Vista previa en español

Fórmulas matemáticas

Consulta fórmulas seleccionadas con LaTeX, variables y enlace a la referencia inglesa.

Esta página permanece fuera del índice de búsqueda hasta completar una revisión lingüística humana. Los datos matemáticos proceden de la referencia inglesa.

Arc Length from a Radian Angles=r\thetaVer fórmula y variables Arithmetic Sequence Formulaa_n=a_1+(n-1)dVer fórmula y variables Bayes’ TheoremP(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}Ver fórmula y variables Binet Formula for Fibonacci NumbersF_n=\frac{\varphi^n-(1-\varphi)^n}{\sqrt5}Ver fórmula y variables Binomial Probability FormulaP(X=k)=\binom{n}{k}p^k(1-p)^{n-k}Ver fórmula y variables Binomial Theorem(a+b)^n=\sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^kVer fórmula y variables Catalan NumberC_n=\frac{1}{n+1}\binom{2n}{n}Ver fórmula y variables Cauchy–Schwarz Inequality|\langle x,y\rangle|^2\le \langle x,x\rangle\langle y,y\rangleVer fórmula y variables Chain Rule\frac{d}{dx}f(g(x))=f'(g(x))g'(x)Ver fórmula y variables Logarithm Change of Base\log_b x=\frac{\log_k x}{\log_k b}Ver fórmula y variables Chi-Square Statistic\chi^2=\sum\frac{(O-E)^2}{E}Ver fórmula y variables Area of a CircleA=\pi r^2Ver fórmula y variables Circumference of a CircleC=2\pi r=\pi dVer fórmula y variables Circular Arc Lengths=r\thetaVer fórmula y variables Combination Formula\binom{n}{r}=\frac{n!}{r!(n-r)!}Ver fórmula y variables Operator Commutator[A,B]=AB-BAVer fórmula y variables Complex Number Modulus|z|=\sqrt{a^2+b^2},\quad z=a+biVer fórmula y variables Complex Number Polar Formz=r(\cos\theta+i\sin\theta)=re^{i\theta}Ver fórmula y variables Compound Interest FormulaA=P\left(1+\frac{r}{n}\right)^{nt}Ver fórmula y variables Conditional ProbabilityP(A\mid B)=\frac{P(A\cap B)}{P(B)}Ver fórmula y variables Cone VolumeV=\frac{1}{3}\pi r^2hVer fórmula y variables Mean Confidence Interval\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt n}Ver fórmula y variables Cosine Double-Angle Identity\cos(2\theta)=\cos^2\theta-\sin^2\thetaVer fórmula y variables Coulomb's LawF=k\frac{|q_1q_2|}{r^2}Ver fórmula y variables Covariance\operatorname{Cov}(X,Y)=E[(X-E[X])(Y-E[Y])]Ver fórmula y variables Covariance Matrix\Sigma=\mathbb E[(X-\mu)(X-\mu)^T]Ver fórmula y variables Cramer's Rule for a 2×2 Systemx=\frac{d_1b_2-b_1d_2}{a_1b_2-b_1a_2},\quad y=\frac{a_1d_2-d_1a_2}{a_1b_2-b_1a_2}Ver fórmula y variables Cross Product Components\mathbf a\times\mathbf b=\begin{bmatrix}a_2b_3-a_3b_2\\a_3b_1-a_1b_3\\a_1b_2-a_2b_1\end{bmatrix}Ver fórmula y variables Curl\nabla\times\mathbf FVer fórmula y variables Total Surface Area of a CylinderS=2\pi r^2+2\pi rhVer fórmula y variables Cylinder VolumeV=\pi r^2hVer fórmula y variables De Morgan Law for Logic\neg(p\land q)\equiv(\neg p)\lor(\neg q)Ver fórmula y variables De Morgan Law for Sets(A\cup B)^c=A^c\cap B^cVer fórmula y variables Density Formula\rho=\frac{m}{V}Ver fórmula y variables Derivative of Cosine\frac{d}{dx}\cos x=-\sin xVer fórmula y variables Derivative Definitionf'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}Ver fórmula y variables Derivative of Exponential\frac{d}{dx}e^x=e^xVer fórmula y variables Derivative of Natural Logarithm\frac{d}{dx}\ln x=\frac{1}{x}Ver fórmula y variables Derivative of Sine\frac{d}{dx}\sin x=\cos xVer fórmula y variables Distance Formulad=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}Ver fórmula y variables Divergence\nabla\cdot\mathbf F=\sum_i\frac{\partial F_i}{\partial x_i}Ver fórmula y variables Divergence Theorem\iiint_V \nabla\cdot\mathbf F\,dV=\iint_{\partial V}\mathbf F\cdot\mathbf n\,dSVer fórmula y variables Vector Dot Product\mathbf{a}\cdot\mathbf{b}=\sum_{i=1}^{n}a_ib_i=\|\mathbf{a}\|\|\mathbf{b}\|\cos\thetaVer fórmula y variables Eigenvalue EquationA\mathbf v=\lambda\mathbf vVer