental set of solutions for, general solution of, matrix form of, repeated eigenvalues, – superposition principle for, – HoënéWronski, Józef Maria, Hooke, Robert, Hooke’s law, , – Horizontal component of a vector, Hurricane Hugo, – Huygens, Christiaan, , Hydrogen atoms, distance between, – Hyperbolic functions, complex: definitions of, derivatives of, zeros of, Hyperbolic partial differential equation, I IC, i, j vectors, i, j, k vectors, Iceman (Ötzi), – Identity matrix, Identity property of power series, Illconditioned system of equations, Image of a point under a transformation, Images of curves, Imaginary axis, Imaginary part of a complex number, Imaginary unit, Immigration model, – , Impedance, Implicit finite difference method, Implicit solution, Improper integral: convergent, , – , APP divergent, , – Improved Euler’s method, Improved Euler’s method, truncation errors for, Impulse response, Incompressible flow, , Incompressible fluid, Inconsistent system of linear equations, Indefinite integral, , Indented contours, Independence of path: definition of, , test for, , , , Independent variables, Indicial equation, Indicial roots, Inductance, , Infinitedimensional vector space, – Infinite linearly dependent set, Infinite linearly independent set, Infinite series of complex numbers: absolute convergence, convergence of, – definition of, geometric, necessary condition for convergence, nth term test for divergence, sum of, – Infusion of a drug, Initial conditions (IC), , Initialvalue problem (IVP): definition of, , firstorder, , nthorder, , secondorder, for systems of linear differential equations, unique solution of, Inner partition, Inner product: definition of, , , , properties of, , space, , of two column matrices, of two functions, of two vectors, , Inner product space, , Input function, , Insulated boundary, , Integers: modulo , modulo , Integrable function: of three variables, of two variables, Integraldefined function, , , – , , APP Integral equation, Integral transform: definition of, finite Fourier cosine, finite Fourier sine, Fourier, Fourier cosine, Fourier sine, inve rse, kernel of, , Laplace, , pair, Integral transforms of derivatives: finite Fourier cosine, finite Fourier sine, Fourier, Fourier cosine, Fourier sine, Laplace, – Integral of a vector function, Integrating factor, , – Integration along a curve, – Integration by parts, Integrodifferential equation, Interest, compounded continuously, Interior mesh points, Interior point, , Interior point of a set in the complex plane, Interpolating function, Interval: of convergence, of definition of a solution, of existence and uniqueness, of validity of solution, Invariant region: definition of, Types I and II, Invasion of the marine toads, – Inverse cosine function: derivative of, as a logarithm, Inverse of finite Fourier cosine transform, Inverse of finite Fourier sine transform, Inverse hyperbolic functions: derivatives of, as logarithms, Inverse integral transform: Fourier, Fourier cosine, Fourier sine, Laplace, , Inverse of a matrix: by the adjoint method, – definition of, by elementary row operations, properties of, using to solve a system, – Inverse power method, Inverse sine function: definition of, derivative of, as a logarithm, Inverse tangent function: derivative of, as a logarithm, Inverse transform, , , Inverse transformation, Inverse trigonometric functions: definitions of, derivatives of, Invertible matrix, Irregular singular point, Irrotational flow, , Isocline, , Isolated critical point, Isolated singularity: classification of, – definition of, Iterated integral, IVP, , J Jacobi, Carl Gustav Jacob, Jacobian determinant, Jacobian matrix, Joukowski airfoil, Joukowski transformation, K Kepler’s first law of planetary motion, Kernel of an integral transform, , Kinetic friction, Kirchhoff, Gustav Robert, Kirchhoff’s first law, Kirchhoff’s point and loop rules, Kirchhoff’s second law, , , Kutta, Martin Wilhelm, L Lagrange, JosephLouis, Lagrange’s identity, Laguerre, Edmond, Laguerre polynomials, Laguerre’s differential equation, , Laplace, PierreSimon Marquis de, Laplace transform: alternative form of second