Ciro Santilli
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Calculus
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↑ parent "Mathematics"
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10
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91
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4k
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⇓ toc
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↑ parent "Mathematics"
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Wikipedia
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10
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91
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4k
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Fancy name for it with the "more advanced" connotation:
https://en.wikipedia.org/wiki/Real_analysis
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Table of contents
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10
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91
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4k
1. Limit (mathematics)
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44
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↑ parent "Calculus"
2. Riemann integral
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↑ parent "Calculus"
3. Lebesgue integral
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23
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12
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821
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3.1. Lebesgue integral vs Riemann integral
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211
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1
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274
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↑ parent "Lebesgue integral"
3.1.1. Real world applications of the Lebesgue integral
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63
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↑ parent "Lebesgue integral vs Riemann integral"
3.2. Lebesgue measurable
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↑ parent "Lebesgue integral"
3.3. Lebesgue integral of
L
p
is complete but Riemann isn't
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83
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7
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516
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↑ parent "Lebesgue integral"
3.3.1. Riesz-Fischer theorem
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56
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4
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287
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↑ parent "Lebesgue integral of
L
p
is complete but Riemann isn't"
3.3.1.1.
L
p
is complete
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1
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↑ parent "Riesz-Fischer theorem"
3.3.1.2. Fourier basis is complete for
L
2
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55
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2
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230
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↑ parent "Riesz-Fischer theorem"
3.3.1.2.1.
L
p
norm sequence convergence does not imply pointwise convergence
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41
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↑ parent "Fourier basis is complete for
L
2
"
3.3.1.2.2. Carleson's theorem
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134
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↑ parent "Fourier basis is complete for
L
2
"
3.3.2.
L
p
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28
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1
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146
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↑ parent "Lebesgue integral of
L
p
is complete but Riemann isn't"
3.3.2.1.
L
2
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118
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↑ parent "
L
p
"
3.4. Every Riemann integrable function is Lebesgue integrable
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8
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↑ parent "Lebesgue integral"
4. Measure theory
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53
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↑ parent "Calculus"
5. Fourier series
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125
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8
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358
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5.1. Applications of the Fourier series
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0
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1
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65
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↑ parent "Fourier series"
5.1.1. Solving partial differential equations with the Fourier series
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65
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↑ parent "Applications of the Fourier series"
5.2. Discrete Fourier transform (DFT)
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↑ parent "Fourier series"
5.3. Fourier transform
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22
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3
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152
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↑ parent "Fourier series"
5.3.1. Multidimensional Fourier transform
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40
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↑ parent "Fourier transform"
5.3.2. Fourier inversion theorem
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38
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↑ parent "Fourier transform"
5.3.3. Laplace transform
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52
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↑ parent "Fourier transform"
5.4. History of the Fourier series
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16
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↑ parent "Fourier series"
6. Topology
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12
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3
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55
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↑ parent "Calculus"
6.1. Manifold
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↑ parent "Topology"
6.2. Complete metric space
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43
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↑ parent "Topology"
6.3. Dense set
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↑ parent "Topology"
7. Distribution (mathematics)
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55
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1
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125
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↑ parent "Calculus"
7.1. Dirac delta function
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70
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↑ parent "Distribution"
8. Complex analysis
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14
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6
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273
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↑ parent "Calculus"
8.1. Holomorphic function
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68
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↑ parent "Complex analysis"
8.2. Analytic continuation
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50
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4
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191
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↑ parent "Complex analysis"
8.2.1. Visualizing the Riemann hypothesis and analytic continuation by 3Blue1Brown
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21
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↑ parent "Analytic continuation"
8.2.2. Identity theorem
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89
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2
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120
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↑ parent "Analytic continuation"
8.2.2.1. Riemann zeta function
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0
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1
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31
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↑ parent "Identity theorem"
8.2.2.1.1. Riemann hypothesis
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31
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↑ parent "Riemann zeta function"
9. Hilbert space
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31
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↑ parent "Calculus"
10. Differential equation
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0
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44
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2k
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↑ parent "Calculus"
10.1. Ordinary differential equation
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↑ parent "Differential equation"
10.2. Partial differential equation (PDE)
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0
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14
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502
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↑ parent "Differential equation"
10.2.1. Important partial differential equations
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36
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13
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502
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↑ parent "Partial differential equation"
10.2.1.1. Laplace's equation
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81
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4
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133
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↑ parent "Important partial differential equations"
10.2.1.1.1. Poisson's equation
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15
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1
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15
