← 学习库 OpenStax Calculus Vol 3 目录

Index

Calculus Volume 3Index

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Symbols $\delta$ ball 4.2 Limits and Continuity $\delta$ disk 4.2 Limits and Continuity A acceleration vector 3.4 Motion in Space angular coordinate 1.3 Polar Coordinates angular frequency 7.3 Applications arc-length function 3.3 Arc Length and Curvature arc-length parameterization 3.3 Arc Length and Curvature Archimedean spiral 1.3 Polar Coordinates B Bessel functions 7.4 Series Solutions of Differential Equations binormal vector 3.3 Arc Length and Curvature boundary conditions 7.1 Second-Order Linear Equations boundary point 4.2 Limits and Continuity boundary-value problem 7.1 Second-Order Linear Equations Brahe 3.4 Motion in Space C cardioid 1.3 Polar Coordinates chain rule 3.2 Calculus of Vector-Valued Functions chambered nautilus Introduction, 1.3 Polar Coordinates characteristic equation 7.1 Second-Order Linear Equations circulation 6.2 Line Integrals *cissoid of Diocles* 1.4 Area and Arc Length in Polar Coordinates Clairaut’s theorem 6.1 Vector Fields closed curve 6.2 Line Integrals, 6.3 Conservative Vector Fields closed set 4.2 Limits and Continuity Cobb-Douglas function 4.8 Lagrange Multipliers Cobb-Douglas production function 4.3 Partial Derivatives complementary equation 7.2 Nonhomogeneous Linear Equations complex conjugates 7.1 Second-Order Linear Equations complex number 7.1 Second-Order Linear Equations component functions 3.1 Vector-Valued Functions and Space Curves components 2.1 Vectors in the Plane conic section 1.5 Conic Sections connected region 6.3 Conservative Vector Fields connected set 4.2 Limits and Continuity conservative field 6.1 Vector Fields constant multiple rule 3.2 Calculus of Vector-Valued Functions constraints 4.8 Lagrange Multipliers contour map 4.1 Functions of Several Variables, 4.3 Partial Derivatives coordinate planes 2.2 Vectors in Three Dimensions critical point of a function of two variables 4.7 Maxima/Minima Problems cross product 2.4 The Cross Product *cross-partial property* 6.1 Vector Fields curl 6.5 Divergence and Curl curtate cycloid 1.1 Parametric Equations curvature 3.3 Arc Length and Curvature cusps 1.1 Parametric Equations cycloid 1.1 Parametric Equations cylinder 2.6 Quadric Surfaces cylindrical coordinate system 2.7 Cylindrical and Spherical Coordinates D definite integral of a vector-valued function 3.2 Calculus of Vector-Valued Functions derivative 3.2 Calculus of Vector-Valued Functions derivative of a vector-valued function 3.2 Calculus of Vector-Valued Functions determinant 2.4 The Cross Product differentiable 4.4 Tangent Planes and Linear Approximations direction angles 2.3 The Dot Product direction cosines 2.3 The Dot Product direction vector 2.5 Equations of Lines and Planes in Space *directional cosines* 4.6 Directional Derivatives and the Gradient directional derivative 4.6 Directional Derivatives and the Gradient directrix 1.5 Conic Sections discriminant 1.5 Conic Sections, 4.7 Maxima/Minima Problems divergence 6.5 Divergence and Curl divergence theorem 6.8 The Divergence Theorem domain 6.1 Vector Fields dot product 2.3 The Dot Product double integral 5.1 Double Integrals over Rectangular Regions double Riemann sum 5.1 Double Integrals over Rectangular Regions E Earth’s orbit 1.1 Parametric Equations eccentricity 1.5 Conic Sections electrical potential 4.6 Directional Derivatives and the Gradient Electrical power 4.4 Tangent Planes and Linear Approximations electrical resistance 4.4 Tangent Planes and Linear Approximations electrostatic fields 6.8 The Divergence Theorem ellipsoid 2.6 Quadric Surfaces Elliptic Cone 2.6 Quadric Surfaces elliptic paraboloid 2.6 Quadric Surfaces Elliptic Paraboloid 2.6 Quadric Surfaces *epitrochoid* 1.1 Parametric Equations equivalent vectors 