translation theorem, – behavior as s → θ change of scale theorem for, conditions for existence, convolution theorem for, – definition of, , of a derivative, – derivatives of a, of differential equations, – differentiation of, – of Dirac delta function, of an integral, inve rse of, , linearity of, linearity of the inverse transform, and the matrix exponential, operational properties of, , , , , , , , , , , , of a partial derivative, of a periodic function, sufficient conditions for existence of, of systems of ordinary differential equations, – tables of, , APP translation theorems for, , of unit step function, Laplace’s partial differential equation: in cylindrical coordinates, – difference equation replacement for, maximum principle for, in polar coordinates, , solution of, – in three dimensions, in two rectangular coordinates, , – , Laplacian: in cylindrical coordinates, definition of, in polar coordinates, in rectangular coordinates, in spherical coordinates, in three dimensions, , Lascaux cave paintings, dating of, Latitude, Lattice points, Laurent, Pierre Alphonse, Laurent series, Laurent’s theorem, – Law of conservation of mechanical energy, Law of mass action, Law of universal gravitation, Laws of exponents for complex numbers, Laws of heat conduction, LCseries circuit, integrodifferential equation of, Leaking tank, Leaning Tower of Pisa, Learning theory, Least squares, method of, – Least squares line, , Least squares parabola, – Least squares solution, Legendre, AdrienMarie, Legendre associated functions, Legendre functions, – , , Legendre polynomials: first six, graphs of, properties of, recurrence relation for, Rodrigues’ formula for, Legendre’s differential equation: associated, of order n, series solution of, – Leibniz, Gottfried Wilhelm, Leibniz notation, Leibniz’s rule, , APP Length of a space curve, Length of a vector: in space, in nspace, Leonardo of Pisa, Leonardo da Vinci, Level curves, , Level of resolution of a mathematical model, Level surfaces, L’Hôpital’s rule, , , , Liber Abaci, Libby, Willard Frank, – Libby halflife, Limit cycle, , Limit of a function of a complex variable: definition of, properties of, Limit of a vector function, Line of best fit, Line integrals: around closed paths, , , – as circulation, complex, definition of, evaluation of, – , fundamental theorem for, ind ependent of the path, in the plane, in space, as work, Line segment, Lineal element, Linear algebraic equations, systems of, – Linear combination of vectors, Linear damping, Linear dependence: of a set of functions, – of a set of vectors, , of solution vectors, Linear donorcontrolled hypothesis, Linear equation in n variables, Linear firstorder differential equation: definition of, , general solution of, homogeneous, int egrating factor for, method of solution, nonhomogeneous, – singular points of, standard form of, variation of parameters for, Linear fractional transformation, Linear independence: of a set of functions, – of a set of vectors, of solution vectors, of solutions of linear DEs, – Linear momentum, Linear operator, , Linear ordinary differential equations: applications of, , – , , associated homogeneous, auxiliary equation for, , boundaryvalue problems for, , , complementary function for, – with constant coefficients, definition, firstorder, , general solution of, , , , – , – higherorder, , , – , homogeneous, , , ind ic ia l equation for, infinit e series solutions for, , initia lvalue problems for, , , , , – , nonhomogeneous, – , , , – nthorder, nthorder initialvalue problem for, ordinary points of, particular solution for, , , , – piecewise, reduction of order, – secondorder, , , – , – singular points of, , , , standard forms of, , , , , superposition principles for, , with variable coefficients, , , , , – , Linear regression, Linear secondorder partial differential equation, Linear secondorder partial differential equations: classification of, homogeneous, nonhomogeneous, solution of, superposition principle for, Linear spring, Linear system of algebraic equations: consistent, definition of, elementary operations on, homogeneous, inc onsistent, nonhomogeneous, Linear system