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| Constants | Vector Functions | |
| Basic Functions | Functions of User-Defined Functions | |
| Trigonometric Functions | Other Functions | |
| Advanced Mathematical Functions |
ConstantsBoltzmann() = 1.3806504e-23 J / degK CLight() = 299792458.0 m/s (speed of light) euler() = 0.5772156649015328606065120900824024310422 gas() = 8.31434 J / mol / degK = kg m^2 / s^2 degK mol GEarth() = 6.67428e11 m^3 / kg s^2 (Earth's gravitational constant) grav() = 9.806652 m / s^2 pi() = 3.1415926535897932384626433832795028841972 Planck() = 6.62606896e-34 kg m^2 / s (Planck's constant) StefanBoltzmann() = 5.670400e-8 W m^2 / degK^4 Basic Functionsabs(x) = absolute value of x ceil(x) = round x up to nearest integer exp(x) = exponential of x floor(x) = round x down to nearest integer int(x) = round x down to nearest integer LinInterp(x1, y1, x2, y2, x) = y1 + (x - x1) * (y2 - y1) / (x2 - x1) ln(x) = natural logarithm of x log(x) = natural logarithm of x log10(x) = log base 10 of x mod(x, y) = floating point remainder of y / x Normsdist(z) = standard normal cumulative distribution (mean = 0, stdev = 1) Normsinv(z) = inverse of the standard normal cumulative distribution (mean = 0, stdev = 1) Number(x, units) = dimensionless value of x in units round(x) = round x to nearest (up or down) integer sign(x) = sign of x sqrt(x) = square root of x Trigonometric Functionsacos(x) = arccosine of x acot(x) = arccotangent of x acsc(x) = arccosecant of x asec(x) = arcsecant of x asin(x) = arcsine of x atan(x) = arctangent of x atan2(y, x) = arctangent in correct quadrant of y/x cos(x) = cosine of x cosh(x) = hyperbolic cosine of x cot(x) = cotangent of x coth(x) = hyperbolic cotangent of x csc(x) = cosecant of x csch(x) = hyperbolic cosecant of x sec(x) = secant of x sech(x) = hyperbolic secant of x sin(x) = sine of x sinh(x) = hyperbolic sine of x tan(x) = tangent of x tanh(x) = hyperbolic tangent of x Advanced Mathematical FunctionsAiryAi(x) = Airy function Ai(x) AiryBi(x) = Airy function Bi(x) BesselI(n, x) = modified Bessel function of the first kind, I(n, x) BesselJ(n, x) = Bessel function of the first kind, J(n, x) BesselK(n, x) = modified Bessel function of the second kind, K(n, x) BesselY(n, x) = Bessel function of the second kind, Y(n, x) BetaFunc(z, w) = beta function B(z, w) EllipticE(phi, k) = Legendre elliptic integral of the second kind, E(phi, k) EllipticF(phi, k) = Legendre elliptic integral of the first kind F(phi, k) EllipticPi(phi, n, k) = Legendre elliptic integral of the third kind, Pi(phi, n, k) Erf(x) = error function Erfc(x) = complimentary error function ExpInt(x) = exponential integral E(1, x) ExpIntEi(x) = exponential integral Ei(x) ExpIntN(n, x) = exponential integral E(n, x) GammaFunc(x) = gamma function of x GammaPFunc(a, x) = incomplete Gamma function P(a, x) GammaQFunc(a, x) = incomplete Gamma function Q(a, x) = 1 - P(a, x) IncBetaFunc(a, b, x) = incomplete Beta function I(a, b, x) JacobiCN(u, kc) = Jacobian elliptic function, cn(u, kc) JacobiDN(u, kc) = Jacobian elliptic function, dn(u, kc) JacobiSN(u, kc) = Jacobian elliptic function, sn(u, kc) LogGammaFunc(x) = natural log of the gamma function of x Vector Functionsangle(x, y) = angle between vectors x and y component(x, n) = the nth componet of a vector x cross(x, y) = cross product of vectors x and y dot(x, y) = dot product of vectors x and y mag(x) = magnitude of vector x PolarAngle(x) = atan2(x[2], x[1]) = atan2(component(x, 2), component(x, 1)) PolarVec(f, q) = [cos(q), sin(q), 0] * f Functions of User-Defined Functionsfmax(y, x1, x2, ...) = choose x1, x2, ... to maximize y fmin(y, x1, x2, ...) = choose x1, x2, ... to minimize y func(x1, val1, x2, val2, ...) = evaluate func(x1 = val1, x2 = val2, ...) solve(y1, y2, ..., x1, x2 ... ) = choose x1, x2, ... such that y1 = y2 = ... 0 Other FunctionsBEGIN = marks the start of a user-defined function cgs(e1, e2, ...) = use centimeter-gram-second default units with exceptions e1, e2, ... (args are optional) DefUnit(name, x) = user defined unit 'name' set = x END = marks the end of a user-defined function FPS(e1, e2, ...) = use Foot-Pound-Second default units with exceptions e1, e2, ... (args are optional) IPS(e1, e2, ...) = use Inch-Pound-Second default units with exceptions e1, e2, ... (args are optional) MKS(e1, e2, ...) = use Meter-Kilogram-Second default units with exceptions e1, e2, ... (args are optional) PrintFunc = print the currently defined user-function |