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Subset of lambda calculus
and computer science, kappa calculus is a formal system for defining first-order functions. Unlike lambda calculus, kappa calculus has no higher-order functions;
Kappa_calculus
Topics referred to by the same term
connections to computational theory Kappa calculus, a reformulation of the first-order fragment of typed lambda calculus Rho calculus, introduced as a general means
Calculus_(disambiguation)
Formalism in computer science
expressions. Kappa calculus—an analogue of typed lambda calculus which excludes higher-order functions Brandl, Helmut (27 April 2024). "Typed Lambda Calculus / Calculus
Typed_lambda_calculus
Mathematical-logic system
Lambda-mu calculus – An extension of the lambda calculus for treating classical logic These formal systems are variations of lambda calculus: Kappa calculus –
Lambda_calculus
Non-commutative algebraic structure
The icosian calculus is a non-commutative algebraic structure discovered by the Irish mathematician William Rowan Hamilton in 1856. In modern terms, he
Icosian_calculus
connections to computational theory Kappa calculus, a reformulation of the first-order fragment of typed lambda calculus Rho calculus, introduced as a general means
List_of_formal_systems
Programming language feature
Explicit currying with [1]. Defunctionalization eval First-class message Kappa calculus – a formalism which excludes first-class functions Man or boy test Partial
First-class_function
Form of calculus
stochastic calculus is a generalization of stochastic calculus to noncommuting variables. The tools provided by quantum stochastic calculus are of great
Quantum_stochastic_calculus
Function that takes one or more functions as an input or that outputs a function
Combinatory logic Function-level programming Functional programming Kappa calculus - a formalism for functions which excludes higher-order functions Strategy
Higher-order_function
Type of quartic plane curve
geometry, the kappa curve or Gutschoven's curve is a two-dimensional algebraic curve resembling the Greek letter ϰ (kappa). The kappa curve was first
Kappa_curve
Theorem in combinatorial set theory extending Ramsey's theorem to uncountable sets
In partition calculus, part of combinatorial set theory, a branch of mathematics, the Erdős–Rado theorem is a basic result extending Ramsey's theorem to
Erdős–Rado_theorem
Formulas in differential geometry
\mathbf {T} }{\mathrm {d} s}}&=\kappa \mathbf {N} ,\\[4pt]{\frac {\mathrm {d} \mathbf {N} }{\mathrm {d} s}}&=-\kappa \mathbf {T} +\tau \mathbf {B} ,\\[4pt]{\frac
Frenet–Serret_formulas
English Christian theologian, and mathematician
in the development of infinitesimal calculus; in particular, for a proof of the fundamental theorem of calculus. His work centered on the properties
Isaac_Barrow
Extension of ideas in combinatorics to infinite sets
\displaystyle \kappa \rightarrow (\lambda )_{m}^{n}} as a shorthand way of saying that every partition of the set [ κ ] n {\displaystyle [\kappa ]^{n}} of
Infinitary_combinatorics
Infinite cardinal number
the infinity ( ∞ {\displaystyle \infty } ) commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly
Aleph_number
Calculus using a logically rigorous notion of infinitesimal numbers
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard
Nonstandard_analysis
Mathematical measure of how much a curve or surface deviates from flatness
'\end{pmatrix}}={\begin{pmatrix}0&\kappa _{\mathrm {g} }&\kappa _{\mathrm {n} }\\-\kappa _{\mathrm {g} }&0&\tau _{\mathrm {r} }\\-\kappa _{\mathrm {n} }&-\tau _{\mathrm
Curvature
Generalization of tensor fields
{\displaystyle T_{\mu \nu }={\frac {\partial {\bar {x}}^{\kappa }}{\partial {x}^{\mu }}}{\bar {T}}_{\kappa \lambda }{\frac {\partial {\bar {x}}^{\lambda }}{\partial
