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Calculus
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Mathematics
Area of mathematics
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Words: 7k
Articles: 248
Well summarized as "the branch of mathematics that deals with
limits
".
Table of contents
7k
248
Mathematical analysis
Calculus
10
Limit
(mathematics)
Calculus
139
7
Convergent series
Limit
Continuous function
Limit
54
3
Continuous problems are simpler than discrete ones
Continuous function
44
Discrete
Continuous function
10
1
Discretization
Discrete
Infinity
(
∞
)
Limit
53
L'Hôpital's rule
(limit of a ratio)
Limit
Derivative
Calculus
339
19
Chain rule
Derivative
46
1
Multivariable chain rule
Chain rule
Differentiable function
Derivative
4
Smoothness
Differentiable function
Infinitely differentiable function
(
C
∞
)
Differentiable function
2
Bump function
Infinitely differentiable function
1
Flat top bump function
Bump function
Maxima and minima
Derivative
67
3
Lifegard problem
Maxima and minima
Derivative test
Maxima and minima
Saddle point
Maxima and minima
Newton dot notation
Derivative
Partial derivative
Derivative
132
4
Partial derivative notation
Partial derivative
132
3
Partial derivative symbol
(
∂
)
Partial derivative notation
64
Partial label partial derivative notation
(
∂
x
F
,
∂
y
F
)
Partial derivative notation
Partial index partial derivative notation
(
∂
0
F
,
∂
1
F
)
Partial derivative notation
68
Total derivative
Derivative
68
Directional derivative
Derivative
Integral
Calculus
778
19
Area
Integral
1
1
Volume
Area
1
Riemann integral
Integral
12
Lebesgue integral
Integral
765
15
Lebesgue integral vs Riemann integral
Lebesgue integral
219
1
Real world applications of the Lebesgue integral
Lebesgue integral vs Riemann integral
50
Lebesgue measurable
Lebesgue integral
Lebesgue integral of
L
p
is complete but Riemann isn't
Lebesgue integral
490
11
Riesz-Fischer theorem
Lebesgue integral of
L
p
is complete but Riemann isn't
207
4
L
p
is complete
Riesz-Fischer theorem
1
Fourier basis is complete for
L
2
Riesz-Fischer theorem
169
2
L
p
norm sequence convergence does not imply pointwise convergence
Fourier basis is complete for
L
2
40
Carleson's theorem
Fourier basis is complete for
L
2
99
Lp space
(
L
p
)
Lebesgue integral of
L
p
is complete but Riemann isn't
231
5
L
1
Lp space
L
2
Lp space
215
3
Plancherel theorem
L
2
135
2
The Fourier transform is a bijection in
L
2
Plancherel theorem
53
Every Riemann integrable function is Lebesgue integrable
Plancherel theorem
7
Measure theory
Calculus
46
Fourier series
Calculus
834
11
Applications of the Fourier series
Fourier series
30
1
Solving partial differential equations with the Fourier series
Applications of the Fourier series
30
Discrete Fourier transform
(DFT)
Fourier series
524
3
Discrete Fourier transform of a real signal
Discrete Fourier transform
145
Normalized DFT
Discrete Fourier transform
72
Fast Fourier transform
Discrete Fourier transform
6
Fourier transform
Fourier series
189
3
Multidimensional Fourier transform
Fourier transform
36
Fourier inversion theorem
Fourier transform
20
Laplace transform
Fourier transform
41
History of the Fourier series
Fourier series
10
Topology
Calculus
1k
64
Covering space
Topology
63
1
Double cover
Covering space
Neighbourhood
(mathematics)
Topology
5
Topological space
Topology
Manifold
Topology
272
7
Atlas
(topology)
Manifold
12
1
Coordinate chart
Atlas
Covariant derivative
Manifold
20
Differentiable manifold
Manifold
25
Tangent space
Manifold
98
1
Tangent vector to a manifold
Tangent space
5
One-form
Manifold
23
Metric
(mathematics,
d
(
x
,
y
)
)
Topology
254
10
Metric space
Metric
196
9
Metric space vs normed vector space vs inner product space
Metric space
47
Complete metric space
Metric space
37
Normed vector space
Metric space
21
2
Inner product space
Normed vector space
21
1
Inner product
Inner product space
12
Norm
(mathematics,
∣
x
∣
)
Metric space
74
2
Norm induced by an inner product
Norm
11
Metric induced by a norm
Norm
19
Pseudometric space
Metric space
14
Compact space
Topology
Dense set
Topology
Connected space
Topology
26
3
Connected component
Connected space
26
Simply connected space
Connected space
1
Loop
(topology)
Simply connected space
Homotopy
Topology
380
7
