Function
Summary
A function from a set to a set assigns to each element of exactly one element of .
What this node needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
The writing levels say how complete the text of a node is. They do not measure its truth.
What depends on this
274 nodes use this node, directly or through other nodes.
- Exterior derivative 004FRCXH6M
- Picard–Lindelöf theorem in integral form 00BT70ND50
- Non-uniqueness for a non-Lipschitz equation 00K7ASZ1PR
- Saddle point 00N3T18QNA
- Change of variables in multiple integrals 00N5FHP1CV
- Arc length parametrisation 00R1JDDV5X
- Exponential growth and decay 00SVP6W3CB
- Picard operator 00WAVB68F9
- Lotka–Volterra equations 00Y5QZ82AA
- Volume of a ball in R^n 00YH28R457
- Additivity of line integrals under concatenation 00ZEBSMNNV
- Differentiable function of several variables 0135XZZQ8M
- Strict differentiability 0146MBQNNE
- Integral equation form of an initial value problem 015KK993C5
- Vector-valued function 018GTRS7A4
- Maximal solution 019VSXSFMQ
- Periodic orbit 01DSNP0B4R
- Function with unequal mixed partial derivatives 01NN8NY497
- Integrating factor 01THH3Y3YP
- Symmetry of second derivatives 01V9FPBBVK
- Uniqueness of solutions for Lipschitz vector fields 025PKW8AMR
- Flow of a vector field 02903SSA48
- Vector field 0299VCW1TH
- Mean value inequality 02CYB184RC
- Newton's law of cooling 02HB5F40VR
- Divergence 02NSMQVQWK
- Line integral of a scalar field 02QJVFCNYD
- Higher partial derivatives 02RSXVM1ZN
- Reduction of order 02SRXDAM3X
- Tangent plane to a graph 035V802J58
- Chain rule for Jacobian matrices 03GGQEAG9S
- Mean value theorem in several variables 03HGK7EW6R
- Jacobian determinant 03W6Q1MFR5
- C^1 vector fields satisfy the Picard–Lindelöf hypotheses 03Z9V0Y78A
- Closed curve 045YFKRW0P
- Jacobian matrix 047NDTEPCV
- Lagrange multiplier with one constraint 04A2XEX4D4
- Local maximum and minimum 04CPG9K1C4
- Lyapunov function 04P7B5XC22
- Solution of an ordinary differential equation 04SW7WECS8
- Lipschitz condition 055VVSN00V
- Parametrised surface 05788J51WZ
- Partial derivative 05AXG3QRKR
- Poincaré lemma for one-forms on convex sets 05MC3HND79
- Conservative vector field 05R9NF2J49
- Laplacian as a sum of second partial derivatives 05RCT1522R
- Phase plane 05VDGH129F
- Jacobian of spherical coordinates 05WKRC7HWT
- Laplace transform 05XT5AVJBK
- Asymptotic stability 05Y1JAM3Y5
- LaSalle's invariance principle 0659J5X7B5
- Tonelli's theorem 067SYD2J4B
- Hessian matrix 0693Y2METT
- Triple integral 0698M7C7AX
- Solution formula for linear first-order equations 06B9W45XV0
- Fréchet derivative 06EH97V2A7
- Regular curve 06JMR2XWXW
- Directional derivative 06KWGHDN2J
- Simply connected domain 075C629XTH
- Initial value problem 075VBY4K4X
- Autonomous system 07BNRFQ0PJ
- Convex function on R^n 07GR3TNW4H
- Phase line 081QSEAGEY
- Moment of inertia 08ANASGBXV
- Power series solution 08RT9GDDPQ
- Differentiable on an open set 08S7FDRS5Z