2.1 Vectors in the Plane Ernest Rutherford 4.3 Partial Derivatives *error term* 4.4 Tangent Planes and Linear Approximations Euler’s formula 7.1 Second-Order Linear Equations expected values 5.2 Double Integrals over General Regions F Faraday’s law 6.7 Stokes’ Theorem *flow line* 6.1 Vector Fields flux 6.2 Line Integrals flux integral 6.6 Surface Integrals focal parameter 1.5 Conic Sections focus 1.5 Conic Sections force 2.1 Vectors in the Plane Fourier’s law of heat transfer 6.8 The Divergence Theorem Frenet frame of reference 3.3 Arc Length and Curvature Fubini’s theorem 5.1 Double Integrals over Rectangular Regions Fubini’s thereom 5.4 Triple Integrals function of two variables 4.1 Functions of Several Variables Fundamental Theorem for Line Integrals 6.8 The Divergence Theorem Fundamental Theorem for Line Integrals. 6.3 Conservative Vector Fields Fundamental Theorem of Calculus 6.8 The Divergence Theorem G Gauss’ law 6.8 The Divergence Theorem Gauss’s law for magnetism 6.5 Divergence and Curl general bounded region 5.4 Triple Integrals general form 1.5 Conic Sections general form of the equation of a plane 2.5 Equations of Lines and Planes in Space general solution to a differential equation 7.1 Second-Order Linear Equations generalized chain rule 4.5 The Chain Rule gradient 4.6 Directional Derivatives and the Gradient gradient field 6.1 Vector Fields graph of a function of two variables 4.1 Functions of Several Variables gravitational force 6.3 Conservative Vector Fields Green’s theorem 6.4 Green’s Theorem, 6.8 The Divergence Theorem grid curves 6.6 Surface Integrals H *harmonic* function 6.4 Green’s Theorem heat equation 4.3 Partial Derivatives heat flow 6.6 Surface Integrals helix 3.1 Vector-Valued Functions and Space Curves, 3.1 Vector-Valued Functions and Space Curves higher-order partial derivatives 4.3 Partial Derivatives homogeneous functions 4.5 The Chain Rule homogeneous linear equation 7.1 Second-Order Linear Equations Hooke’s law 7.3 Applications hurricanes 6.1 Vector Fields Hyperboloid of One Sheet 2.6 Quadric Surfaces Hyperboloid of Two Sheets 2.6 Quadric Surfaces hypocycloid 1.1 Parametric Equations I implicit differentiation 4.5 The Chain Rule improper double integral 5.2 Double Integrals over General Regions indefinite integral of a vector-valued function 3.2 Calculus of Vector-Valued Functions independent of path 6.3 Conservative Vector Fields independent random variables 5.2 Double Integrals over General Regions independent variables 4.5 The Chain Rule initial point 2.1 Vectors in the Plane, 3.1 Vector-Valued Functions and Space Curves initial-value problems 7.1 Second-Order Linear Equations interior point 4.2 Limits and Continuity intermediate variables 4.5 The Chain Rule inverse-square law 6.8 The Divergence Theorem iterated integral 5.1 Double Integrals over Rectangular Regions J Jacobian 5.7 Change of Variables in Multiple Integrals joint density function 5.2 Double Integrals over General Regions K Kepler 3.4 Motion in Space Kepler’s laws of planetary motion 3.4 Motion in Space L Lagrange multiplier 4.8 Lagrange Multipliers *Laplace operator* 6.5 Divergence and Curl Laplace’s equation 4.3 Partial Derivatives, 6.4 Green’s Theorem level curve of a function of two variables 4.1 Functions of Several Variables level surface of a function of three variables 4.1 Functions of Several Variables limaçon 1.3 Polar Coordinates limit of a function of two variables 4.2 Limits and Continuity limit of a vector-valued function 3.1 Vector-Valued Functions and Space Curves line integral 6.2 Line Integrals linear approximation 4.4 Tangent Planes and Linear Approximations linearly dependent 7.1 Second-Order Linear Equations linearly independent 7.1 Second-Order Linear Equations *local extremum* 4.7 Maxima/Minima Problems lunes of Alhazen 5.2 