In this post, the following topics are presented:
(a) Linear Algebraic Systems
(b) 1-D discrete data analysis
(b-1) Lagrange interpolation
(b-2) Spline interpolation
(b-3) Least squares method
(c) Curvilinear Coordinates
(d) Higher Order Ordinary Differential Equations (ODEs)
(d-1) Turning a higher order ODE to a system of 1st-order ODEs
(d-2) Finding solutions for homogeneous equations
(e) Partial Differential Equations - Classification
(e-1) Hyperbolic PDEs
(e-2) Parabolic PDEs
(e-3) Elliptic PDEs
(f) Finite Difference Approximations
(g) Finite Differences - Higher Order Approximations
(h) Stability of the Finite Difference Schemes
(i) Integration: quadrature formulae
(j) Runge-Kutta Method
(k) Newton's Method (1-D, 2-D, and 3-D)
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