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↑ parent "Laplace's equation"
10.2.1.1.1.1. Uniqueness theorem for Poisson's equation
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↑ parent "Poisson's equation"
10.2.1.1.2. Harmonic function
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10
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1
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37
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↑ parent "Laplace's equation"
10.2.1.1.2.1. Spherical harmonic
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27
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↑ parent "Harmonic function"
10.2.1.2. Heat equation
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139
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↑ parent "Important partial differential equations"
10.2.1.3. Wave equation
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62
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4
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175
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↑ parent "Important partial differential equations"
10.2.1.3.1. 2D wave equation on a circular domain
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0
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2
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98
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↑ parent "Wave equation"
10.2.1.3.1.1. Bessel function
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77
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1
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98
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↑ parent "2D wave equation on a circular domain"
10.2.1.3.1.1.1. Fourier-Bessel series
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21
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↑ parent "Bessel function"
10.2.1.3.2. Helmholtz equation
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15
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↑ parent "Wave equation"
10.2.1.4. Navier-Stokes equations
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0
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1
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19
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↑ parent "Important partial differential equations"
10.2.1.4.1. Navier-Stokes existence and smoothness
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19
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↑ parent "Navier-Stokes equations"
10.3. Existence and uniqueness of solutions of partial differential equations
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104
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↑ parent "Differential equation"
10.4. System of partial differential equations
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71
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↑ parent "Differential equation"
10.5. Classification of second order partial differential equations into elliptic, parabolic and hyperbolic
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37
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4
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107
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↑ parent "Differential equation"
10.5.1. Elliptic partial differential equation
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↑ parent "Classification of second order partial differential equations into elliptic, parabolic and hyperbolic"
10.5.2. Parabolic partial differential equation
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↑ parent "Classification of second order partial differential equations into elliptic, parabolic and hyperbolic"
10.5.3. Hyperbolic partial differential equation
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↑ parent "Classification of second order partial differential equations into elliptic, parabolic and hyperbolic"
10.5.4. Which boundary conditions lead to existence and uniqueness of a second order PDE
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70
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↑ parent "Classification of second order partial differential equations into elliptic, parabolic and hyperbolic"
10.6. Boundary condition
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0
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13
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483
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↑ parent "Differential equation"
10.6.1. Boundary value problem
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↑ parent "Boundary condition"
10.6.2. Dirichlet boundary condition
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41
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↑ parent "Boundary condition"
10.6.3. Neumann boundary condition
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26
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4
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316
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↑ parent "Boundary condition"
10.6.3.1. Cauchy boundary condition
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67
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↑ parent "Neumann boundary condition"
10.6.3.2. Robin boundary condition
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107
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↑ parent "Neumann boundary condition"
10.6.3.3. Open boundary condition
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104
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↑ parent "Neumann boundary condition"
10.6.3.4. Mixed boundary condition
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12
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↑ parent "Neumann boundary condition"
10.6.4. Theoretical methods to solve partial differential equation
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0
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1
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55
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↑ parent "Boundary condition"
10.6.4.1. Separation of variables
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55
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↑ parent "Theoretical methods to solve partial differential equation"
10.6.5. Numerical methods to solve partial differential equation
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19
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3
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71
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↑ parent "Boundary condition"
10.6.5.1. Variational formulation of a partial differential equation
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27
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1
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27
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↑ parent "Numerical methods to solve partial differential equation"
10.6.5.1.1. Weak solution
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↑ parent "Variational formulation of a partial differential equation"
10.6.5.2. Finite element method
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25
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↑ parent "Numerical methods to solve partial differential equation"
10.7. Partial differential equation solver
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0
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6
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936
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↑ parent "Differential equation"
10.7.1. FreeFem
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601
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3
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634
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↑ parent "Partial differential equation solver"
10.7.1.1. FreeFem examples
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0
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2
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33
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↑ parent "FreeFem"
10.7.1.1.1. heat-dirichlet.1d.freefem
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16
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🔗 link
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↑ parent "FreeFem examples"
10.7.1.1.2. heat-dirichlet-2d-freefem
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17
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🔗 link
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↑ parent "FreeFem examples"
10.7.2. FEniCS Project
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202
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1
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302
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🔗 link
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↑ parent "Partial differential equation solver"
10.7.2.1. Hans Petter Langtangen
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100
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🔗 link
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↑ parent "FEniCS Project"
11. Taylor series
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↑ parent "Calculus"
12. Gradient, Divergence, Curl, and Laplacian
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0
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4
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84
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↑ parent "Calculus"
12.1. Nabla symbol (
∇
)
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62
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↑ parent "Gradient, Divergence, Curl, and Laplacian"
12.2. Divergence (
∇
â‹…
)
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11
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↑ parent "Gradient, Divergence, Curl, and Laplacian"
12.3. Gradient (
∇
)
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11
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↑ parent "Gradient, Divergence, Curl, and Laplacian"
12.4. Laplace operator (
Δ
,
∇
2
)
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🔗 link
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↑ parent "Gradient, Divergence, Curl, and Laplacian"
13. Infinitesimal
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22
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↑ parent "Calculus"
🔗
Incoming links
Limit
Topology