site_name: Mathematics and physics wiki docs_dir: '../../docs/en' theme: name: material features: - navigation.instant - navigation.tabs - navigation.indexes - toc.follow palette: - media: "(prefers-color-scheme: light)" scheme: default primary: white accent: blue toggle: icon: material/brightness-7 name: Switch to dark mode - media: "(prefers-color-scheme: dark)" scheme: slate primary: black accent: teal toggle: icon: material/brightness-3 name: Switch to light mode language: en extra: generator: false alternate: - name: English link: /en/ lang: en - name: Nederlands link: /nl/ lang: nl plugins: - search: lang: en markdown_extensions: - pymdownx.arithmatex: generic: true - pymdownx.critic - pymdownx.caret - pymdownx.keys - pymdownx.mark - pymdownx.tilde - def_list - admonition - pymdownx.details - pymdownx.superfences extra_javascript: - javascripts/katex.js - https://unpkg.com/katex@0/dist/katex.min.js - https://unpkg.com/katex@0/dist/contrib/auto-render.min.js extra_css: - stylesheets/extra.css - https://unpkg.com/katex@0/dist/katex.min.css nav: - 'Welcome': index.md - 'Mathematics': - mathematics/index.md - 'Logic': mathematics/logic.md - 'Set theory': - 'Sets': mathematics/set-theory/sets.md - 'Relations': mathematics/set-theory/relations.md - 'Maps': mathematics/set-theory/maps.md - 'Permutations': mathematics/set-theory/permutations.md - 'Orders': mathematics/set-theory/orders.md - 'Recursion and induction': mathematics/set-theory/recursion-induction.md - 'Cardinalities': mathematics/set-theory/cardinalities.md - 'Additional axioms': mathematics/set-theory/additional-axioms.md - 'Number theory': - 'Integer arithmetic': mathematics/number-theory/integer-arithmetic.md - 'Modular arithmetic': mathematics/number-theory/modular-arithmetic.md - 'Complex numbers': mathematics/number-theory/complex-numbers.md - 'Linear algebra': - 'Systems of linear equations': mathematics/linear-algebra/systems-of-linear-equations.md - 'Matrices': - 'Matrix arithmetic': mathematics/linear-algebra/matrices/matrix-arithmetic.md - 'Matrix algebra': mathematics/linear-algebra/matrices/matrix-algebra.md - 'Elementary matrices': mathematics/linear-algebra/matrices/elementary-matrices.md - 'Determinants': mathematics/linear-algebra/determinants.md - 'Vector spaces': mathematics/linear-algebra/vector-spaces.md - 'Linear transformations': mathematics/linear-algebra/linear-transformations.md - 'Inner product spaces': mathematics/linear-algebra/inner-product-spaces.md - 'Orthogonality': mathematics/linear-algebra/orthogonality.md - 'Eigenspaces': mathematics/linear-algebra/eigenspaces.md - 'Dual vector spaces': mathematics/linear-algebra/dual-vector-spaces.md - 'Tensors': - 'Tensor formalism': mathematics/linear-algebra/tensors/tensor-formalism.md - 'Tensor symmetries': mathematics/linear-algebra/tensors/tensor-symmetries.md - 'Volume forms': mathematics/linear-algebra/tensors/volume-forms.md - 'Tensor transformations': mathematics/linear-algebra/tensors/tensor-transformations.md - 'Functional analysis': - 'Metric spaces': - 'Metric spaces': mathematics/functional-analysis/metric-spaces/metric-spaces.md - 'Topological notions': mathematics/functional-analysis/metric-spaces/topological-notions.md - 'Convergence': mathematics/functional-analysis/metric-spaces/convergence.md - 'Completeness': mathematics/functional-analysis/metric-spaces/completeness.md - 'Completion': mathematics/functional-analysis/metric-spaces/completion.md - 'Normed spaces': - 'Vector spaces': mathematics/functional-analysis/normed-spaces/vector-spaces.md - 'Normed spaces': mathematics/functional-analysis/normed-spaces/normed-spaces.md - 'Compactness': mathematics/functional-analysis/normed-spaces/compactness.md - 'Linear