# Calculus
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## Microsims — p5.js
### Calculus (p5.js) · `d/dt, ∫`
<div class="microsim-player">
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*The mathematics of change and accumulation — the language every continuous signal is written in.*
**Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/1qoztrPh5) · movement *IX · Foundations & the rest of the toolbox* · library `p5js`
### Related microsims
Live sims on neighbouring articles — 6 of them inside this article's own Wikipedia link tree:
- [[Complex_analysis]] *(in tree)*
- [[Control_theory]] *(in tree)*
- [[Fourier_analysis]] *(in tree)*
- [[Functional_analysis]] *(in tree)*
- [[Graph_theory]] *(in tree)*
- [[Information_theory]] *(in tree)*
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## Links (Wikipedia order)
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`A_Biography_of_Maria_Gaetana_Agnesi` · `A_History_of_Western_Philosophy` · `Abacus` · `Abel's_test` · `Abraham_Robinson` · `Abraham_de_Moivre` · `Absolute_space_and_time` · `Abstract_algebra` · `Acceleration` · `Actuarial_science` · `Adequality` · [[Aerospace_engineering]] · `Affine_geometry` · `Agnes_Scott_College` · `Albert_Einstein` · `Algebra` · `Algebraic_analysis` · `Algebraic_geometry` · `Algebraic_number_theory` · `Algebraic_topology` · `Alternating_series` · `Alternating_series_test` · `American_Mathematical_Society` · `An_Historical_Account_of_Two_Notable_Corruptions_of_Scripture` · `Analytic_combinatorics` · `Analytic_function` · `Analytic_geometry` · `Analytic_number_theory` · `Ancient_Greek` · `Andrew_M._Gleason` · `André_Weil` · `Annette_Imhausen` · `Antiderivative` · `Antonella_Cupillari` · `Apostrophe` · `Applied_mathematics` · `Arc_length` · `Archimedes` · `Area` · `Arithmetic` · `Arithmetic_geometry` · `Arithmetica_Universalis` · `Arithmetico-geometric_sequence` · `Astronomers_Monument` · `Augustin-Louis_Cauchy` · `Axiom` · `BBC` · `Babylon` · `Barton_Zwiebach` · `Basel_problem` · `Benjamin_Pulleyn` · `Bernhard_Riemann` · `Bernoulli_number` · `Bertrand_Russell` · `Beyond_Infinity_(mathematics_book)` · `Bhāskara_II` · `Binomial_series` · `Binomial_theorem` · `Biology` · `Black–Scholes_model` · `Blood_vessel` · `Bochner_integral` · `Bonaventura_Cavalieri` · `Brook_Taylor` · `Bucket_argument` · `Burkill_integral` · `Business` · `Calculus_(Apostol_books)` · `Calculus_(disambiguation)` · `Calculus_(medicine)` · `Calculus_Made_Easy` · [[Calculus_of_variations]] · `Calculus_on_Euclidean_space` · `Cambridge_University_Press` · `Cancer` · `Carl_Benjamin_Boyer` · `Category_theory` · `Catherine_Barton` · `Cauchy_condensation_test` · `Cavalieri's_principle` · `Center_of_mass` · `Chain_rule` · `Chinese_mathematics` · `Classical_mechanics` · `Claudia_Neuhauser` · `Colin_Maclaurin` · `Combinatorics` · `Common_integrals_in_quantum_field_theory` · `Commutative_algebra` · `Complete_Fermi–Dirac_integral` · [[Complex_analysis]] · `Complex_geometry` · `Complex_number` · `Complex_plane` · `Computational_complexity_theory` · `Computational_geometry` · `Computational_mathematics` · `Computer_algebra` · [[Computer_science]] · `Concave_function` · `Constant_of_integration` · `Constructive_analysis` · `Constructive_nonstandard_analysis` · `Continuous_function` · `Contour_integration` · [[Control_theory]] · `Convergence_tests` · `Convergent_series` · `Convex_geometry` · `Corpuscular_theory_of_light` · `Cours_d'analyse` · `Cranbury_Park` · `Criticism