of firstorder differential equations: definition of, , , homogeneous, matrix form of, nonhomogeneous, normal form of, solution of, Linear transform, , , Linearity: of a differential operator, of the Fourier transforms, of the inverse Laplace transform, of the Laplace transform, Linearity property, , , , Linearization: of a function f(x) at a number, , of a function f(x, y) at a point, of a nonlinear differential equation, of a nonlinear system of differential equations, – Linearly dependent set of functions, Linearly independent set of functions, Lines of force, Lines in space: direction numbers for, direction vector for, normal, parametric equations of, symmetric equations of, vector equation for, Liouville, Joseph, Liouville’s theorem, Lissajous curve, , Loblolly pines, bending in high winds, – Local linear approximation, , Local truncation error, Locally stable critical point, Lockheed Electra, Logarithm of a complex number: branch cut for, branch of, definition of, derivative of, principal branch, principal value of, properties of, Logarithmic integral function, APP Logistic curve, Logistic equation: definition of, , modifications of, – solution of, Logistic function, Logistic growth, – Longitude, Loop rule, Kirchhoff’s, Losing a solution, – Lotka, Alfred James, Lotka–Volterra competition model, – Lotka–Volterra predator–prey model, – , Lower bound for the radius of convergence, Lower triangular matrix, LRCseries circuit: differential equation of, , – int egrodifferential equation of, LRseries circuit, differential equation of, LUdecomposition of a matrix, LUfactorization of a matrix, – M M aclaurin, Colin, Maclaurin series, , , Maclaurin series representation: for the cosine function, for the exponential function, for the sine function, Magnification in the zplane, Magnitude of a complex number, Magnitude of the cross product, Magnitude of a vector, , , , Main diagonal entries of a matrix, Malthus, Thomas Robert, Malthusian model, Mapping, , Mapping, conformal, Marching soldiers, Marine toad invasion model, – Mass: center of, as a double integral, of a surface, Mass action, law of, Mathematical model, – , , , , Matrix (matrices): addition of, , , adjoint, anticommute, associative law, , augmented, , banded, characteristic equation of, coefficient, column vector, commutative law, decomposed, definition of, determinant of, – , diagonal, , diagonalizable, difference of, distributive law, , dominant eigenvalue of, – eigenvalues of, , , – , eigenvectors of, , , elementary, elementary row operations on, – entries (or elements) of, equality of, exponential, – factored, fundamental, identity, inve rse of, , – inve rtible, Jacobian, – lo wer triangular, , LUfactorization of, – main diagonal entries of, multiplication, multiplicative identity, multiplicative inverse, nilpotent, , , nonsingular, , nullspace of, order n, orthogonal, , – orthogonally diagonalizable, partitioned, powers of, , product of, rank of, – reduced rowechelon form, rotation, rowechelon form, , row equivalent, row reduction of, – , row space of, row vector, scalar, scalar multiple of, similar, singular, size, skewsymmetric, sparse, square, stochastic, sum of, symmetric, , of a system, trace of a, transpose of, triangular, , tridiagonal, upper triangular, , zero, Matrix addition, properties of, Matrix exponential: computation of, , definition of, derivative of, as a fundamental matrix, as an inverse Laplace transform, Matrix form of a system of linear differential equations, Matrix form of a system of linear equations, Maximum principle, Maxwell, James Clerk, Maxwell’s equations, Meander function, Memorization, mathematical model for, Meridian, Mesh: points, , size, Message, Methane molecule, – Method of deflation, Method of diagonalization: for homogeneous systems of linear DEs, – for nonhomogeneous systems of linear DEs, Method of Frobenius, Method of isoclines, Method of least squares, – Method of separation of variables: for ordinary differential equations, – for partial differential equations, Method of undetermined coefficients: for nonhomogeneous linear DEs, for nonhomogeneous systems of linear DEs, – Method