Double Integrals over General Regions M magnitude 2.1 Vectors in the Plane, 2.1 Vectors in the Plane major axis 1.5 Conic Sections mass flux 6.6 Surface Integrals mass of a wire 6.2 Line Integrals method of Lagrange multipliers 4.8 Lagrange Multipliers method of undetermined coefficients 7.2 Nonhomogeneous Linear Equations method of variation of parameters 7.2 Nonhomogeneous Linear Equations minor axis 1.5 Conic Sections mixed partial derivatives 4.3 Partial Derivatives N nappes 1.5 Conic Sections nonhomogeneous linear equation 7.1 Second-Order Linear Equations *normal* 2.3 The Dot Product normal component of acceleration 3.4 Motion in Space *normal form* of Green’s theorem 6.4 Green’s Theorem normal plane 3.3 Arc Length and Curvature normal vector 2.5 Equations of Lines and Planes in Space normalization 2.1 Vectors in the Plane O objective function 4.8 Lagrange Multipliers octants 2.2 Vectors in Three Dimensions one-to-one transformation 5.7 Change of Variables in Multiple Integrals open set 4.2 Limits and Continuity optimization problem 4.8 Lagrange Multipliers orientation 1.1 Parametric Equations orientation of a curve 6.2 Line Integrals orientation of a surface 6.6 Surface Integrals *orthogonal* 2.3 The Dot Product orthogonal vectors 2.3 The Dot Product osculating circle 3.3 Arc Length and Curvature *overdamped* 7.3 Applications P parallelepiped 2.4 The Cross Product parallelogram method 2.1 Vectors in the Plane parameter 1.1 Parametric Equations parameter domain 6.6 Surface Integrals parameter space 6.6 Surface Integrals parameterization of a curve 1.1 Parametric Equations parameterized surface 6.6 Surface Integrals parametric curve 1.1 Parametric Equations parametric equations 1.1 Parametric Equations parametric equations of a line 2.5 Equations of Lines and Planes in Space parametric surface 6.6 Surface Integrals partial derivative 4.3 Partial Derivatives partial differential equation 4.3 Partial Derivatives particular solution 7.2 Nonhomogeneous Linear Equations path independent 6.3 Conservative Vector Fields *perpendicular* 2.3 The Dot Product piecewise smooth curve 6.2 Line Integrals planar transformation 5.7 Change of Variables in Multiple Integrals plane curve 3.1 Vector-Valued Functions and Space Curves polar axis 1.3 Polar Coordinates polar coordinate system 1.3 Polar Coordinates polar equations 1.3 Polar Coordinates polar rectangle 5.3 Double Integrals in Polar Coordinates pole 1.3 Polar Coordinates potential function 6.1 Vector Fields power series 7.4 Series Solutions of Differential Equations principal unit normal vector 3.3 Arc Length and Curvature principal unit tangent vector 3.2 Calculus of Vector-Valued Functions product rule 3.2 Calculus of Vector-Valued Functions projectile motion 3.4 Motion in Space prolate cycloid 1.1 Parametric Equations Q Quadric surfaces 2.6 Quadric Surfaces R radial coordinate 1.3 Polar Coordinates radial field 6.1 Vector Fields radius of curvature 3.3 Arc Length and Curvature radius of gyration 5.6 Calculating Centers of Mass and Moments of Inertia region 4.2 Limits and Continuity regular parameterization 6.6 Surface Integrals reparameterization 3.1 Vector-Valued Functions and Space Curves *resolution of a vector into components* 2.3 The Dot Product *resonance* 7.3 Applications Reuleaux triangle 5.2 Double Integrals over General Regions right-hand rule 2.2 Vectors in Three Dimensions *RLC* series circuit 7.3 Applications rose 1.3 Polar Coordinates rotational field 6.1 Vector Fields rulings 2.6 Quadric Surfaces S saddle point 4.7 Maxima/Minima Problems scalar 2.1 Vectors in the Plane scalar equation of a plane 2.5 Equations of Lines and Planes in Space scalar line integral 6.2 Line Integrals scalar multiplication 2.1 Vectors in the Plane scalar projection 2.3 The Dot Product simple curve 6.3 Conservative