_of_nonstandard_analysis` · `Curl_(mathematics)` · `Curvature` · `Curve` · `Cycloid` · `Daniell_integral` · `Darboux_integral` · `David_Bressoud` · `De_analysi_per_aequationes_numero_terminorum_infinitas` · `De_motu_corporum_in_gyrum` · `Deborah_Hughes_Hallett` · `Demography` · [[Density]] · `Derivative` · `Difference_quotient` · `Differentiable_function` · `Differential_(mathematics)` · `Differential_calculus` · [[Differential_equation]] · `Differential_form` · `Differential_geometry` · `Differential_geometry_of_surfaces` · `Differential_of_a_function` · `Differential_operator` · `Differential_topology` · `Differentiation_rules` · `Diophantine_geometry` · `Diophantus` · `Direct_comparison_test` · `Directional_derivative` · `Dirichlet's_test` · `Dirichlet_integral` · `Disc_integration` · `Discrete_geometry` · `Discrete_mathematics` · `Divergence` · `Divergence_theorem` · `Division_by_zero` · `Domain_of_a_function` · `Dual_number` · `E_(mathematical_constant)` · `Early_life_of_Isaac_Newton` · `Economics` · `Edmund_Landau` · `Edwin_Mellen_Press` · `Einar_Hille` · [[Electrical_engineering]] · `Electromagnetic_field` · `Electromagnetism` · `Elementary_Calculus:_An_Infinitesimal_Approach` · `Elementary_algebra` · `Encyclopedia_of_Mathematics` · [[Engineering]] · [[Engineering_mathematics]] · `Eric_W._Weisstein` · `Ethical_calculus` · `Euclidean_geometry` · `Euclidean_space` · `Eudoxus_of_Cnidus` · `Eugenia_Cheng` · `Euler_method` · `Euler_substitution` · `Euler–Lagrange_equation` · `Euler–Maclaurin_formula` · `Exponential_decay` · `Exponential_function` · `Exterior_derivative` · `Extreme_value_theorem` · `Factorial` · `Faà_di_Bruno's_formula` · `Felicific_calculus` · `Fermat's_principle` · `Field_(mathematics)` · `Finite_difference` · `Finite_geometry` · `Florian_Cajori` · `Fluxion` · [[Force]] · `Foundations_of_mathematics` · [[Fourier_analysis]] · `Fourier_series` · `Fourth_power` · `Fractional_calculus` · `Free_variables_and_bound_variables` · `Fritz_John` · `Frullani_integral` · `Frustum` · `Fubini's_theorem` · `Function_(mathematics)` · `Function_of_several_real_variables` · `Functional_(mathematics)` · [[Functional_analysis]] · `Functional_equation` · `Fundamental_theorem_of_calculus` · `Future_of_mathematics` · `Gabriel's_horn` · [[Game_theory]] · `Gaussian_integral` · `Gauss–Newton_algorithm` · `General_Leibniz_rule` · `General_Scholium` · `General_relativity` · `General_topology` · `Generality_of_algebra` · `Generalizations_of_the_derivative` · `Generalized_Gauss–Newton_method` · `Generalized_Stokes_theorem` · `Generalized_function` · `Geodesic` · `Geometric_calculus` · `Geometric_series` · `Geometric_topology` · [[Geometry]] · `George_B._Thomas` · `George_Berkeley` · `Gilbert_Strang` · `Glossary_of_Arabic_toponyms` · `Glossary_of_Hebrew_toponyms` · [[Glossary_of_aerospace_engineering]] · `Glossary_of_agriculture` · `Glossary_of_archaeology` · `Glossary_of_architecture` · `Glossary_of_areas_of_mathematics` · `Glossary_of_artificial_intelligence` · `Glossary_of_astronomy` · `Glossary_of_biology` · `Glossary_of_bird_terms` · `Glossary_of_botanical_terms` · `Glossary_of_calculus` · `Glossary_of_cellular_and_molecular_biology_(0–L)` · `Glossary_of_cellular_and_molecular_biology_(M–Z)` · `Glossary_of_chemistry_terms` · [[Glossary_of_civil_engineering]] · `Glossary_of_clinical_research` · `Glossary_of_computer_hardware_terms` · `Glossary_of_computer_science` · `Glossary_of_developmental_biology` · `Glossary_of_ecology` · `Glossary_of_economics` · [[Glossary_of_electrical_and_electronics_engineering]] · `Glossary_of_engineering:_A–L` · `Glossary_of_engineering:_M–Z` · `Glossary_of_entomology_terms` · `Glossary_of_environmental_science` · `Glossary_of_genetics_and_evolutionary_biology` · `Glossary_of_geography_terms_(A–M)` · `Glossary_of_geography_terms_(N–Z)` · `Glossary_of_geology` · `Glossary_of_ichthyology` · `Glossary_of_machine_vision` · `Glossary_of_mathematical_symbols` · [[Glossary_of_mechanical_engineering]] · `Glossary_of_medicine` · `Glossary_of_meteorology` · `Glossary_of_mycology` · `Glossary_of_nanotechnology` · `Glossary_of_physics` · `Glossary_of_probability_and_statistics` · `Glossary_of_protistology` · `Glossary_of_psychiatry` · `Glossary_of_quantum_computing` · `Glossary_of_robotics` · `Glossary_of_scientific_naming` · [[Glossary_of_structural_engineering]] · `Glossary_of_virology` · `Gottfried_Wilhelm_Leibniz` · `Gradient` · `Gradient_theorem` · [[Graph_of_a_function]] · [[Graph_theory]] · `Gravitational_constant` · [[Gravitational_field]] · `Green's_theorem` · `Greg_Gbur` · `Group_theory` · `Haar_measure` · `Harmonic_analysis` · `Harmonic_series_(mathematics)` · `Heaviside_cover-up_method` · `Hellenistic_period` · `Hellinger_integral` · `Helmholtz_decomposition` · `Henri_Lebesgue` · `Henstock–Kurzweil_integral` · `Hessian_matrix` · `Historia_Mathematica` · `History_of_calculus` · `History_of_mathematics` · `Homological_algebra` · `Homotopy_theory` · `Hugh_Chisholm` · `Hypercomplex_analysis` · `Hyperfinite_set` · `Hyperinteger` · `Hyperreal_number` · `Hypotheses_non_fingo` · `Ibn_al-Haytham` · `Impact_depth` · `Implicit_differentiation` · `Improper_integral` · `Imre_Leader` · `In_Our_Time_(radio_series)` · `Incomplete_Fermi–Dirac_integral` · `Increment_theorem` · `Indeterminate_form` · `Indian_mathematics` · `Inertia` · `Infinitesimal` · `Infinitesimal_strain_theory` · `Infinity` · `Informal_mathematics` · `Information_geometry` · [[Information_theory]] · `Integral` · `Integral_equation` · `Integral_of_inverse_functions` · `Integral_of_secant_cubed` · `Integral_of_the_secant_function` · `Integral_symbol` · `Integral_test_for_convergence` · [[Integral_transform]] · `Integration_Bee` · `Integration_by_parts` · `Integration_by_reduction_formulae` · `Integration_by_substitution` · `Integration_using_Euler's_formula` · `Integration_using_parametric_derivatives` · `Integro-differential_equation` · `Internal_set` · `Internal_set_theory` · `Inverse_function_rule` · `Inverse_function_theorem` · `Isaac_Barrow` · [[Isaac_Newton]] · `Isaac_Newton's_occult_studies` · `Isaac_Newton_Gargoyle` · `Isaac_Newton_Group_of_Telescopes` · `Isaac_Newton_Institute` · `Isaac_Newton_Telescope` · `Isaac_Newton_in_popular_culture` · `Isis_(journal)` · `Itô_calculus` · `Ivor_Grattan-Guinness` · `Jackie_Stedall` · `Jacobian_matrix_and_determinant` · `James_Stewart_(mathematician)` · `Japanese_mathematics` · `Jeremy_Bentham` · `Joel_Hass` · [[Johannes_Kepler]] · `John_Conduitt` · `John_Keill` · `John_Lane_Bell` · `John_Wallis` · [[John_von_Neumann]] · `Joseph_Mazur` · `Judith_Grabiner` · `June_Barrow-Green` · [[Jupiter]] · `Karl_Weierstrass` · `Kepler's_laws_of_planetary_motion` · `Kerala_school_of_astronomy_and_mathematics` · `Khinchin_integral` · `Kissing_number` · `Kolmogorov_integral` · `L'Hôpital's_rule` · `Lagrange_multiplier` · `Lambda_calculus` · `Laplace's_method` · `Laplace_operator` · [[Laplace_transform]] · `Large_numbers` · `Larry_Gonick