Tensor_density
Formalism in general relativity
Regge calculus is a formalism for producing simplicial approximations of spacetimes that are solutions to the Einstein field equation. The calculus was
Regge_calculus
Tensor describing energy momentum density in spacetime
electric and magnetic fields Maxwell stress tensor Poynting vector Ricci calculus Segre classification "All the stress–energy tensors explored above were
Stress–energy_tensor
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
delta have found applications in differential geometry and modern tensor calculus, particularly in formulations of gauge theory and topological field models
Kronecker_delta
Symbols for constants, special functions
compensation for the risk borne in investment the α-conversion in lambda calculus the independence number of a graph a placeholder for ordinal numbers in
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
Fourth letter in the Greek alphabet
variable in calculus. A functional derivative in functional calculus. The (ε, δ)-definition of limits, in mathematics and more specifically in calculus. The
Delta_(letter)
Algebraization of first-order logic with equality
d κ λ ) κ , λ < α {\displaystyle (A,+,\cdot ,-,0,1,c_{\kappa },d_{\kappa \lambda })_{\kappa ,\lambda <\alpha }} such that ( A , + , ⋅ , − , 0 , 1 ) {\displaystyle
Cylindric_algebra
Tensor used in general relativity
}+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu },} where Λ {\displaystyle \Lambda } is the cosmological constant and κ {\displaystyle \kappa } is the Einstein gravitational
Einstein_tensor
{\displaystyle \kappa \rightarrow (\kappa ,\aleph _{0})^{2}} . This means that, for every set S {\displaystyle S} of cardinality κ {\displaystyle \kappa } , and
Erdős–Dushnik–Miller_theorem
American mathematics honor society
Kappa Mu Epsilon (ΚΜΕ) is an American mathematics honor society. It was founded by Emily Kathryn Wyant in 1931 at Northeastern Oklahoma State Teachers
Kappa_Mu_Epsilon
Type of cardinal number in mathematics
\kappa } is a regular cardinal if and only if every unbounded subset C ⊆ κ {\displaystyle C\subseteq \kappa } has cardinality κ {\displaystyle \kappa }
Regular_cardinal
Differential geometry measure
vary. The maximal curvature κ 1 {\displaystyle \kappa _{1}} and minimal curvature κ 2 {\displaystyle \kappa _{2}} are known as the principal curvatures of
Mean_curvature
Collection of random variables
processes uses mathematical knowledge and techniques from probability, calculus, linear algebra, set theory, and topology as well as branches of mathematical
Stochastic_process
Field-equations in general relativity
+ Λ g μ ν = κ T μ ν , {\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu },} where G μ ν {\displaystyle G_{\mu \nu }} is the Einstein
Einstein_field_equations
Statistical physics approach
{\displaystyle \exp _{\kappa }(x)={\begin{cases}{\Big (}{\sqrt {1+\kappa ^{2}x^{2}}}+\kappa x{\Big )}^{\frac {1}{\kappa }}&{\text{if }}0<\kappa <1.\\[6pt]\exp(x)&{\text{if
Kaniadakis_statistics
Theorem in set theory
κ i {\displaystyle \kappa _{i}} and λ i {\displaystyle \lambda _{i}} are cardinal numbers with κ i < λ i {\displaystyle \kappa _{i}<\lambda _{i}} , for
Kőnig's_theorem_(set_theory)
Tensor that describes the 4D geometry of spacetime
mathematics of general relativity Mathematics of general relativity Ricci calculus For the details, see Section 2.11, The Metric Tensor and the Classical
Metric tensor (general relativity)
Metric_tensor_(general_relativity)
Function's sensitivity to argument change
a rule of thumb, if the condition number κ ( A ) = 10 k {\displaystyle \kappa (A)=10^{k}} , then up to k {\displaystyle k} digits of accuracy may be lost
Condition_number
Type of infinite number in set theory