Generalized Poincaré conjecture
Homotopy
380
6
Exotic sphere
Generalized Poincaré conjecture
Poincaré conjecture
Generalized Poincaré conjecture
Classification of closed surfaces
Generalized Poincaré conjecture
167
3
Torus
Classification of closed surfaces
Möbius strip
Classification of closed surfaces
Klein bottle
Classification of closed surfaces
9
Real coordinate space
(
R
n
)
Topology
212
26
Real line
(
R
1
)
Real coordinate space
Real plane
(
R
2
)
Real coordinate space
Real coordinate space of dimension three
(
R
3
)
Real coordinate space
Real coordinate space of dimension four
(
R
4
, 4D)
Real coordinate space
18
1
Visualizing 4D
Real coordinate space of dimension four
15
Dimension
Real coordinate space
2
Infinite dimensional
Dimension
1
Finite dimensional
Infinite dimensional
Complex coordinate space
(
C
n
)
Real coordinate space
162
3
Complex coordinate space of dimension 2
(
C
2
)
Complex coordinate space
Complex dot product
Complex coordinate space
162
1
Norm induced by the complex dot product
Complex dot product
52
Euclidean space
Real coordinate space
32
13
Euclidean metric signature matrix
Euclidean space
2
Cartesian coordinate system
Euclidean space
Polar coordinate system
Euclidean space
1
Spherical coordinate system
Polar coordinate system
Pythagorean theorem
Euclidean space
Non-Euclidean geometry
Euclidean space
20
7
Elliptic geometry
Non-Euclidean geometry
20
2
Model of elliptic geometry
Elliptic geometry
20
1
Projective elliptic geometry
Model of elliptic geometry
20
Hyperbolic gemoetry
Non-Euclidean geometry
3
Hyperbolic functions
Hyperbolic gemoetry
2
Hyperbolic sine
Hyperbolic functions
Hyperbolic cossine
Hyperbolic functions
Distribution
(mathematics)
Calculus
157
4
Dirac delta function
Distribution
41
2
Green's function
Dirac delta function
Heaviside step function
Dirac delta function
Normal distribution
Distribution
Complex analysis
Calculus
221
8
Complex analysis bibliography
Complex analysis
1
Complex Analysis by Juan Carlos Ponce Campuzano
Complex analysis bibliography
Holomorphic function
Complex analysis
62
Analytic continuation
Complex analysis
145
4
Visualizing the Riemann hypothesis and analytic continuation by 3Blue1Brown (2016)
Analytic continuation
13
Identity theorem
Analytic continuation
94
2
Riemann zeta function
Identity theorem
23
1
Riemann hypothesis
Riemann zeta function
23
Hilbert space
Calculus
57
1
Complete basis
Hilbert space
44
Differential equation
Calculus
2k
86
Euler number
(
e
)
Differential equation
5
3
Natural logarithm
(
l
n
(
n
)
,
l
o
g
e
(
n
)
)
Euler number
5
2
Logarithmic integral function
(
l
i
(
x
)
=
∫
0
x
l
n
t
d
t
, Logarithm integral)
Natural logarithm
4
Euler-Mascheroni constant
Natural logarithm
1
Linear differential equation
Differential equation
142
1
Holonomic function
Linear differential equation
Order of a differential equation
Differential equation
7
Ordinary differential equation
(ODE)
Differential equation
5
Existence and uniqueness of solutions of ordinary differential equations
Ordinary differential equation
2
Peano existence theorem
Existence and uniqueness of solutions of ordinary differential equations
Picard-Lindelöf theorem
Existence and uniqueness of solutions of ordinary differential equations
System of ordinary differential equations
Ordinary differential equation
1
System of linear ordinary differential equations
System of ordinary differential equations
Partial differential equation
(PDE)
Differential equation
2k
57
Analytical method to solve a partial differential equation
Partial differential equation
30
1
Separation of variables
Analytical method to solve a partial differential equation
30
Numerical method to solve a partial differential equation
Partial differential equation
40
3
Variational formulation of a partial differential equation
Numerical method to solve a partial differential equation
14
1
Weak solution
Variational formulation of a partial differential equation
Finite element method
Numerical method to solve a partial differential equation
13
Important partial differential equation
Partial differential equation
805
36
Laplace's equation
Important partial differential equation
111
5
Legendre polynomials
Laplace's equation
15
Poisson's equation
Laplace's equation
9
1
Uniqueness theorem for Poisson's equation
