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MMP:010117The symmetric matrix A=[[5,2],[2,2]] has principal values 6 and 1 with tan(2θ)=4/3

Mathematical Methods Symmetric Tensor Principal AxesMathematical Methods Quadratic Form Invariants

Vector calculus, tensors, and coordinate systemsMathematical Methods for Physics · Mixed review

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)

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Mathematical Methods Oblique Metric TensorMathematical Methods Reciprocal Basis Components

Vector calculus, tensors, and coordinate systemsMathematical Methods for Physics · Mixed review

MMP:010129Rodrigues rotation by π/2 about (1,2,2)/3 is (1/9)[[1,-4,8],[8,4,1],[-4,7,4]]

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Mathematical Methods Skew Generator RodriguesMathematical Methods Rotation Axis Invariants

Vector calculus, tensors, and coordinate systemsMathematical Methods for Physics · Mixed review

MMP:010225The J0 Frobenius sum through m=4 at x=1 is 12537/16384 and brackets J0(1) from below by 1/14745600

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Mmp Bessel J0 FrobeniusMmp Alternating Truncation Bound

ODEs, Sturm-Liouville theory, and Green functionsMathematical Methods for Physics · Mixed review

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 8/175

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Mmp Legendre X4 ExpansionMmp Three Point Gauss Exactness

ODEs, Sturm-Liouville theory, and Green functionsMathematical Methods for Physics · Mixed review

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 7/3

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Mathematical Methods Inverse Laplace Repeated PolesMathematical Methods Laplace Moment Mean Variance

Fourier and Laplace methodsMathematical Methods for Physics · Mixed review

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)

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Mathematical Methods Negative Exponent Dft BinsMathematical Methods Circular Versus Linear Aliasing

Fourier and Laplace methodsMathematical Methods for Physics · Mixed review

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|>2

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Mathematical Methods Forced Recurrence Closed FormMathematical Methods Unilateral Z Transform Roc

Fourier and Laplace methodsMathematical Methods for Physics · Mixed review

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/3

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Mathematical Methods Rational Partial FractionsMathematical Methods Uhp Residue Theorem Arc

Complex-variable and asymptotic methodsMathematical Methods for Physics · Mixed review

MMP:010420The keyhole integral of x^{1/3}/(1+x^2) from 0 to ∞ equals (π/2)csc(2π/3)=π/√3

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Mathematical Methods Keyhole Branch ResiduesMathematical Methods Beta Reflection Mellin

Complex-variable and asymptotic methodsMathematical Methods for Physics · Mixed review

MMP:010430The [2/2] Padé of e^z at z=-1 is 7/19, erring from e^{-1} by 0.0005416114601366

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Mathematical Methods Diagonal Pade ExponentialMathematical Methods Pade Poles Reciprocity Error

Complex-variable and asymptotic methodsMathematical Methods for Physics · Mixed review

MMP:010521The disk extension of 3+2cos2θ-4sin3θ is 3+2r^2 cos2θ-4r^3 sin3θ with energy 56π

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Mathematical Methods Disk Harmonic ModesMathematical Methods Dirichlet TO Neumann Energy

PDE classification and boundary-value structureMathematical Methods for Physics · Mixed review

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 1/2

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Mmp Discrete Five Point DirichletMmp Jacobi Grid Spectrum

PDE classification and boundary-value structureMathematical Methods for Physics · Mixed review

MMP:010623The triple box convolution B=χχχ equals 3/4-x^2 on |x|≤1/2 and has variance 1/4

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Mmp Triple Box ConvolutionMmp Quadratic Bspline Moments

Distributions, delta functions, and variational methodsMathematical Methods for Physics · Mixed review

MMP:010624PV(1/x) equals D(log|x|), annihilates e^{-x^2}, and pairs x e^{-x^2} to sqrt(pi)

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Mmp Cauchy Principal Value PairingMmp Distributional Log Derivative

Distributions, delta functions, and variational methodsMathematical Methods for Physics · Mixed review

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MMP:010117The symmetric matrix A=[[5,2],[2,2]] has principal values 6 and 1 with tan(2θ)=4/3

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)

MMP:010129Rodrigues rotation by π/2 about (1,2,2)/3 is (1/9)[[1,-4,8],[8,4,1],[-4,7,4]]

MMP:010225The J0 Frobenius sum through m=4 at x=1 is 12537/16384 and brackets J0(1) from below by 1/14745600

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 8/175

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 7/3

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)

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|>2

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/3

MMP:010420The keyhole integral of x^{1/3}/(1+x^2) from 0 to ∞ equals (π/2)csc(2π/3)=π/√3

MMP:010430The [2/2] Padé of e^z at z=-1 is 7/19, erring from e^{-1} by 0.0005416114601366

MMP:010521The disk extension of 3+2cos2θ-4sin3θ is 3+2r^2 cos2θ-4r^3 sin3θ with energy 56π

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 1/2

MMP:010623The triple box convolution B=χχχ equals 3/4-x^2 on |x|≤1/2 and has variance 1/4

MMP:010624PV(1/x) equals D(log|x|), annihilates e^{-x^2}, and pairs x e^{-x^2} to sqrt(pi)

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MMP:010117The symmetric matrix A=[[5,2],[2,2]] has principal values 6 and 1 with tan(2θ)=4/3

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)

MMP:010129Rodrigues rotation by π/2 about (1,2,2)/3 is (1/9)[[1,-4,8],[8,4,1],[-4,7,4]]

MMP:010225The J0 Frobenius sum through m=4 at x=1 is 12537/16384 and brackets J0(1) from below by 1/14745600

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 8/175

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 7/3

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)

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|>2

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/3

MMP:010420The keyhole integral of x^{1/3}/(1+x^2) from 0 to ∞ equals (π/2)csc(2π/3)=π/√3

MMP:010430The [2/2] Padé of e^z at z=-1 is 7/19, erring from e^{-1} by 0.0005416114601366

MMP:010521The disk extension of 3+2cos2θ-4sin3θ is 3+2r^2 cos2θ-4r^3 sin3θ with energy 56π

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 1/2

MMP:010623The triple box convolution B=χχχ equals 3/4-x^2 on |x|≤1/2 and has variance 1/4

MMP:010624PV(1/x) equals D(log|x|), annihilates e^{-x^2}, and pairs x e^{-x^2} to sqrt(pi)

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MMP:010117The symmetric matrix A=[[5,2],[2,2]] has principal values 6 and 1 with tan(2θ)=4/3View problem statement

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MMP:010117The symmetric matrix A=[[5,2],[2,2]] has principal values 6 and 1 with tan(2θ)=4/3View problem statement

MMP:010117The symmetric matrix A=[[5,2],[2,2]] has principal values 6 and 1 with tan(2θ)=4/3

MMP:010117The symmetric matrix A=[[5,2],[2,2]] has principal values 6 and 1 with tan(2θ)=4/3