notions of an inaccessible cardinal κ {\displaystyle \kappa } describe a cardinality κ {\displaystyle \kappa } which can not be obtained as the cardinality of
Inaccessible_cardinal
Fundamental mechanical principles
states of the system is called the action. Action principles apply the calculus of variation to the action. The action depends on the energy function,
Action_principles
derivative is a generalization of the directional derivative from vector calculus. As with the directional derivative, the covariant derivative is a rule
Introduction to the mathematics of general relativity
Introduction_to_the_mathematics_of_general_relativity
Radius of the circle which best approximates a curve at a given point
{\displaystyle R\equiv \left|{\frac {ds}{d\varphi }}\right|={\frac {1}{\kappa }},} where s is the arc length from a fixed point on the curve, φ is the
Radius_of_curvature
Set of quantities in probability theory
'_{6}={}&\kappa _{6}+6\kappa _{5}\kappa _{1}+15\kappa _{4}\kappa _{2}+15\kappa _{4}\kappa _{1}^{2}+10\kappa _{3}^{2}+60\kappa _{3}\kappa _{2}\kappa _{1}+20\kappa
Cumulant
Study of curves from a differential point of view
plane and the Euclidean space by methods of differential and integral calculus. Many specific curves have been thoroughly investigated using the synthetic
Differentiable_curve
Thirteenth letter in the Greek alphabet
point of a function, as commonly used in the μ-calculus. Free names of a process, as used in the π-calculus. One of the Greeks in mathematical finance, known
Nu_(Greek)
Monte Carlo distribution shifting technique
[e^{(\eta +\theta )X-\kappa (\theta )}]\\&=\log(e^{\kappa (\eta +\theta )-\kappa (\theta )})\\&=\kappa (\eta +\theta )-\kappa (\theta ).\end{aligned}}}
Exponential_tilting
Russian mathematician (1930–2004)
{\displaystyle \inf _{p\in S}|\kappa _{2}(p)-\kappa _{1}(p)|=0,} where κ 1 {\displaystyle \kappa _{1}} and κ 2 {\displaystyle \kappa _{2}} are the principal
Victor_Andreevich_Toponogov
Existence and cardinality of models of logical theories
publication "Über Möglichkeiten im Relativkalkül" [On possibilities in the calculus of relatives] (1915): For every countable signature σ, every σ-sentence
Löwenheim–Skolem_theorem
Theorem in mathematical logic
is finitely consistent. The compactness theorem for the propositional calculus is a consequence of Tychonoff's theorem (which says that the product of
Compactness_theorem
Last letter of the Greek alphabet
usually with a superscript). A variable for a 2-dimensional region in calculus, usually corresponding to the domain of a double integral. In topos theory
Omega
Size of a set in mathematics
infinite cardinal, κ + κ = κ ⋅ κ = κ {\displaystyle \kappa +\kappa =\kappa \cdot \kappa =\kappa } . In this way, infinite cardinal addition and multiplication
Cardinality
Theory of gravitation as curved spacetime
the proportionality constant κ {\displaystyle \kappa } is found to be κ = 8 π G / c 4 {\textstyle \kappa ={8\pi G}/{c^{4}}} , where G {\displaystyle G}
General_relativity
Eleventh letter in the Greek alphabet
to introduce anonymous functions expressed with the concepts of lambda calculus. λ indicates an eigenvalue in the mathematics of linear algebra. In the
Lambda
Model of shear deformation and bending effects
{\displaystyle \kappa } , called the Timoshenko shear coefficient, depends on the geometry. Normally, κ = 5 / 6 {\displaystyle \kappa =5/6} for a rectangular
Timoshenko–Ehrenfest beam theory
Timoshenko–Ehrenfest_beam_theory
Product of the principal curvatures of a surface
curvatures, κ1 and κ2, at the given point: K = κ 1 κ 2 . {\displaystyle K=\kappa _{1}\kappa _{2}.} For example, a sphere of radius r has Gaussian curvature 1/r2
Gaussian_curvature
Large cardinal number
notation of the partition calculus, κ {\displaystyle \kappa } is α {\displaystyle \alpha } -Erdős if κ → ( α ) < ω {\displaystyle \kappa \rightarrow (\alpha
