Numerical calculus

• Polynomials
  • Polynomial evaluation (polyval)
  • Polynomial roots (polyroots)
• Root-finding and optimization
  • Root-finding (findroot)
• Sums, products, limits and extrapolation
  • Summation
  • Products
  • Limits (limit)
  • Extrapolation
• Differentiation
  • Numerical derivatives (diff, diffs)
  • Composition of derivatives (diffs_prod, diffs_exp)
  • Fractional derivatives / differintegration (differint)
• Numerical integration (quadrature)
  • Standard quadrature (quad)
  • Oscillatory quadrature (quadosc)
  • Quadrature rules
• Ordinary differential equations
  • Solving the ODE initial value problem (odefun)
• Function approximation
  • Taylor series (taylor)
  • Pade approximation (pade)
  • Chebyshev approximation (chebyfit)
  • Fourier series (fourier, fourierval)
• Numerical inverse Laplace transform
  • One-step algorithm (invertlaplace)
  • Specific algorithms
  • Manual approach
  • Credit