Ciro Santilli
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中国独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件 邓家贵、低端人口、西藏骚乱
Calculus
wiki
Mathematics
toc
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words:
6k
Well summarized as "the branch of mathematics that deals with
limits
".
Table of contents
6k
Mathematical analysis
link
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Calculus
10
Limit (mathematics)
link
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Calculus
32
Convergent series
link
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Limit
0
Continuous function
link
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Limit
0
Continuous problems are simpler than discrete ones
link
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Continuous function
44
Discrete
link
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Continuous function
10
Discretization
link
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Discrete
0
Infinity (
∞
)
link
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Limit
53
L'Hôpital's rule (limit of a ratio)
link
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Limit
0
Derivative
link
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Calculus
0
Chain rule
link
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Derivative
45
Multivariable chain rule
link
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Chain rule
0
Differentiable function
link
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Derivative
0
Smoothness
link
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Differentiable function
0
Infinitely differentiable function (
C
∞
)
link
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Differentiable function
0
Bump function
link
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Infinitely differentiable function
0
Flat top bump function
link
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Bump function
0
Maxima and minima
link
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Derivative
67
Lifegard problem
link
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Maxima and minima
0
Derivative test
link
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Maxima and minima
0
Saddle point
link
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Maxima and minima
0
Newton dot notation
link
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Derivative
0
Partial derivative
link
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Derivative
0
Partial derivative notation
link
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Partial derivative
0
Partial derivative symbol (
∂
)
link
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Partial derivative notation
64
Partial label partial derivative notation (
∂
x
F
,
∂
y
F
)
link
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Partial derivative notation
0
Partial index partial derivative notation (
∂
0
F
,
∂
1
F
)
link
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Partial derivative notation
68
Total derivative
link
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Derivative
68
Directional derivative
link
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Derivative
0
Integral
link
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Calculus
0
Area
link
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Integral
0
Volume
link
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Area
1
Riemann integral
link
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Integral
12
Lebesgue integral
link
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Integral
56
Lebesgue integral vs Riemann integral
link
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Lebesgue integral
169
Real world applications of the Lebesgue integral
link
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Lebesgue integral vs Riemann integral
50
Lebesgue measurable
link
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Lebesgue integral
0
Lebesgue integral of
L
p
is complete but Riemann isn't
link
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Lebesgue integral
52
Riesz-Fischer theorem
link
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Lebesgue integral of
L
p
is complete but Riemann isn't
37
L
p
is complete
link
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Riesz-Fischer theorem
1
Fourier basis is complete for
L
2
link
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Riesz-Fischer theorem
30
L
p
norm sequence convergence does not imply pointwise convergence
link
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Fourier basis is complete for
L
2
40
Carleson's theorem
link
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Fourier basis is complete for
L
2
99
Lp space (
L
p
)
link
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Lebesgue integral of
L
p
is complete but Riemann isn't
16
L
1
link
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Lp space
0
L
2
link
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Lp space
80
Plancherel theorem
link
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L
2
75
The Fourier transform is a bijection in
L
2
link
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Plancherel theorem
53
Every Riemann integrable function is Lebesgue integrable
link
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Plancherel theorem
7
Measure theory
link
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Calculus
46
Fourier series
link
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Calculus
90
Applications of the Fourier series
link
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Fourier series
0
Solving partial differential equations with the Fourier series
link
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Applications of the Fourier series
30
Discrete Fourier transform (DFT)
link
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Fourier series
0
Fourier transform
link
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Fourier series
93
Multidimensional Fourier transform
link
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Fourier transform
36
Fourier inversion theorem
link
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Fourier transform
20
Laplace transform
link
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Fourier transform
41
History of the Fourier series
link
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Fourier series
10
Topology
link
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Calculus
89
Covering space
link
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Topology
63
Double cover
link
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Covering space
0
Neighbourhood (mathematics)
link
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Topology
5
Topological space
link
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Topology
0
Manifold
link
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Topology
94
Atlas (topology)
link
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Manifold
12
Coordinate chart
link
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Atlas
0
Covariant derivative
link
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Manifold
20
Differentiable manifold
link
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Manifold
25
Tangent space
link
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Manifold
93
Tangent vector to a manifold
link
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Tangent space
5
One-form
link
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Manifold
23
Metric (mathematics,
d
(
x
,
y
)
)
link
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Topology
58
Metric space
link
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Metric
3
Metric space vs normed vector space vs inner product space
link
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Metric space
47
Complete metric space
link
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Metric space
37
Normed vector space
link
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Metric space
0
Inner product space
link
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Normed vector space
9
Inner product
link
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Inner product space
12
Norm (mathematics,
∣
x
∣
)
link
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Metric space
44
Norm induced by an inner product
link
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Norm
11
Metric induced by a norm
link
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Norm
19