Erdős_cardinal
Fifth letter of the Greek alphabet
to extensometer testing of metallic materials. In mathematics (In early calculus or nonstandard analysis) An infinitesimally small positive quantity is
Epsilon
Foundational law of electromagnetism relating electric field and charge distributions
{\displaystyle F^{\kappa 0}{\sqrt {-g}}\,\mathrm {d} S_{\kappa }} where c {\displaystyle c} is the speed of light; F κ 0 {\displaystyle F^{\kappa 0}} denotes
Gauss's_law
Twenty-first letter in the Greek alphabet
needed] A common symbol for the parametrization of a surface in vector calculus. In Lacanian algebra, Φ stands for the imaginary phallus and also represents
Phi
Concept in theoretical mathematical physics
differential calculus on the quantum spacetime algebra, compatible with the (quantum) symmetry and preferably reducing to the usual differential calculus as λ
Quantum_spacetime
Speed of convergence of a mathematical sequence
. . . ) . {\displaystyle y_{n}=y_{0}(1-h\kappa )^{n}=y_{0}\left(1-nh\kappa +{\frac {n(n-1)}{2}}h^{2}\kappa ^{2}+....\right).} The exact analytical solution
Rate_of_convergence
American astronomer
television program, Exploration of the Universe. He founded the Phi Beta Kappa chapter at Columbia's School of General Studies. A scholarship was established
Lloyd_Motz
Seventh letter in the Greek alphabet
constellation. See Bayer designation. Mathematics, η-reduction in lambda calculus. Mathematics, the Dirichlet eta function, Dedekind eta function, and Weierstrass
Eta
United States Army general (1922–2017)
second year at the academy, he studied more complicated subjects like calculus, electrical engineering, thermodynamics and historic military campaigns
Hal_Moore
Infinite set that is not countable
cardinal κ {\displaystyle \kappa } are equivalent: κ ≰ ℵ 0 ; {\displaystyle \kappa \nleq \aleph _{0};} κ > ℵ 0 ; {\displaystyle \kappa >\aleph _{0};} and κ
Uncountable_set
Hilbert–Einstein Lagrangian
2 κ R − g d 4 x {\displaystyle {\mathcal {L}}_{\mathrm {G} }={1 \over 2\kappa }R{\sqrt {-g}}\,\mathrm {d} ^{4}x} , is the tensor density: U α β ( L G
Komar_superpotential
Branch of physics
_{ij}\nabla \cdot \mathbf {v} \right)+\kappa \delta _{ij}\nabla \cdot \mathbf {v} } where κ {\displaystyle \kappa } is the second viscosity coefficient
Fluid_mechanics
Force directed to the center of rotation
text by Lamb: Horace Lamb (1897). An Elementary Course of Infinitesimal Calculus. University Press. p. 406. ISBN 978-1-108-00534-0. osculating circle. {{cite
Centripetal_force
Method for load calculation in construction
up to that point, and depends on flexural rigidity. Through the use of calculus, and boundary conditions describing the beam's curvature at its supports
Euler–Bernoulli_beam_theory
Model parameters in mathematical finance
In mathematical finance, the Greeks are the quantities (known in calculus as partial derivatives; first-order or higher) representing the sensitivity of
Greeks_(finance)
Function uniquely mapping two numbers into a single number
{\displaystyle \kappa ^{2}=\kappa } holds for all infinite cardinal κ {\displaystyle \kappa } . Conversely, the statement " κ 2 = κ {\displaystyle \kappa ^{2}=\kappa
Pairing_function
Spatial geometry with curvature
− 1 R 2 {\displaystyle \kappa ^{-1}R^{2}} where R 2 {\displaystyle R^{2}\,} now is positive and κ ≡ ± 1 {\displaystyle \kappa \equiv \pm 1} . We can now
Curved_space
Proposition in mathematical logic
consistent that 2 κ > κ + {\displaystyle 2^{\kappa }>\kappa ^{+}} holds for every infinite cardinal κ {\displaystyle \kappa } . Later Woodin extended this by showing
Continuum_hypothesis
American mathematician (1871–1958)
The Dependence of the Focal Point on Curvature in Space Problems of the Calculus of Variations. She began teaching at the University of Kansas in 1910.