of variation of parameters: for nonhomogeneous linear DEs, , – for nonhomogeneous systems of linear DEs, – Midpoint of a line segment in space, Minor determinant, Mises, Richard von, Mixed boundary conditions, Mixed partial derivatives: definition of, equality of, Mixtures, , , , MLinequality, M vector space, Möbius strip, Modeling process, steps in, Modifications of the logistic equation, – Modified Bessel equation: general solution of, of order ν, parametric form of, Modified Bessel function: of the first kind, of the second kind, Modulus of a complex number, Moments of inertia, Moments of inertia, polar, Motion: on a curve, in a force field, Moulton, Forest Ray, Moving trihedral, Multiplication: of complex numbers, , of matrices, of power series, by scalars, , , Multiplication rule for undetermined coefficients, Multiplicative inverse of a matrix, Multiplicity of eigenvalues, , – Multiply connected domain, Multiply connected region, Multistep numerical method, N ndimensional vector, – Negative criterion, , Negative direction on a curve, Negative of a vector, Neighborhood, Networks, – , Neumann, Carl Gottfried, Neumann condition, Neumann function, Neumann problem: for a circular plate, for a rectangle, Newton, Sir Isaac, Newton’s dot notation, Newton’s law of air resistance, Newton’s law of cooling/warming, , Newton’s law of universal gravitation, Newton’s laws of motion: first, second, , , , – Nicolson, Phyllis, Nilpotent matrix, , , Nodal line, Nodes: of a plane autonomous system, – , m,nof a standing wave, Nonconservative force, Nonelementary integral, , , APP Nonhomogeneous boundary condition, Nonhomogeneous boundaryvalue problem, , , , Nonhomogeneous linear differential equation: boundaryvalue problem for, definition of, general solution of, initia lvalue problem for, ordinary, – , partial, particular solution of, Nonhomogeneous systems of linear differential equations: complementary function of, definition of, general solution of, initia lvalue problem for, matrix form of, normal form of, particular solution of, solution vector of, Nonhomogeneous systems of linear equations, Nonisolated singular point, Nonlinear air resistance, Nonlinear mathematical models, , – Nonlinear ordinary differential equation, , Nonlinear oscillations, – Nonlinear pendulum, – , – Nonlinear spring, Nonlinear systems of differential equations, , Nonoriented surface, Nonpolynomial coefficients, Nonsingular matrix, , , Nontrivial solution, Norm: of a column vector (matrix), of a function, of a partition, , square, of a vector, , , Normal components of acceleration, Normal form: of an ordinary differential equation, of a system of linear firstorder equations, Normal line to a surface, Normal modes, Normal plane, Normal vector to a plane, Normalization of a vector, , Normalized eigenvector, – Normalized set of orthogonal functions, Notation for derivatives, nparameter family of solutions, NSolve command, nspace (R coordinates relative to an orthonormal basis, dimension of, dot (or inner) product in, le ngth (or norm) in, orthogonal vectors in, standard basis for, unit vector in, vector in, zero vector in, nthorder differential operator, nthorder differential equation expressed as a system, – nthorder initialvalue problem, , nthorder ordinary differential equation, – , , nth root of a nonzero complex number, – nth roots of unity, nth term test for divergence, Nullcline, nNullspace of a matrix, Number of parameters in a solution of a linear system of equations, Numerical methods: absolute error in, Adams–Bashforth–Moulton, adaptive methods, continuing method, Crank–Nicolson method, – deflation method, difference equation replacement, errors in, , – , Euler’s method, – , , , , finitedifference methods, – , , , , Gauss–Seidel iteration, imp roved Euler’s method, inve rse power method, multistep method, power method, predictor–corrector methods, , Runge–Kutta methods, , , – , Runge–Kutta–Fehlberg method, shooting method, singlestep method, stability of, stable, starting method, unstable, using the tangent line, Numerical solution curve, Numerical solutions of partial differential equations, Numerical