Numerical-Methods-Coursework
MY coursework and project for an introductory course in Probability, Statistics and Numerical Methods
Course Content
Probability and Statistics
Random Experiments; Events; Probability; Random variables; Probability Distributions: Discrete and Continuous Distributions, Mean and Variance of Distributions, Distributions of Several random variables; Random sampling; Estimation of parameters; Confidence Intervals; Testing of Hypotheses; Goodness of fit-chi-squared test; Quality control and Acceptance Sampling; Confidence intervals for regression parameters.
Numerical Methods
Mathematical Modeling, Approximations and Round-off errors, Truncation errors and the Taylor series, Roots of Equations: Graphical methods, bisection method, simple fixed-point iteration, Newton-Raphson method, Secant method, Systems of nonlinear equations, Linear algebraic equations: Gauss elimination, Gauss-Jordan, LU and QR Decomposition, Matrix norms and condition numbers, Special matrices and Gauss-Seidel method; Interpolation: Newton's divided difference, Lagrange Interpolating polynomials; Numerical Integration: Trapezoidal, Simpson's, Gauss; Numerical differentiation, Finite Difference methods for ODEs: Euler's method, Runge Kutta Method, Stiff solvers, multistep methods, Boundary value problems (shooting method and finite difference method), Eigenvalue problems: Inclusion of Matrix Eigenvalues, Eigenvalues by Iteration (Power Method); Finite Difference methods for PDEs: Elliptic equations, Parabolic equations.
PS: I will add more info here later.