- Explicit and implicit differential equations 08WWTN738R
- An iterate of the Picard operator is a contraction 08XDXP86XE
- Eigenvalue method for linear systems 08ZWFDJP3H
- Lyapunov stability 092S6VBECQ
- Peano existence theorem 098YP831QY
- Heaviside step function 09C4JP7Y0M
- Area of a region as a line integral 09CBQB6V67
- Partial derivative 09EGC6F8PT
- Order of a differential equation 09M2RDB61G
- Liouville's formula 09PS3S0EF6
- Linearisation at an equilibrium 09ZWYRQ41J
- Higher partial derivatives 09ZXGX55DM
- Linear equation with constant coefficients 0A6PGTTP2A
- Derivative gives the directional derivatives 0A6PMR20N4
- System of linear differential equations 0A6QZ367GX
- Chain rule for a composition with a curve 0A8TJ0VHC7
- Gradient 0ABK9V9Y64
- Stokes' theorem 0AKRKVHW94
- Differentiation under the integral sign 0AR06W1E1B
- Curl-free vector field on a convex set is conservative 0B22P010D6
- Level set 0B2RZ0778N
- Strict differentiability 0B6QWX3086
- Solutions for complex conjugate roots 0BEZX8F2XW
- Global existence for globally Lipschitz vector fields 0BFD3A6CRH
- Path independence of line integrals 0BFN21TF5F
- Limit along different paths 0BJ6H85DRQ
- Tangent plane and normal vector of a surface 0BJDQ2HBH1
- Trajectory 0BVT6VSB3S
- Implicit function theorem 0BXBADR94C
- Having a gradient 0BXE0S1XER
- Zero derivative on a connected open set implies constant 0BYZTFM0DJ
- Separately continuous but not continuous function 0C0KPAKK9Y
- Rectifiable curve 0C28RT5BG7
- Hamiltonian system 0C2AKPDCD9
- Hyperbolic equilibrium point 0C5PREPZWG
- Logistic equation 0CC4VC7KR3
- Work done by a force field 0CDZ684TCD
- Improper multiple integral 0CWK2NFSEW
- Integrating factor for a non-exact equation 0CX86CR8JV
- Singular solution 0CZA0NCFWP
- Closed curve 0D032NSZKY
- Tangent vector of a curve 0D98771SM0
- Harmonic function 0DEB0JMN0W
- Surface integral 0DQ8ERJZNS
- Laplacian 0E0B6RA8K0
- Riccati equation 0E1ZZBHZ3Z
- Blow-up in finite time 0E4GXX7SJP
- Chain rule in several variables 0EAAS2EHDR
- Exact equation 0EC7AGJ0PX
- Limit cycle 0EERDDPSVT
- Orientable surface 0EKZW08FQ5
- Constrained optimisation 0EPW94MJ1P
- Homogeneous linear equation 0EQZSAB9EC
- Poincaré–Bendixson theorem 0EW1X61ZT1
- Iterated derivative 0EY05Z9RPN
- Closed and exact forms 0F1AVGX26N
- Superposition principle 0F2VBPXNP9
- Iterated derivative 0F32S73FJN
- Derivative vanishes at a local extremum 0F405477F8
- Divergence of a curl is zero 0F56CMMC5P
- Total derivative 0FNKFT8H6E
- Scalar potential 0FP4BVDAAQ
- Reversing a path changes the sign of a line integral 0FSCXYG856
- Continuous dependence on initial data 0G3DBXRRQJ
- Cylindrical coordinates 0G4MFRQSGN
- Equilibrium point 0G4X36AE0X
- Derivative of the inverse function 0G65751VSW
- Parametrised curve 0G7WM8DX4P
- Curl 0GDNHS9J2X
- General solution of an inhomogeneous linear equation 0GHWEH6H15
- Function for which the iterated integrals differ 0GJZE2E4RX