Marion_Ballantyne_White
Exterior algebraic map taking tensors from p forms to n-p forms
\\{\star }(dx^{\mu }\wedge dx^{\nu })&=\eta ^{\mu \kappa }\eta ^{\nu \lambda }\varepsilon _{\kappa \lambda \rho \sigma }{\frac {1}{2!}}dx^{\rho }\wedge
Hodge_star_operator
Statement in mathematical combinatorics
{\displaystyle \kappa } axiomatically defined to satisfy the related formula: κ → ( κ ) 2 < ω {\displaystyle \kappa \rightarrow (\kappa )_{2}^{<\omega
Ramsey's_theorem
Surface specified with parameters
representation. Surfaces that occur in two of the main theorems of vector calculus, Stokes' theorem, and the divergence theorem, are frequently given in a
Parametric_surface
American mathematics honor society
least the equivalent of two semesters of calculus and two additional courses in mathematics, at or above the calculus level, all of which lead to the fulfillment
Pi_Mu_Epsilon
Special function defined by an integral
curvature κ can be expressed as κ = 1 R = d θ d t = 2 t . {\displaystyle \kappa ={\frac {1}{R}}={\frac {d\theta }{dt}}=2t.} Thus the rate of change of curvature
Fresnel_integral
Element of a nonstandard model of the reals, which can be infinite or infinitesimal
Informal notations for non-real quantities have historically appeared in calculus in two contexts: as infinitesimals, like d x {\displaystyle dx} , and as
Hyperreal_number
Type of statistical measure over subsets of a dataset
_{\varepsilon \to 0}M_{f,\ \varepsilon }=f} by fundamental theorem of calculus and L'Hôpital's rule. Continuous moving average sine and polynom - visualization
Moving_average
Tensor in differential geometry
topological arguments. Curvature of Riemannian manifolds Scalar curvature Ricci calculus Ricci decomposition Ricci-flat manifold Christoffel symbols Introduction
Ricci_curvature
Size of a possibly infinite set
κ ≤ ν + μ ) ) . {\displaystyle (\kappa \leq \mu )\rightarrow ((\kappa +\nu \leq \mu +\nu ){\mbox{ and }}(\nu +\kappa \leq \nu +\mu )).} Assuming the axiom
Cardinal_number
Property of all triangles on a Euclidean plane
n + 1 . {\displaystyle \sin _{\kappa }(x)=x-{\frac {\kappa }{3!}}x^{3}+{\frac {\kappa ^{2}}{5!}}x^{5}-{\frac {\kappa ^{3}}{7!}}x^{7}+\cdots =\sum _{n=0}^{\infty
Law_of_sines
American political philosopher (1938–2002)
claims, namely his counterfactual theory of knowledge. It won Phi Beta Kappa society's Ralph Waldo Emerson Award the following year. Nozick's other work
Robert_Nozick
Dirac equation for self-interacting fermions
See Ricci calculus and Van der Waerden notation for the notation. In quantum field theory, the nonlinear Dirac equation is a model of self-interacting
Nonlinear_Dirac_equation
Mathematics of smooth surfaces
is well illustrated by the non-linear Euler–Lagrange equations in the calculus of variations: although Euler developed the one variable equations to understand
Differential geometry of surfaces
Differential_geometry_of_surfaces
Type of average of a collection of numbers
with n {\displaystyle n} numbers being averaged). In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average
Arithmetic_mean
Axiom of set theory
determined. Every infinite cardinal κ {\displaystyle \kappa } satisfies 2 κ = κ {\displaystyle 2\kappa =\kappa } . Measure theory The Vitali theorem: There exist
Axiom_of_choice
Tensor field in Riemannian geometry
p. 154. ISBN 978-0-691-08542-5. Synge J.L., Schild A. (1949). Tensor Calculus. first Dover Publications 1978 edition. pp. 83, 107. ISBN 978-0-486-63612-2
Riemann_curvature_tensor
Mathematical proposition equivalent to the axiom of choice
ordinal κ {\displaystyle \kappa } that is bijective with P . {\displaystyle P.} Take α = κ + {\displaystyle \alpha =\kappa ^{+}} , the successor cardinal
Zorn's_lemma
Self-similar growth curve
This property was first realized by Evangelista Torricelli even before calculus had been invented. Sector area: A = r ( φ 2 ) 2 − r ( φ 1 ) 2 4 k {\displaystyle
Logarithmic_spiral
Curve that winds around a central point
