MMP:010117The symmetric matrix A=[[5,2],[2,2]] has principal values 6 and 1 with tan(2θ)=4/3Mathematical Methods Symmetric Tensor Principal AxesMathematical Methods Quadratic Form InvariantsPrivateLabels unavailablePrivate saving unavailableVector calculus, tensors, and coordinate systemsMathematical Methods for Physics · Mixed reviewProgress not loaded
MMP:010118The frame a1=(2,0,0), a2=(1,1,0), a3=(0,1,3) has det G=36 and dual a^1=(1/2,-1/2,1/6)Mathematical Methods Oblique Metric TensorMathematical Methods Reciprocal Basis ComponentsPrivateLabels unavailablePrivate saving unavailableVector calculus, tensors, and coordinate systemsMathematical Methods for Physics · Mixed reviewProgress not loaded
MMP:010129Rodrigues rotation by π/2 about (1,2,2)/3 is (1/9)[[1,-4,8],[8,4,1],[-4,7,4]]Mathematical Methods Skew Generator RodriguesMathematical Methods Rotation Axis InvariantsPrivateLabels unavailablePrivate saving unavailableVector calculus, tensors, and coordinate systemsMathematical Methods for Physics · Mixed reviewProgress not loaded
MMP:010225The J0 Frobenius sum through m=4 at x=1 is 12537/16384 and brackets J0(1) from below by 1/14745600Mmp Bessel J0 FrobeniusMmp Alternating Truncation BoundPrivateLabels unavailablePrivate saving unavailableODEs, Sturm-Liouville theory, and Green functionsMathematical Methods for Physics · Mixed reviewProgress not loaded
MMP:010226x^4=(8/35)P4+(4/7)P2+(1/5)P0 is Gauss-3 exact, while x^6 misses the integral 2/7 by 8/175Mmp Legendre X4 ExpansionMmp Three Point Gauss ExactnessPrivateLabels unavailablePrivate saving unavailableODEs, Sturm-Liouville theory, and Green functionsMathematical Methods for Physics · Mixed reviewProgress not loaded
MMP:010327Inverse Laplace of 1/[(s+1)^2(s+3)] is (1/4)e^{-3t}-(1/4)e^{-t}+(1/2)t e^{-t} with mean 7/3Mathematical Methods Inverse Laplace Repeated PolesMathematical Methods Laplace Moment Mean VariancePrivateLabels unavailablePrivate saving unavailableFourier and Laplace methodsMathematical Methods for Physics · Mixed reviewProgress not loaded
MMP:010328Length-4 circular convolution of (1,2,0,-1) with (1,0,1,0) is (1,1,1,1) and aliases the linear (1,2,1,1,0,-1)Mathematical Methods Negative Exponent Dft BinsMathematical Methods Circular Versus Linear AliasingPrivateLabels unavailablePrivate saving unavailableFourier and Laplace methodsMathematical Methods for Physics · Mixed reviewProgress not loaded
MMP:010331The causal solution of u_{n+2}-3u_{n+1}+2u_n=1 with u_0=u_1=0 is 2^n-n-1, ROC |z|>2Mathematical Methods Forced Recurrence Closed FormMathematical Methods Unilateral Z Transform RocPrivateLabels unavailablePrivate saving unavailableFourier and Laplace methodsMathematical Methods for Physics · Mixed reviewProgress not loaded
MMP:010419The UHP residues of x^2/[(x^2+1)(x^2+4)] at i and 2i sum to -i/6 and the line integral is π/3Mathematical Methods Rational Partial FractionsMathematical Methods Uhp Residue Theorem ArcPrivateLabels unavailablePrivate saving unavailableComplex-variable and asymptotic methodsMathematical Methods for Physics · Mixed reviewProgress not loaded
MMP:010420The keyhole integral of x^{1/3}/(1+x^2) from 0 to ∞ equals (π/2)csc(2π/3)=π/√3Mathematical Methods Keyhole Branch ResiduesMathematical Methods Beta Reflection MellinPrivateLabels unavailablePrivate saving unavailableComplex-variable and asymptotic methodsMathematical Methods for Physics · Mixed reviewProgress not loaded
MMP:010430The [2/2] Padé of e^z at z=-1 is 7/19, erring from e^{-1} by 0.0005416114601366View access optionsMathematical Methods Diagonal Pade ExponentialMathematical Methods Pade Poles Reciprocity ErrorPrivateLabels unavailablePrivate saving unavailableComplex-variable and asymptotic methodsMathematical Methods for Physics · Mixed reviewProgress not loaded
MMP:010521The disk extension of 3+2cos2θ-4sin3θ is 3+2r^2 cos2θ-4r^3 sin3θ with energy 56πView access optionsMathematical Methods Disk Harmonic ModesMathematical Methods Dirichlet TO Neumann EnergyPrivateLabels unavailablePrivate saving unavailablePDE classification and boundary-value structureMathematical Methods for Physics · Mixed reviewProgress not loaded
MMP:010522The 2-by-2 five-point Dirichlet Laplace system with b=(1,4,5,14) has u=(13,21,23,39)/8 and Jacobi radius 1/2View access optionsMmp Discrete Five Point DirichletMmp Jacobi Grid SpectrumPrivateLabels unavailablePrivate saving unavailablePDE classification and boundary-value structureMathematical Methods for Physics · Mixed reviewProgress not loaded
MMP:010623The triple box convolution B=χ*χ*χ equals 3/4-x^2 on |x|≤1/2 and has variance 1/4View access optionsMmp Triple Box ConvolutionMmp Quadratic Bspline MomentsPrivateLabels unavailablePrivate saving unavailableDistributions, delta functions, and variational methodsMathematical Methods for Physics · Mixed reviewProgress not loaded
MMP:010624PV(1/x) equals D(log|x|), annihilates e^{-x^2}, and pairs x e^{-x^2} to sqrt(pi)View access optionsMmp Cauchy Principal Value PairingMmp Distributional Log DerivativePrivateLabels unavailablePrivate saving unavailableDistributions, delta functions, and variational methodsMathematical Methods for Physics · Mixed reviewProgress not loaded