- Solution space of a homogeneous linear equation has dimension n 0GK68PZ6KH
- Curl-free field that is not conservative 0GRM3BS0DD
- Triple integral 0GTBGMZXV8
- Cavalieri's principle 0GTZ2F3PQY
- Moment of inertia 0GVMR0C3S6
- Second derivative test in several variables 0GYDV9FE98
- Divergence theorem on a rectangle in the plane 0GZ3D8F921
- Fundamental system of solutions 0H4KNNCHPY
- Line integral of a vector field 0H5MR9B6GT
- Changing the order of integration 0H60H1Q0SX
- Del operator 0H6DP8CHND
- Scalar potential 0H7C3T1GJY
- Rectifiable curve 0HATW2VWAZ
- Differentiable function of several variables 0HHHDCXZV4
- Solutions for distinct real roots 0HJ0HDA6W7
- Centre of mass 0HNK6KT05K
- Generalised Stokes theorem 0HPHKCGEQ0
- Green's theorem 0HR3N02317
- Solutions for repeated roots 0HRVY67CNV
- Lyapunov's stability theorem 0J6A752DTZ
- Picard–Lindelöf hypotheses 0J7HF2PF1H
- Taylor's theorem in several variables 0J8T4K4YTE
- Limit of a function of several variables 0J8Y1NCY0K
- Euler method 0JARTXX4XP
- Vector calculus identities 0JC5X4HWR2
- Continuity in R^n 0JEJATBVD7
- Parametrised curve 0JF1XXGWB4
- Underdamped 0JJ6GDDE7Z
- Convolution theorem for the Laplace transform 0JNMJEDD93
- Function of several variables 0JPCHTXWG0
- Inverse Laplace transform 0JRW4X1MDC
- Estimate for approximate solutions 0JTPMCCZT2
- Saddle point 0JW6MDHAZD
- Divergence theorem 0JX86PSSA9
- Laplace transform of a derivative 0K090GVHVN
- Solving initial value problems with the Laplace transform 0K3HFZJK5Q
- Homogeneous first-order equation 0K4ZWTFSV5
- Inverse function theorem 0K9HSJFCMJ
- Dirac delta function 0KPHENZ5S7
- Jordan measure 0KTGJW1ZTH
- Continuous partial derivatives imply differentiability 0KXSK8TEEB
- Diffeomorphism 0KZZ70ZHXP
- Convex function on R^n 0M1GJSWZDA
- Curl of a gradient is zero 0M2JRW1J0N
- Line integral of a scalar field 0M50E4WYWJ
- Wronskian test for linear independence of solutions 0MHE4B1QCQ
- Centre of mass 0MPZGAZ2GK
- Fundamental matrix 0MQ24RBG93
- Test for exactness 0MSCQNFTM8
- One-form 0MTENFBW3Q
- Divergence 0MWV6ZTK6S
- Vector field 0N67NBKQ5T
- Classification of equilibria of planar linear systems 0N7ATVF2X8
- Implicit function theorem for a surjective derivative 0NE2W2XPQJ
- Curl 0NF6GQNXMY
- Double integral 0NKBMFC18R
- Schwarz's theorem for C^2 functions 0NNQY8WCW6
- Derivative of a map into R^n by components 0NS0X75RS1
- Gradient 0NS2QYVC4Y
- Second-order Taylor expansion 0P30YYZN85
- Iterated integral 0P4WX7Y502
- Picard–Lindelöf theorem 0P6KRD5B7A
- Ordinary differential equation 0P97V20RW7
- Linear differential equation of order n 0PB7K8M7FG
- Multi-index notation 0PJXBR6QA3
- Conservative vector field 0PKG97PX9Y
- Arc length parametrisation 0Q4CJ5NAT1
- Contour line 0QD83RAN8G
- Characteristic equation 0QDXMG46QW
- Differential form 0QHTX7WQEY
- Implicit differentiation 0QKA345AW1
- Fubini's theorem 0R0T1VWH5X
- Picard iteration 0RJ5NHWYTP
- Polar coordinates 0RJZV05MJA
- Slope field 0RKQQQACY7