and tan α {\displaystyle \tan \alpha } the polar slope. From vector calculus in polar coordinates one gets the formula tan α = r ′ r . {\displaystyle
Spiral
Physical theory describing classical fields
Modern field theories are usually expressed using the mathematics of tensor calculus. A more recent alternative mathematical formalism describes classical fields
Classical_field_theory
Branch of physics which studies the behavior of materials modeled as continuous media
=\kappa _{t}(\mathbf {X} ).} This function needs to have various properties so that the model makes physical sense. κ t ( ⋅ ) {\displaystyle \kappa _{t}(\cdot
Continuum_mechanics
Fundamental theorem in probability theory and statistics
its tails". The abstract of the paper On the central limit theorem of calculus of probability and the problem of moments by Pólya in 1920 translates as
Central_limit_theorem
Mode of convergence of an infinite series
analysis Fubini's theorem – Conditions for switching order of integration in calculus Modes of convergence (annotated index) – Property of a sequence or seriesPages
Absolute_convergence
All numbers between two given numbers
cardinality κ {\displaystyle \kappa } is embeddable into the product [ 0 , 1 ] κ {\displaystyle [0,1]^{\kappa }} of κ {\displaystyle \kappa } copies of the intervals
Interval_(mathematics)
German American mathematician (born 1931)
2023) was a German-born American mathematician and former professor of calculus, finite mathematics, and measure and integration at George Washington University
Dagmar_R._Henney
ultrafilter is the most basic case of an extender. A ( κ , λ ) {\displaystyle (\kappa ,\lambda )} -extender can be defined as an elementary embedding of some
Extender_(set_theory)
Aspect of general relativity
Λ g μ ν = κ T μ ν , {\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }\,=\kappa T_{\mu \nu },} where G μ ν {\displaystyle G_{\mu \nu }} is the Einstein
Solutions of the Einstein field equations
Solutions_of_the_Einstein_field_equations
Superconductivity theory
which κ < 1 / 2 {\displaystyle \kappa <1/{\sqrt {2}}} are of type I, and those for which κ > 1 / 2 {\displaystyle \kappa >1/{\sqrt {2}}} are of type II
Ginzburg–Landau_theory
Geometric structure
bundle S = P × κ Δ n {\displaystyle {\mathbf {S} }={\mathbf {P} }\times _{\kappa }\Delta _{n}\,} associated to the spin structure P {\displaystyle {\mathbf
Spinor_bundle
KAPPA CALCULUS
KAPPA CALCULUS
Boy/Male
Hindu, Indian, Tamil, Telugu
Of Vishnu and Shiva; Ayya means Vishnu and Appa means Shiva
Girl/Female
Gujarati, Indian
Meaningful
Girl/Female
Hindu, Indian
Father; Daddy
Boy/Male
Tamil
Attitude
Boy/Male
Hindu, Indian
Attitude
Surname or Lastname
English
English : from Middle English cappe ‘cap’, ‘hat’ (Old English cæppe), hence a metonymic occupational name for a maker of caps and hats, or a nickname for someone who wore distinctive headgear. Compare Capper.Americanized spelling of German Kapp.
Boy/Male
Tamil
Able, Fit
Boy/Male
Hindu, Indian, Kannada, Marathi, Sanskrit, Telugu
Able; Fit
Surname or Lastname
English
English : unexplained; perhaps from either of two medicinal and edible plants commonly known by this name (Arctium lappa and A. minus). However, the word is not recorded in OED before 1597, rather too late for surname formation.
Surname or Lastname
English
English : topographic name for someone who lived by a maple tree, Middle English mapel (Old English mapul).French : from Latin mapula, a diminutive of mappa ‘piece of cloth’, ‘napkin’, presumably a metonymic occupational name for a cloth merchant or a weaver.
Girl/Female
Gujarati, Hindu, Indian
Thought; Able; Fit
Boy/Male
Indian, Sanskrit
Universal Father
Surname or Lastname
English
English : variant spelling of Chappell.French : from a diminutive of Old French chape ‘hooded cloak’, ‘cape’, ‘hood’, or ‘hat’ (from Late Latin cappa, capa), hence a metonymic occupational name for a maker of cloaks or hats, or a nickname for a habitual wearer of a distinctive cloak or hat.
KAPPA CALCULUS
KAPPA CALCULUS
KAPPA CALCULUS
KAPPA CALCULUS
KAPPA CALCULUS
KAPPA CALCULUS
KAPPA CALCULUS