Vector Fields simple harmonic motion 7.3 Applications simple pendulum 4.4 Tangent Planes and Linear Approximations simply connected region 6.3 Conservative Vector Fields skew lines 2.5 Equations of Lines and Planes in Space smooth 3.3 Arc Length and Curvature space curve 3.1 Vector-Valued Functions and Space Curves space-filling curves 1.1 Parametric Equations speed 2.1 Vectors in the Plane sphere 2.2 Vectors in Three Dimensions spherical coordinate system 2.7 Cylindrical and Spherical Coordinates spring-mass system 7.3 Applications standard equation of a sphere 2.2 Vectors in Three Dimensions standard form 1.5 Conic Sections *standard position* 3.1 Vector-Valued Functions and Space Curves standard unit vectors 2.1 Vectors in the Plane standard-position vector 2.1 Vectors in the Plane steady-state solution 7.3 Applications Stokes’ theorem 6.7 Stokes’ Theorem, 6.8 The Divergence Theorem stream function 6.4 Green’s Theorem sum and difference rules 3.2 Calculus of Vector-Valued Functions superposition principle 7.1 Second-Order Linear Equations surface 4.1 Functions of Several Variables surface area 6.6 Surface Integrals surface independent 6.7 Stokes’ Theorem surface integral 6.6 Surface Integrals surface integral of a scalar-valued function 6.6 Surface Integrals surface integral of a vector field 6.6 Surface Integrals symmetric equations of a line 2.5 Equations of Lines and Planes in Space symmetry 1.3 Polar Coordinates, 5.3 Double Integrals in Polar Coordinates T Tacoma Narrows Bridge 7.3 Applications tangent plane 4.4 Tangent Planes and Linear Approximations tangent vector 3.2 Calculus of Vector-Valued Functions tangential component of acceleration 3.4 Motion in Space *tangential form* of Green’s theorem 6.4 Green’s Theorem terminal point 2.1 Vectors in the Plane, 3.1 Vector-Valued Functions and Space Curves three-dimensional rectangular coordinate system 2.2 Vectors in Three Dimensions topographical map 4.1 Functions of Several Variables Torque 2.4 The Cross Product total differential 4.4 Tangent Planes and Linear Approximations traces 2.6 Quadric Surfaces transformation 5.7 Change of Variables in Multiple Integrals *transient solution* 7.3 Applications tree diagram 4.5 The Chain Rule triangle inequality 2.1 Vectors in the Plane triangle method 2.1 Vectors in the Plane triple integral 5.4 Triple Integrals triple integral in cylindrical coordinates 5.5 Triple Integrals in Cylindrical and Spherical Coordinates triple integral in spherical coordinates 5.5 Triple Integrals in Cylindrical and Spherical Coordinates triple scalar product 2.4 The Cross Product Type I 5.2 Double Integrals over General Regions Type II 5.2 Double Integrals over General Regions U unit vector 2.1 Vectors in the Plane unit vector field 6.1 Vector Fields V vector 2.1 Vectors in the Plane vector addition 2.1 Vectors in the Plane vector difference 2.1 Vectors in the Plane vector equation of a line 2.5 Equations of Lines and Planes in Space vector equation of a plane 2.5 Equations of Lines and Planes in Space vector field 6.1 Vector Fields vector line integral 6.2 Line Integrals vector parameterization 3.1 Vector-Valued Functions and Space Curves vector product 2.4 The Cross Product vector projection 2.3 The Dot Product vector sum 2.1 Vectors in the Plane vector-valued function 3.1 Vector-Valued Functions and Space Curves vector-valued functions 3.4 Motion in Space velocity vector 3.4 Motion in Space vertex 1.5 Conic Sections vertical trace 4.1 Functions of Several Variables W wave equation 4.3 Partial Derivatives William Thomson (Lord Kelvin) 4.3 Partial Derivatives witch of Agnesi 1.1 Parametric Equations work done by a vector field 6.2 Line Integrals work done by the force 2.3 The Dot Product Z zero vector 2.1 Vectors in the Plane

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