fórmula y variables Einstein Summation Conventiona_i b^i=\sum_i a_i b^iVer fórmula y variables Electric PowerP=VIVer fórmula y variables Area of an EllipseA=\pi abVer fórmula y variables Euclidean Algorithm\gcd(a,b)=\gcd(b,a\bmod b)Ver fórmula y variables Euler Identitye^{i\pi}+1=0Ver fórmula y variables Euler Methody_{n+1}=y_n+h f(t_n,y_n)Ver fórmula y variables Euler Totient Formula for Prime Powers\varphi(p^k)=p^k-p^{k-1}Ver fórmula y variables Exponent Product Rulea^m a^n=a^{m+n}Ver fórmula y variables Exponent Quotient Rule\frac{a^m}{a^n}=a^{m-n}Ver fórmula y variables Fourier Transform\hat f(\omega)=\int_{-\infty}^{\infty}f(t)e^{-i\omega t}\,dtVer fórmula y variables Fundamental Theorem of Calculus\int_a^b f(x)\,dx=F(b)-F(a),\quad F'=fVer fórmula y variables Geometric MeanG=\left(\prod_{i=1}^{n}x_i\right)^{1/n}Ver fórmula y variables Geometric Distribution PMFP(X=k)=(1-p)^{k-1}pVer fórmula y variables Geometric Sequence Formulaa_n=a_1r^{n-1}Ver fórmula y variables Gradient\nabla f=\left(\frac{\partial f}{\partial x_1},\ldots,\frac{\partial f}{\partial x_n}\right)Ver fórmula y variables Gradient Descent Updatex_{k+1}=x_k-\eta\nabla f(x_k)Ver fórmula y variables Gravitational Potential EnergyU=mghVer fórmula y variables Handshake Lemma\sum_{v\in V}\deg(v)=2|E|Ver fórmula y variables Harmonic MeanH=\frac{n}{\sum_{i=1}^{n}1/x_i}Ver fórmula y variables Heat Equation\frac{\partial u}{\partial t}=\alpha\nabla^2uVer fórmula y variables Heron FormulaA=\sqrt{s(s-a)(s-b)(s-c)},\quad s=\frac{a+b+c}{2}Ver fórmula y variables Ideal Gas LawPV=nRTVer fórmula y variables Two-Set Inclusion–Exclusion Formula|A\cup B|=|A|+|B|-|A\cap B|Ver fórmula y variables Inclusion–Exclusion for Two Sets|A\cup B|=|A|+|B|-|A\cap B|Ver fórmula y variables Integral of Exponential\int e^x\,dx=e^x+CVer fórmula y variables Integral Power Rule\int x^n\,dx=\frac{x^{n+1}}{n+1}+CVer fórmula y variables Integration by Parts\int u\,dv=uv-\int v\,duVer fórmula y variables Two by Two Matrix InverseA^{-1}=\frac{1}{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}Ver fórmula y variables Jensen’s Inequalityf(\mathbb E[X])\leq\mathbb E[f(X)]Ver fórmula y variables Kinetic EnergyK=\frac{1}{2}mv^2Ver fórmula y variables Kullback–Leibler DivergenceD_{\mathrm{KL}}(p\|q)=\sum_x p(x)\log\frac{p(x)}{q(x)}Ver fórmula y variables Single-Constraint Lagrange Condition\nabla f(x)=\lambda\nabla g(x)Ver fórmula y variables Laplace TransformF(s)=\int_0^{\infty}f(t)e^{-st}\,dtVer fórmula y variables Law of Cosinesc^2=a^2+b^2-2ab\cos CVer fórmula y variables Law of Sines\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}Ver fórmula y variables Law of Total ProbabilityP(A)=\sum_i P(A\mid B_i)P(B_i)Ver fórmula y variables Level Loan PaymentPMT=P\frac{r(1+r)^n}{(1+r)^n-1}Ver fórmula y variables Logarithm Product Rule\log_b(xy)=\log_b x+\log_b yVer fórmula y variables Logistic Growth FunctionP(t)=\frac{K}{1+Ae^{-rt}}Ver fórmula y variables Mass Energy EquivalenceE=mc^2Ver fórmula y variables Matrix Multiplication(AB)_{ij}=\sum_k A_{ik}B_{kj}Ver fórmula y variables Matrix Trace\operatorname{tr}(A)=\sum_{i=1}^{n}a_{ii}Ver fórmula y variables Mean Squared ErrorMSE=\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat y_i)^2Ver fórmula y variables Midpoint FormulaM=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)Ver fórmula y variables Molarity FormulaM=\frac{n}{V}Ver fórmula y variables Linear Momentum\mathbf p=m\mathbf vVer fórmula y variables Mutual InformationI(X;Y)=\sum_{x,y}p(x,y)\log\frac{p(x,y)}{p(x)p(y)}Ver fórmula y variables Newton–Raphson Iterationx_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}Ver fórmula y variables Newton Second Law\mathbf F_{net}=m\mathbf aVer fórmula y variables Normal Distribution Densityf(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}Ver fórmula y variables Ohm LawV=IRVer fórmula y variables Parallelogram AreaA=bhVer fórmula y variables Pearson Correlationr=\frac{\sum (x_i-\bar x)(y_i-\bar y)}{\sqrt{\sum(x_i-\bar x)^2\sum(y_i-\bar y)^2}}Ver fórmula y variables Percentage Change Formula\%\text{ change}=\frac{\text{new}-\text{old}}{|\text{old}|}\times100\%Ver fórmula y variables Permutation FormulaP(n,r)=\frac{n!