- Damped harmonic oscillator 0RNXVVTJTJ
- Spherical coordinates 0RW8KPMXF6
- Wedge product of forms 0S166D363M
- Variation of constants formula for linear systems 0S1KG0XE40
- Hartman–Grobman theorem 0S8WX8A4V9
- Continuity in R^n 0S9EK5MQPE
- Hessian matrix 0SCSQWXRA4
- Gradient theorem 0SD237FEJD
- Product rule in several variables 0SF85PY0QN
- Pendulum equation 0SHPXM2HWH
- Stability of linear systems via eigenvalues 0SKVEMXJWF
- General solution and particular solution 0SKYFQAFYD
- First integral 0SS1P1YC9A
- C^1 functions are strictly differentiable 0STPPDXGME
- Phase portrait 0T3GK0XCBC
- Clairaut's equation 0T6D4PE51C
- Integration in polar coordinates 0T89W1QZ9K
- C^k function characterised by continuous derivatives 0TCBZMEYGN
- Reduction of a higher-order equation to a first-order system 0TH9CPW3VS
- Bounded derivative on a convex set implies Lipschitz 0TKG7T3K0E
- Partial derivatives do not imply differentiability 0TNZC55X3J
- Integration over a non-rectangular region 0TXCQ9CST1
- Separable equation 0V4E623THY
- Regular curve 0V7090SSPC
- Volume of a box 0VEKNG02W0
- Abel's identity 0VGWKX2JHB
- Homogeneous linear system with constant coefficients 0VJF99CZ0Z
- Lagrange multipliers 0VKKP8X6Q6
- Limit of a function of several variables 0VMG8TA8VF
- Gradient is orthogonal to level sets 0VXYV3NQQ1
- Linear approximation 0W276SSSCG
- Line integral as an integral over the parameter interval 0W3W1VYWBP
- Harmonic function 0W5NJQ8MKY
- Time translation of solutions of an autonomous system 0WA7ZR95V4
- Double integral 0WAR4F23B4
- Cauchy–Euler equation 0WDNRBXX7K
- Local maximum and minimum 0WFBH1Q3WC
- Volume of a ball in R^3 0WMDV48VSN
- Surface area 0WQE3G7B88
- Nullcline 0WW060JR6P
- Iterated integral 0WZCHE1ZF9
- The exterior derivative squares to zero 0X308R2DBE
- Forced oscillation and resonance 0X4NT20S3G
- Laplacian 0XQ2ZVN1PZ
- Method of undetermined coefficients 0XRB469Z32
- Level set 0Y5Q8Q9WJ7
- Variation of parameters 0Y6TH5PQVS
- Directional derivative 0Y7PVW4Q44
- Matrix exponential as the solution of a linear system 0YC8JT513J
- Jacobian matrix 0YF0VXKXGB
- Harmonic oscillator 0YG0ZJPTWG
- Flux through a surface 0YPRY7T4PK
- Line integral of a vector field 0YS8RX87F4
- Homotopy invariance of line integrals of closed forms 0YVVN6R715
- Tangent plane to a graph 0YXEHVA93R
- Diffeomorphism 0Z1Y7JHGBR
- Linear first-order equation 0Z3YKRQZ48
- Local homeomorphism from the inverse function theorem 0Z8CSYVHDJ
- Bernoulli equation 0ZB84QCDKR
- Gradient points in the direction of steepest ascent 0ZC78099PA
- Jacobian determinant 0ZCSMYHTBP
- Tangent vector of a curve 0ZCZK72B45
Sources
- Web https://en.wikipedia.org/wiki/Function_(mathematics), lead section
What links here
Used by
- Vector-valued function 018GTRS7A4
- Lipschitz condition 055VVSN00V
- Laplace transform 05XT5AVJBK
- Function of several variables 0JPCHTXWG0
- Ordinary differential equation 0P97V20RW7
Definitions
- Function 0XHDTE5YMZ