solver, Numerical values of Bessel functions, O Octants, Odd function: definition of, properties of, ODE, Ohm, Georg Simon, Ohms (Σ), Ohm’s law, Onedimensional heat equation: definition of, – derivation of, – Onedimensional phase portrait, Onedimensional wave equation: definition of, – derivation of, Oneparameter family of solutions, Onetoone transformation, Open annulus, Open disk, Open region, Open set, Operational properties of the Laplace transform, , , , – , , – , , , – , , , Operator, differential, , Order, exponential, Order of a differential equation, Order of integration, , – Order of a matrix, Order of a Runge–Kutta method, – Ordered ntuple, , Ordered pair, , , , Ordered triple, , , Ordinary differential equation, Ordinary point of an ordinary differential equation: definition of, – solution about, Orientable surface:of a closed, definition of, Orientation of a surface: downward, inw ard, outward, upward, Orthogonal basis for a vector space, – Orthogonal diagonalizability: criterion for, definition of, Orthogonal eigenvectors, – Orthogonal family of curves, , Orthogonal functions, Orthogonal matrix: constructing an, – definition of, Orthogonal projection of a vector onto a subspace, Orthogonal with respect to a weight function, Orthogonal series expansion, – Orthogonal set of functions, – Orthogonal surfaces at a point, Orthogonal trajectories, Orthogonal vectors, Orthogonally diagonalizable matrix, – Orthonormal basis: definition of, for R , for a vector space, Orthonormal set of functions, Orthonormal set of vectors, Oscillating chain, Osculating plane, Ötzi (the Iceman), – Output function, , Overdamped electrical circuit, Overdamped spring/mass system, – Overdamped system, , Overdetermined system of linear equations, Overtones, P Pacemaker, heart, , Parabolic partial differential equation, Parallel vectors: criterion for, definition of, Parallels, Parametric curve: closed, definition of, piecewise smooth, positive direction on, simple closed, smooth, , in space, Parametric equations for a line in space, Parametric form of Bessel equation: of order n, of order ν, in selfadjoint form, Parametric form of modified Bessel equation of order ν, Parent isotope, Paris Guns, – Parity, Parity check bits, Parity check code, Parity check equations, Parity check matrix, Parity error, Partial derivatives: nChain Rule for, – definition of, generalizations of, higherorder, mixed, with respect to x, with respect to y, secondorder, symbols for, thirdorder, tree diagrams for, Partial differential equation, linear second order: definition of, elliptic, , homogeneous, hyperbolic, , , linear, nonhomogeneous, parabolic, , , separation of variables, – solution of, Partial fractions, , Particular solution: of Bessel’s equation, – definition of, , of Legendre’s equation, – of a nonhomogeneous system of linear DEs, , , by undetermined coefficients, – by variation of parameters, – Partitioned matrix, Path independence: definition of, tests for, , Path of integration, Pauli, Wolfgang Ernst, Pauli spin matrices, PDE, Pendulum: ballistic, double, linear, nonlinear, – oscillating, physical, rotating, – simple, spring, springcoupled, of varying length, whirling, Percentage relative error, Perihelion, Period: of the complex exponential function, of the complex hyperbolic sine and cosine, , of the complex sine and cosine, Period of free vibrations, Periodic boundary conditions, , Periodic boundaryvalue problem, Periodic driving force, , Periodic extension, Periodic functions: definition of, , , , Laplace transform of, – Periodic solution of a plane autonomous system, Phase angle, Phase line, Phase plane, , , Phase portrait: for firstorder differential equations, for systems of two linear firstorder differential equations, , – for systems of two nonlinear firstorder differential equations, – Phaseplane method, Physical pendulum, Piecewisecontinuous function
كلمة سر فك الضغط : booksworld.net The Unzip Password : booksworld.net أتمنى أن تستفيدوا من محتوى الموضوع وأن ينال إعجابكم رابط من موقع عالم الكتب لتنزيل كتاب Advanced Engineering Mathematic 7ed رابط مباشر لتنزيل كتاب Advanced Engineering Mathematics 7ed