Poisson's equation
Harmonic function
Laplace's equation
18
1
Spherical harmonic
Harmonic function
14
Heat equation
Important partial differential equation
110
1
Heat equation solution with Fourier series
Heat equation
1
Wave equation
Important partial differential equation
578
27
Damped wave equation
Wave equation
105
1
Plucked string model
Damped wave equation
105
Wave equation boundary condition
Wave equation
Wave equation on string with one vibrating side
Wave equation
7
Wave equation solver
Wave equation
64
Wave equation solution with Fourier series
Wave equation
5
The wave equation can be seen as infinitely many infinitesimal coupled oscillators
Wave equation
29
Lossy 1D Wave Equation
Wave equation
Wave
Wave equation
7
3
Wavelength
Wave
Standing wave
Wave
7
Envelope
(waves)
Wave
Polarization
Wave equation
30
1
String polarization
Polarization
23
Diffraction
Wave equation
36
4
Huygens-Fresnel principle
Diffraction
36
3
Kirchhoff's diffraction formula
Huygens-Fresnel principle
36
2
Fraunhofer diffraction
Kirchhoff's diffraction formula
17
Fresnel diffraction
Kirchhoff's diffraction formula
16
Refraction
Wave equation
Resonance
Wave equation
183
Wave interference
Wave equation
19
1
Interference pattern
Wave interference
19
2D wave equation on a circular domain
Wave equation
53
2
Bessel function
2D wave equation on a circular domain
53
1
Fourier-Bessel series
Bessel function
8
Helmholtz equation
Wave equation
3
Existence and uniqueness of solutions of partial differential equations
Partial differential equation
79
Partial differential equation solver
Partial differential equation
767
6
FreeFem
Partial differential equation solver
550
3
FreeFem examples
FreeFem
7
2
heat-dirichlet.1d.freefem
FreeFem examples
3
heat-dirichlet-2d-freefem
FreeFem examples
4
FEniCS Project
Partial differential equation solver
217
1
Hans Petter Langtangen
FEniCS Project
64
System of partial differential equations
Partial differential equation
37
Classification of second order partial differential equations into elliptic, parabolic and hyperbolic
Partial differential equation
47
4
Elliptic partial differential equation
Classification of second order partial differential equations into elliptic, parabolic and hyperbolic
Parabolic partial differential equation
Classification of second order partial differential equations into elliptic, parabolic and hyperbolic
Hyperbolic partial differential equation
Classification of second order partial differential equations into elliptic, parabolic and hyperbolic
Which boundary conditions lead to existence and uniqueness of a second order PDE
Classification of second order partial differential equations into elliptic, parabolic and hyperbolic
27
Phase space
Differential equation
9
Boundary condition
Differential equation
308
9
Initial condition
Boundary condition
22
Boundary value problem
Boundary condition
Dirichlet boundary condition
Boundary condition
13
Neumann boundary condition
Boundary condition
243
4
Cauchy boundary condition
Neumann boundary condition
50
Robin boundary condition
Neumann boundary condition
81
Open boundary condition
Neumann boundary condition
89
Mixed boundary condition
Neumann boundary condition
7
Time dependent boundary condition
Boundary condition
30
Control theory
Differential equation
70
3
Control engineering
Control theory
Control system
Control theory
Feedback loop
(Control loop)
Control theory
Series
(mathematics)
Calculus
36
8
Power series
Series
36
7
Analytic function
Power series
36
4
Sine and cossine
Analytic function
36
3
Sinusoidal
Sine and cossine
36
Sine
Sine and cossine
Cosine
Sine and cossine
Radius of convergence
Power series
Taylor series
Power series
Gradient, Divergence, Curl, and Laplacian
Calculus
293
7
Curl
(mathematics,
∇
×
)
Gradient, Divergence, Curl, and Laplacian
11
Nabla symbol
(
∇
)
Gradient, Divergence, Curl, and Laplacian
97
1
Del
Nabla symbol
33
Divergence
(
∇
⋅
,
d
i
v
(
)
)
Gradient, Divergence, Curl, and Laplacian
67
Gradient
(
∇
)
Gradient, Divergence, Curl, and Laplacian
89
Laplace operator
(
Δ
,
∇
2
)
Gradient, Divergence, Curl, and Laplacian
29
1
d'Alembert operator
(
□
)
Laplace operator
12
Infinitesimal
Calculus
10
Ancestors
(3)
Area of mathematics
Mathematics
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