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Numerical Analysis I (Approximation of Derivatives (Numerical…
Numerical Analysis I
Approximation of Derivatives
Numerical Differentiation Formulas
Roundoff Error in Numerical Differentiation
Numerical Differentiation using Piecewise Polynomials
Approximation of Integral
Basic Numerical Integration Rules
Rectangle Rules (n = 0)
Midpoint Rule
Trapezoidal Rule (n = 1)
Simpson's Rule (n = 2)
Composite Numerical Integration Rules
Iterative Approaches to the Approximation of Integrals
Interval Doubling
Richardson Extrapolation and Romberg Integration
Polynomial Interpolation
General Forms
Newton Form
Divided Difference
Lagrange Form
Interpolation Error
Interpolation of Moments
Piecewise Polynomial Approximation
1-D
Piecewise cubic Hermite Approximation
Cubic Spline Interpolation
Piecewise Linear Approximation
2-D
Triangulation
The Finite Fourier Transform
Trigonometric Interpolation
The Fast Fourier Transform (FFT)