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Course Weekly Lecture Plan

Week Topic
1 Introduction to numerical methods: Functions, Taylor Series, Algorithms, Numerical Errors
2 Solutions of a single non-linear equation: Direct Iteration, Bisection Method, False Position (Regula-Falsi) Method
3 Newton-Raphson and Secant Methods, Modified Secant Method
4 Solutions of non-linear systems of equations
5 Linear systems of equations: Gauss Elimination, LU Decomposition, Iterative Methods, Thomas Algoritm
6 Iterative Methods: Jacobi, Gauss-Seidel, SOR (Successive Over-Relaxation)
7 Newton Interpolation Polynomial and Lagrange Interpolation Polynomial - 1st MIDTERM EXAM
8 Spline Interpolation
9 Curve Fitting: Least Square Approximation
10 Numerical Integration and Numerical Differentiation: The Trapezoid Rule
11 Numerical Integration: Simpson Rule, Gauss-Legendre Integration (Gauss-Quadrature) - 2nd MIDTERM EXAM
12 Numerical Solution of Ordinary Differential Equations: Euler, Heun and Taylor Methods
13 Numerical Solution of Ordinary Differential Equations: Runge-Kutta Methods
14 Introduction to Solution of Partial Differential Equations
 
 
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