Pseudometric space
link
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Metric space
14
Compact space
link
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Topology
0
Dense set
link
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Topology
0
Connected space
link
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Topology
0
Connected component
link
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Connected space
26
Simply connected space
link
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Connected space
0
Loop (topology)
link
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Simply connected space
0
Homotopy
link
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Topology
0
Generalized Poincaré conjecture
link
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Homotopy
255
Exotic sphere
link
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Generalized Poincaré conjecture
0
Poincaré conjecture
link
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Generalized Poincaré conjecture
0
Classification of closed surfaces
link
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Generalized Poincaré conjecture
158
Torus
link
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Classification of closed surfaces
0
Möbius strip
link
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Classification of closed surfaces
0
Klein bottle
link
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Classification of closed surfaces
9
Real coordinate space (
R
n
)
link
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Topology
0
Real line (
R
1
)
link
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Real coordinate space
0
Real plane (
R
2
)
link
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Real coordinate space
0
Real coordinate space of dimension three (
R
3
)
link
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Real coordinate space
0
Real coordinate space of dimension four (
R
4
, 4D)
link
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Real coordinate space
3
Visualizing 4D
link
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Real coordinate space of dimension four
15
Dimension
link
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Real coordinate space
0
Infinite dimensional
link
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Dimension
0
Finite dimensional
link
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Infinite dimensional
0
Complex coordinate space (
C
n
)
link
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Real coordinate space
0
Complex dot product
link
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Complex coordinate space
87
Euclidean space
link
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Real coordinate space
10
Euclidean metric signature matrix
link
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Euclidean space
2
Cartesian coordinate system
link
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Euclidean space
0
Polar coordinate system
link
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Euclidean space
0
Spherical coordinate system
link
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Polar coordinate system
0
Pythagorean theorem
link
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Euclidean space
0
Non-Euclidean geometry
link
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Euclidean space
0
Elliptic geometry
link
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Non-Euclidean geometry
0
Model of elliptic geometry
link
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Elliptic geometry
0
Projective elliptic geometry
link
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Model of elliptic geometry
20
Hyperbolic gemoetry
link
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Non-Euclidean geometry
0
Hyperbolic functions
link
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Hyperbolic gemoetry
0
Hyperbolic sine
link
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Hyperbolic functions
0
Hyperbolic cossine
link
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Hyperbolic functions
0
Distribution (mathematics)
link
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Calculus
116
Dirac delta function
link
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Distribution
41
Green's function
link
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Dirac delta function
0
Heaviside step function
link
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Dirac delta function
0
Complex analysis
link
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Calculus
14
Complex analysis bibliography
link
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Complex analysis
0
Complex Analysis by Juan Carlos Ponce Campuzano
link
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Complex analysis bibliography
0
Holomorphic function
link
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Complex analysis
62
Analytic continuation
link
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Complex analysis
38
Visualizing the Riemann hypothesis and analytic continuation by 3Blue1Brown (2016)
link
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Analytic continuation
13
Identity theorem
link
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Analytic continuation
71
Riemann zeta function
link
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Identity theorem
0
Riemann hypothesis
link
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Riemann zeta function
15
Hilbert space
link
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Calculus
13
Complete basis
link
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Hilbert space
44
Differential equation
link
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Calculus
0
Euler number (
e
)
link
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Differential equation
0
Natural logarithm (
l
n
(
n
)
,
l
o
g
e
(
n
)
)
link
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Euler number
0
Logarithmic integral function (
l
i
(
x
)
=
∫
0
x
l
n
t
d
t
, Logarithm integral)
link
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Natural logarithm
4
Euler-Mascheroni constant
link
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Natural logarithm
1
Linear differential equation
link
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Differential equation
142
Holonomic function
link
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Linear differential equation
0
Order of a differential equation
link
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Differential equation
7
Ordinary differential equation (ODE)
link
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Differential equation
0
Existence and uniqueness of solutions of ordinary differential equations
link
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Ordinary differential equation
0
Peano existence theorem
link
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Existence and uniqueness of solutions of ordinary differential equations
0
Picard-Lindelöf theorem
link
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Existence and uniqueness of solutions of ordinary differential equations
0
System of ordinary differential equations
link
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Ordinary differential equation
0
System of linear ordinary differential equations
link
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System of ordinary differential equations
0
Partial differential equation (PDE)
link
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Differential equation
0
Analytical method to solve a partial differential equation
link
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Partial differential equation
0
Separation of variables
link
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Analytical method to solve a partial differential equation
30
Numerical method to solve a partial differential equation
link
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Partial differential equation
13
Variational formulation of a partial differential equation
link
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Numerical method to solve a partial differential equation
14
Weak solution
link
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Variational formulation of a partial differential equation
0
Finite element method
link
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Numerical method to solve a partial differential equation
13
Important partial differential equation
link
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Partial differential equation