operators': mathematics/functional-analysis/normed-spaces/linear-operators.md - 'Linear functionals': mathematics/functional-analysis/normed-spaces/linear-functionals.md - 'Inner product spaces': - 'Inner product spaces': mathematics/functional-analysis/inner-product-spaces/inner-product-spaces.md - 'Direct sums': mathematics/functional-analysis/inner-product-spaces/direct-sums.md - 'Orthonormal sets': mathematics/functional-analysis/inner-product-spaces/orthonormal-sets.md - 'Total sets': mathematics/functional-analysis/inner-product-spaces/total-sets.md - 'Fourier series': - 'Formalism': mathematics/functional-analysis/inner-product-spaces/fourier-series/formalism.md - 'Convergence': mathematics/functional-analysis/inner-product-spaces/fourier-series/convergence.md - 'Polynomials': - 'Legendre polynomials': mathematics/functional-analysis/inner-product-spaces/polynomials/legendre-polynomials.md - 'Hermite polynomials': mathematics/functional-analysis/inner-product-spaces/polynomials/hermite-polynomials.md - 'Laguerre polynomials': mathematics/functional-analysis/inner-product-spaces/polynomials/laguerre-polynomials.md - 'Representations of functionals': mathematics/functional-analysis/inner-product-spaces/representations-of-functionals.md - 'Operator classes': mathematics/functional-analysis/inner-product-spaces/operator-classes.md - 'Topology': - 'Fiber bundles': mathematics/topology/fiber-bundles.md - 'Calculus': - 'Limits': mathematics/calculus/limits.md - 'Continuity': mathematics/calculus/continuity.md - 'Differentation': mathematics/calculus/differentation.md - 'Transcendental functions': - 'Inverse functions': mathematics/calculus/transcendental-functions/inverse-functions.md - 'Exponential and logarithmic functions': mathematics/calculus/transcendental-functions/exponential-and-logarithmic-functions.md - 'Extremes values': mathematics/calculus/extremes-values.md - 'Concavity and inflections': mathematics/calculus/concavity-and-inflections.md - 'Taylor polynomials': mathematics/calculus/taylor-polynomials.md - 'Integration': mathematics/calculus/integration.md - 'Integration techniques': mathematics/calculus/integration-techniques.md - 'Improper integrals': mathematics/calculus/improper-integrals.md - 'Multivariable calculus': - 'Functions of several variables': mathematics/multivariable-calculus/functions-of-several-variables.md - 'Limits and continuity': mathematics/multivariable-calculus/limits-and-continuity.md - 'Differentation': mathematics/multivariable-calculus/differentation.md - 'Implicit equations': mathematics/multivariable-calculus/implicit-equations.md - 'Taylor polynomials': mathematics/multivariable-calculus/taylor-polynomials.md - 'Extrema': mathematics/multivariable-calculus/extrema.md - 'Integration': mathematics/multivariable-calculus/integration.md - 'Ordinary differential equations': - 'First order differential equations': mathematics/ordinary-differential-equations/first-order-ode.md - 'Second order differential equations': mathematics/ordinary-differential-equations/second-order-ode.md - 'Systems of linear differential equations': mathematics/ordinary-differential-equations/systems-of-linear-ode.md - 'The Laplace transform': mathematics/ordinary-differential-equations/laplace-transform.md - 'Differential geometry': - 'Differential manifolds': mathematics/differential-geometry/differential-manifolds.md - 'Tangent spaces': mathematics/differential-geometry/tangent-spaces.md - 'Transformations': mathematics/differential-geometry/transformations.md - 'Lengths and volumes': mathematics/differential-geometry/lenghts-and-volumes.md - 'Linear connections': mathematics/differential-geometry/linear-connections.md - 'Derivatives': mathematics/differential-geometry/derivatives.md - 'Torsion': mathematics/differential-geometry/torsion.md - 'Curvature': mathematics/differential-geometry/curvature.md - 'Physics': - physics/index.md - 'Classical Mechanics': - 'Newtonian mechanics': - 'Newtonian formalism': physics/classical-mechanics/newtonian-mechanics/newtonian-formalism.md - 'Momentum': physics/classical-mechanics/newtonian-mechanics/momentum.md - 'Energy': physics/classical-mechanics/newtonian-mechanics/energy.md - 'Rotation': physics/classical-mechanics/newtonian-mechanics/rotation.md - 'Particle systems': physics/classical-mechanics/newtonian-mechanics/particle-systems.md - 'Lagrangian mechanics': - 'Lagrangian formalism': physics/classical-mechanics/lagrangian-mechanics/lagrangian-formalism.md - 'Lagrange equations': physics/classical-mechanics/lagrangian-mechanics/lagrange-equations.md - 'Lagrange generalizations': physics/classical-mechanics/lagrangian-mechanics/lagrange-generalizations.md - 'Hamiltonian mechanics': - 'Hamiltonian formalism': physics/classical-mechanics/hamiltonian-mechanics/hamiltonian-formalism.md - 'Equations of Hamilton': physics/classical-mechanics/hamiltonian-mechanics/equations-of-hamilton.md - 'Relativistic mechanics': - 'Relativistic formalism': physics/relativistic-mechanics/relativistic-formalism.md - 'Schwarzschild geometry': physics/relativistic-mechanics/schwarzschild-geometry.md - 'Kerr geometry': physics/relativistic-mechanics/kerr-geometry.md - 'Wave geometry': physics/relativistic-mechanics/wave-geometry.md # - 'Quantum mechanics': # - 'Statistical mechanics': - 'Electromagnetism': # - 'Electrostatics': # - 'Magnetostatics': - 'Maxwell-equations': physics/electromagnetism/maxwell-equations.md # - 'Electrodynamics': - 'Optics': - 'Waves': physics/electromagnetism/optics/waves.md - 'Electromagnetic waves': physics/electromagnetism/optics/electromagnetic-waves.md - 'Reflection and refraction': physics/electromagnetism/optics/reflection-and-refraction.md - 'Geometric optics': physics/electromagnetism/optics/geometric-optics.md - 'Interference': physics/electromagnetism/optics/interference.md - 'Diffraction': physics/electromagnetism/optics/diffraction.md - 'Polarisation': physics/electromagnetism/optics/polarisation.md # - 'Thermodynamics': # - 'Classical thermodynamics' # - 'Statistical thermodynamics' - 'Mathematical physics': - 'Error analysis': - 'Error analysis formalism': physics/mathematical-physics/error-analysis/formalism.md - 'Maximum error': physics/mathematical-physics/error-analysis/maximum-error.md - 'Standard error': physics/mathematical-physics/error-analysis/standard-error.md - 'Signal analysis': - 'Signals': physics/mathematical-physics/signal-analysis/signals.md - 'Fourier series': physics/mathematical-physics/signal-analysis/fourier-series.md - 'Fourier transform': physics/mathematical-physics/signal-analysis/fourier-transform.md - 'Discrete Fourier transform': physics/mathematical-physics/signal-analysis/discrete-fourier-transform.md - 'Amplitude modulation': physics/mathematical-physics/signal-analysis/amplitude-modulation.md - 'Signal filters': physics/mathematical-physics/signal-analysis/signal-filters.md - 'Systems': physics/mathematical-physics/signal-analysis/systems.md - 'Vector analysis': - 'Vectors': physics/mathematical-physics/vector-analysis/vectors.md - 'Curves': physics/mathematical-physics/vector-analysis/curves.md - 'Curvilinear coordinates': physics/mathematical-physics/vector-analysis/curvilinear-coordinates.md - 'Divergence': physics/mathematical-physics/vector-analysis/divergence.md - 'Gradient': physics/mathematical-physics/vector-analysis/gradient.md - 'Curl': physics/mathematical-physics/vector-analysis/curl.md - 'Vector operators': physics/mathematical-physics/vector-analysis/vector-operators.md - 'Programming': - programming/index.md