}{(n-r)!}Ver fórmula y variables Pigeonhole Principle Bound\max_i n_i\ge\left\lceil\frac{N}{m}\right\rceilVer fórmula y variables Point-Slope Formy-y_1=m(x-x_1)Ver fórmula y variables Poisson Probability Mass FunctionP(X=k)=\frac{e^{-\lambda}\lambda^k}{k!}Ver fórmula y variables Population Variance\sigma^2=\frac{1}{N}\sum_{i=1}^{N}(x_i-\mu)^2Ver fórmula y variables Derivative Power Rule\frac{d}{dx}x^n=nx^{n-1}Ver fórmula y variables Present ValuePV=\frac{FV}{(1+r)^n}Ver fórmula y variables Pressure FormulaP=\frac{F}{A}Ver fórmula y variables Probability Addition RuleP(A\cup B)=P(A)+P(B)-P(A\cap B)Ver fórmula y variables Probability Complement RuleP(A^c)=1-P(A)Ver fórmula y variables Product Rule(fg)'=f'g+fg'Ver fórmula y variables Pythagorean Theorema^2+b^2=c^2Ver fórmula y variables Pythagorean Trigonometric Identity\sin^2\theta+\cos^2\theta=1Ver fórmula y variables Quadratic Discriminant\Delta=b^2-4acVer fórmula y variables Quadratic Formulax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}Ver fórmula y variables Quotient Rule\left(\frac{f}{g}\right)\prime=\frac{f\prime g-fg\prime}{g^2}Ver fórmula y variables Rectangle AreaA=lwVer fórmula y variables Rectangle PerimeterP=2(l+w)Ver fórmula y variables Rectangular Prism VolumeV=lwhVer fórmula y variables Simple Regression Slopeb_1=\frac{\sum(x_i-\bar x)(y_i-\bar y)}{\sum(x_i-\bar x)^2}Ver fórmula y variables Sample Mean\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_iVer fórmula y variables Sample Variances^2=\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^2Ver fórmula y variables Area of a Circular SectorA=\frac12 r^2\thetaVer fórmula y variables Shannon EntropyH(X)=-\sum_i p_i\log_2 p_iVer fórmula y variables Simple Harmonic Motionx(t)=A\cos(\omega t+\varphi)Ver fórmula y variables Sine Double-Angle Identity\sin(2\theta)=2\sin\theta\cos\thetaVer fórmula y variables Slope-Intercept Formy=mx+bVer fórmula y variables Sphere Surface AreaA=4\pi r^2Ver fórmula y variables Volume of a SphereV=\frac{4}{3}\pi r^3Ver fórmula y variables Standard Error of the MeanSE_{\bar{x}}=\frac{s}{\sqrt{n}}Ver fórmula y variables Sum of the First n Cubes\sum_{k=1}^{n}k^3=\left(\frac{n(n+1)}{2}\right)^2Ver fórmula y variables Sum of the First n Positive Integers\sum_{k=1}^{n}k=\frac{n(n+1)}{2}Ver fórmula y variables Sum of the First n Squares\sum_{k=1}^{n}k^2=\frac{n(n+1)(2n+1)}{6}Ver fórmula y variables Taylor Seriesf(x)=\sum_{n=0}^{\infty}\frac{f^{(n)}(a)}{n!}(x-a)^nVer fórmula y variables Three by Three Determinant\det A=a(ei-fh)-b(di-fg)+c(dh-eg)Ver fórmula y variables Time-Dependent Schrödinger Equationi\hbar\frac{\partial}{\partial t}|\psi(t)\rangle=\hat H|\psi(t)\rangleVer fórmula y variables Trapezoid AreaA=\frac{1}{2}(b_1+b_2)hVer fórmula y variables Tree Edge Count|E|=|V|-1Ver fórmula y variables Area of a TriangleA=\frac{1}{2}bhVer fórmula y variables Triangle Inequality for Norms\|x+y\|\le \|x\|+\|y\|Ver fórmula y variables 2×2 Matrix Determinant\det\begin{pmatrix}a&b\\c&d\end{pmatrix}=ad-bcVer fórmula y variables Euclidean Vector Norm\|\mathbf v\|_2=\sqrt{\sum_i v_i^2}Ver fórmula y variables Vector Projection\operatorname{proj}_{\mathbf b}\mathbf a=\frac{\mathbf a\cdot\mathbf b}{\mathbf b\cdot\mathbf b}\mathbf bVer fórmula y variables Quadratic Vertex Formy=a(x-h)^2+kVer fórmula y variables Wave Speedv=f\lambdaVer fórmula y variables Weighted Mean\bar x_w=\frac{\sum_i w_ix_i}{\sum_i w_i}Ver fórmula y variables Z-Score Formulaz=\frac{x-\mu}{\sigma}Ver fórmula y variables