6
Laplace's equation
link
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Important partial differential equation
69
Legendre polynomials
link
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Laplace's equation
15
Poisson's equation
link
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Laplace's equation
9
Uniqueness theorem for Poisson's equation
link
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Poisson's equation
0
Harmonic function
link
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Laplace's equation
4
Spherical harmonic
link
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Harmonic function
14
Heat equation
link
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Important partial differential equation
109
Heat equation solution with Fourier series
link
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Heat equation
1
Wave equation
link
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Important partial differential equation
37
Wave equation solver
link
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Wave equation
64
Wave equation solution with Fourier series
link
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Wave equation
5
The wave equation can be seen as infinitely many infinitesimal coupled oscillators
link
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Wave equation
29
Lossy 1D Wave Equation
link
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Wave equation
0
Wave
link
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Wave equation
0
Polarization
link
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Wave equation
7
String polarization
link
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Polarization
23
Diffraction
link
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Wave equation
0
Huygens-Fresnel principle
link
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Diffraction
0
Kirchhoff's diffraction formula
link
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Huygens-Fresnel principle
3
Fraunhofer diffraction
link
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Kirchhoff's diffraction formula
17
Fresnel diffraction
link
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Kirchhoff's diffraction formula
16
Refraction
link
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Wave equation
0
Resonance
link
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Wave equation
183
Wave interference
link
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Wave equation
0
Interference pattern
link
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Wave interference
19
2D wave equation on a circular domain
link
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Wave equation
0
Bessel function
link
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2D wave equation on a circular domain
45
Fourier-Bessel series
link
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Bessel function
8
Helmholtz equation
link
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Wave equation
3
Existence and uniqueness of solutions of partial differential equations
link
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Partial differential equation
79
Partial differential equation solver
link
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Partial differential equation
0
FreeFem
link
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Partial differential equation solver
543
FreeFem examples
link
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FreeFem
0
heat-dirichlet.1d.freefem
link
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FreeFem examples
3
heat-dirichlet-2d-freefem
link
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FreeFem examples
4
FEniCS Project
link
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Partial differential equation solver
153
Hans Petter Langtangen
link
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FEniCS Project
64
System of partial differential equations
link
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Partial differential equation
37
Classification of second order partial differential equations into elliptic, parabolic and hyperbolic
link
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Partial differential equation
20
Elliptic partial differential equation
link
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Classification of second order partial differential equations into elliptic, parabolic and hyperbolic
0
Parabolic partial differential equation
link
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Classification of second order partial differential equations into elliptic, parabolic and hyperbolic
0
Hyperbolic partial differential equation
link
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Classification of second order partial differential equations into elliptic, parabolic and hyperbolic
0
Which boundary conditions lead to existence and uniqueness of a second order PDE
link
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Classification of second order partial differential equations into elliptic, parabolic and hyperbolic
27
Phase space
link
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Differential equation
9
Boundary condition
link
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Differential equation
0
Initial condition
link
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Boundary condition
22
Boundary value problem
link
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Boundary condition
0
Dirichlet boundary condition
link
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Boundary condition
13
Neumann boundary condition
link
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Boundary condition
16
Cauchy boundary condition
link
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Neumann boundary condition
50
Robin boundary condition
link
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Neumann boundary condition
81
Open boundary condition
link
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Neumann boundary condition
89
Mixed boundary condition
link
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Neumann boundary condition
7
Time dependent boundary condition
link
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Boundary condition
30
Control theory
link
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Differential equation
70
Control engineering
link
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Control theory
0
Control system
link
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Control theory
0
Feedback loop (Control loop)
link
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Control theory
0
Series (mathematics)
link
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Calculus
0
Power series
link
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Series
0
Analytic function
link
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Power series
0
Sine and cossine
link
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Analytic function
0
Sinusoidal
link
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Sine and cossine
36
Sine
link
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Sine and cossine
0
Cosine
link
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Sine and cossine
0
Radius of convergence
link
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Power series
0
Taylor series
link
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Power series
0
Gradient, Divergence, Curl, and Laplacian
link
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Calculus
0
Curl (mathematics,
∇
×
)
link
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Gradient, Divergence, Curl, and Laplacian
11
Nabla symbol (
∇
)
link
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Gradient, Divergence, Curl, and Laplacian
64
Del
link
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Nabla symbol
33
Divergence (
∇
⋅
,
d
i
v
(
)
)
link
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Gradient, Divergence, Curl, and Laplacian
67
Gradient (
∇
)
link
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Gradient, Divergence, Curl, and Laplacian
89
Laplace operator (
Δ
,
∇
2
)
link
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Gradient, Divergence, Curl, and Laplacian
17
D'alembert operator (
□
)
link
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Laplace operator
12
Infinitesimal
link
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Calculus
10
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