` · `Later_life_of_Isaac_Newton` · `Latin` · `Laurent_Schwartz` · `Law_of_continuity` · `Law_of_excluded_middle` · [[Least-squares_spectral_analysis]] · `Lebesgue–Stieltjes_integration` · `Leibniz's_notation` · `Leibniz_integral_rule` · `Leibniz–Newton_calculus_controversy` · `Leonhard_Euler` · `Levi-Civita_field` · `Lewiston,_New_York` · `Limit_(mathematics)` · `Limit_comparison_test` · `Limit_of_a_function` · `Limit_of_a_sequence` · `Limit_of_distributions` · `Line_integral` · [[Linear_algebra]] · `Linear_approximation` · `Linear_function` · `Linear_regression` · `Linearity_of_differentiation` · `List_of_calculus_topics` · `List_of_derivatives_and_integrals_in_alternative_calculi` · `List_of_films_about_mathematicians` · `List_of_integrals_of_exponential_functions` · `List_of_integrals_of_hyperbolic_functions` · `List_of_integrals_of_inverse_hyperbolic_functions` · `List_of_integrals_of_inverse_trigonometric_functions` · `List_of_integrals_of_irrational_algebraic_functions` · `List_of_integrals_of_logarithmic_functions` · `List_of_integrals_of_rational_functions` · `List_of_integrals_of_trigonometric_functions` · `List_of_limits` · `List_of_publications_in_mathematics` · `List_of_things_named_after_Isaac_Newton` · `Lists_of_integrals` · `Lists_of_mathematics_topics` · `Liu_Hui` · `Logarithmic_derivative` · `Logarithmic_differentiation` · [[Logarithmic_spiral]] · `Long_s` · `Luminiferous_aether` · `Lynn_Steen` · `Madhava_of_Sangamagrama` · `Malliavin_calculus` · `Manifold` · `Map_(mathematics)` · `Margaret_Baron` · `Marginal_cost` · `Marginal_revenue` · `Maria_Gaetana_Agnesi` · `Martin_Gardner` · `Mary_L._Boas` · `Mass` · `Massachusetts_Institute_of_Technology` · `MathWorld` · `Mathematical_Association_of_America` · `Mathematical_Methods_in_the_Physical_Sciences` · `Mathematical_analysis` · `Mathematical_and_theoretical_biology` · `Mathematical_chemistry` · `Mathematical_economics` · `Mathematical_finance` · `Mathematical_linguistics` · `Mathematical_logic` · [[Mathematical_model]] · [[Mathematical_optimization]] · `Mathematical_physics` · `Mathematical_proof` · `Mathematical_psychology` · `Mathematical_sociology` · `Mathematical_statistics` · `Mathematics` · `Mathematics_Magazine` · `Mathematics_and_art` · `Mathematics_education` · `Mathematics_in_Ancient_Egypt:_A_Contextual_History` · `Matrix_calculus` · `Maximum_and_minimum` · `Mean_speed_theorem` · `Mean_value_theorem` · `Measure_(mathematics)` · [[Mechanical_engineering]] · `Mechanics` · [[Medicine]] · `Mehran_Kardar` · `Method_of_Fluxions` · `Method_of_exhaustion` · `Michael_Spivak` · `Michel_Rolle` · `Michiel_Hazewinkel` · `Microcontinuity` · `Microlocal_analysis` · `Moment_of_inertia` · `Momentum` · `Monad_(nonstandard_analysis)` · `Morris_Kline` · `Moscow_Mathematical_Papyrus` · `Multiple_discovery` · `Multiple_integral` · `Multivariable_calculus` · `Natural_logarithm` · `Nautilus` · `Newton's_cannonball` · `Newton's_cradle` · `Newton's_identities` · `Newton's_inequalities` · `Newton's_law_of_cooling` · `Newton's_law_of_universal_gravitation` · [[Newton's_laws_of_motion]] · `Newton's_metal` · `Newton's_method` · `Newton's_method_in_optimization` · `Newton's_reflector` · `Newton's_rings` · `Newton's_theorem_about_ovals` · `Newton's_theorem_of_revolving_orbits` · `Newton_(Blake)` · `Newton_(Paolozzi)` · `Newton_(unit)` · `Newton_International_Fellowship` · `Newton_disc` · `Newton_fractal` · `Newton_polygon` · `Newton_polynomial` · `Newton_scale` · `Newtonian_dynamics` · `Newtonian_fluid` · `Newtonian_potential` · `Newtonian_telescope` · `Newtonianism` · `Newton–Cartan_theory` · `Newton–Cotes_formulas` · `Newton–Euler_equations` · `Newton–Okounkov_body` · `Newton–Pepys_problem` · `Nicole_Oresme` · `Nonelementary_integral` · `Nonstandard_analysis` · `Nonstandard_calculus` · `Notation_for_differentiation` · `Notes_on_the_Jewish_Temple` · `Nova_Methodus_pro_Maximis_et_Minimis` · [[Nuclear_engineering]] · `Number` · `Number_theory` · `Numerical_analysis` · [[Numerical_integration]] · `Oikonyms_in_West_and_South_Asia` · `One-sided_limit` · [[Operations_research]] · `Opticks` · `Option_(finance)` · `Order_of_approximation` · `Order_of_integration_(calculus)` · [[Ordinary_differential_equation]] · `Outline_of_calculus` · `Overspill` · `Oxford_Calculators` · `Oxford_English_Dictionary` · `P-adic_analysis` · `P-adic_number` · `Parabola` · `Paraboloid` · `Parallelogram_of_force` · `Parameterized_post-Newtonian_formalism` · `Partial_derivative` · [[Partial_differential_equation]] · `Pathological_(mathematics)` · `Pettis_integral` · `Pfeffer_integral` · `Philosophiæ_Naturalis_Principia_Mathematica` · `Philosophy_of_mathematics` · [[Physics]] · `Pierre_de_Fermat` · `Plagiarism` · `PlanetMath` · `Polygon` · `Portrait_of_Benjamin_Franklin` · `Portrait_of_Isaac_Newton` · `Post-Newtonian_expansion` · `Potential_energy` · `Power_number` · `Power_rule` · `Power_series` · `Precalculus` · `Pressure` · `Prime_(symbol)` · [[Probability_density_function]] · `Probability_theory` · `Problem_of_Apollonius` · `Process_calculus` · `Product_rule` · [[Projective_geometry]] · `Proof_that_22/7_exceeds_π` · `Puiseux_series` · `Quadratic_integral` · `Quadrature_of_the_Parabola` · `Quaestiones_quaedam_philosophicae` · [[Quantum_mechanics]] · `Quaternionic_analysis` · `Quotient_rule` · `Radian` · `Random_variable` · `Ratio_test` · `Real_analysis` · `Real_number` · `Recreational_mathematics` · `Regiomontanus'_angle_maximization_problem` · `Regulated_integral` · `Related_rates` · `Religious_views_of_Isaac_Newton` · `Representation_theory` · `Reynolds_transport_theorem` · `Ricci_calculus` · `Richard_Courant` · `Richard_S._Westfall` · `Riemann_integral` · `Riemann_sum` · `Riemann–Stieltjes_integral` · `Risch_algorithm` · `Roger_Cotes` · `Rolle's_theorem` · `Root_test` · `Rotating_spheres` · `Royal_Society` · `Russo–Vallois_integral` · `Schrödinger–Newton_equation` · [[Science]] · [[Science_(journal)]] · `Scientific_law` · `Secant_line` · `Second_derivative` · [[Sequence]] · `Sequent_calculus` · `Series_(mathematics)` · [[Set_theory]] · `Shell_integration` · `Silvanus_P._Thompson` · `Simpson's_rule` · `Sir_Isaac_Newton_Sixth_Form` · `Skorokhod_integral` · `Slope` · `Smooth_infinitesimal_analysis` · `Smoothness` · `Special_functions` · `Spectrum` · `Sphere` · `Square` · `Standard_part_function` · `Standing_on_the_shoulders_of_giants` · `Stanford_Encyclopedia_of_Philosophy` · `Statal_Institute_of_Higher_Education_Isaac_Newton` · `Stationary_point` · `Statistical_Physics_of_Particles` · `Statistics` · `Steinmetz_solid` · `Steven_Frautschi` · `Stirling's_approximation` · `Stochastic_calculus` · `Stochastic_differential_equation` · `Stokes'_theorem` · `Stratonovich_integral` · `Structural_coloration` · `Surface_integral` · `Surreal_number` · `Symmetry_of_second_derivatives` · `Synthetic_differential_geometry` · [[Systems_science]] · `Table_of_Newtonian_series` · `Tangent` · `Tangent_half-angle_substitution` · `Taylor's_theorem` · `Taylor_series` · `Telescoping_series` · [[Tensor]] · `The_American_Mathematical_Monthly` · `The_Analyst` · `The_Chronology_of_Ancient_Kingdoms_Amended` · `The_History_of_Mathematics:_A_Very_Short_Introduction` · `The_Mechanical_Universe` · `The_Method_of_Mechanical_Theorems` · `The_Princeton_Companion_to_Mathematics` · `Theory_of_computation` · [[Thermodynamics]] · `Timeline_of_mathematics` · `Timothy_Gowers` · `Tom_M._Apostol` · `Topology` · `Transcendental_law_of_homogeneity` · `Transfer_principle` · `Trapezoidal_rule` · `Triangle` · `Trigonometric_substitution` · `Tropical_analysis` · `Truncated_Newton_method` · `Twistor_theory` · `Type_theory` · `Vector_calculus` · `Vector_calculus_identities` · `Vector_field` · [[Velocity]] · `Victor_J._Katz` · `Volume` · `Volume_integral` · [[Wayback_Machine]] · `William_Clarke_(apothecary)` · `William_G._McCallum` · `William_Jones_(mathematician)` · `William_Stukeley` · `William_Whiston` · `Woolsthorpe_Manor` · `Work_(physics)` · `XMM-Newton` · `Zeno's_paradoxes` · `Zeno_of_Elea` · `Zu_Chongzhi` · `Zu_Gengzhi` · `Émile_Borel`
> Signal Processing concept · part of the Signal Processing Portal · movement IX · !09 解析 kaiseki.svg
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*Rendered from the live microsim (▶ motion).*
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## See it next
[](Differential_equations)
*→ Differential equations*
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Back to Signal Processing Portal · the room · Semiotic gateway
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## From the Real GENERATIVE library
*Animated: Calculus — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (STEM and Music room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:Sec2tan.gif).*
> Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. ([Wikipedia](https://en.wikipedia.org/wiki/Calculus))
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## What it is
Calculus is the branch of mathematics that studies continuous change through two central operations: differentiation, which measures instantaneous rates of change, and integration, which accumulates quantities over an interval.
## How it works / why it matters
In signal processing calculus underpins the analysis of continuous-time signals: derivatives describe how a signal changes moment to moment, while integrals compute accumulated energy, area, and running averages. The Fourier and Laplace transforms, convolution integrals, and the differential equations that model linear systems are all built directly on calculus, making it the foundational language for describing how signals evolve and how systems respond to them.
## Signs & universals
Instantiates:
- transformation
- measurement
- system
## Related
See also Differential equations, [[Functional_analysis]], Continuous signal, Continuous-time signal, [[Linear_algebra]], and [[Convolution]] · Signal Processing
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*Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*
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## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Calculus) : [Wikitube](https://en.wikitube.io/wiki/Calculus)
## Previous hub tags
Tree parents: [[Control_theory]] · [[Game_theory]] · [[Graph_theory]] · [[Information_theory]] · [[Operations_research]].
Legacy hubs: none.
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*Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*