Numerical Analysis
Good Books for reference:
Numerical analysis (R. L. Burden and J. D. Faires)
Syllabus for Numerical Analysis
Numerical solutions of algebraic and transcendental equations: bisection, secant method, Newton-Raphson method, fixed point iteration
Lecture 1: Numerical Analysis (Root finding methods)
Lecture 2: Numerical Analysis (Bisection method introduction)
Lecture 3: Numerical Analysis (Problem based on bisection method)
Lecture 4: Numerical Analysis (Number of iterations for bisection method)
Lecture 5: Numerical Analysis (Questions on Bisection method)
Lecture 6: Numerical Analysis (Fixed point iteration method introduction)
Lecture 7: Numerical Analysis (Number of iterations in fixed point iteration method)
Lecture 8: Numerical Analysis (Problems on Fixed point iteration method)
Lecture 9: Numerical Analysis (Problems on fixed point iteration method-2)
Lecture 10: Numerical Analysis (Newton method)
Lecture 11: Numerical Analysis (Problems on Newton method)
Lecture 12: Numerical Analysis (Secant method)
Lecture 13: Numerical Analysis (order of convergence definition)
Lecture 14: Numerical Analysis (Order of convergence of bisection and Newton method)
Lecture 15: Numerical Analysis (Order of convergence of fixed point iteration method)
Lecture 16: Numerical Analysis (Problems on order of convergence of fixed point iteration method)
Lecture 17: Numerical Analysis (Modified Newton method(why do we need it?))
Lecture 18: Numerical Analysis (Modified Newton method)
Interpolation: error of polynomial interpolation, Lagrange and Newton interpolations
Lecture 19: Numerical Analysis (Lagrange interpolation)
Lecture 20: Numerical Analysis (Error introduced in Lagrange interpolation)
Lecture 21: Numerical Analysis (Problems one error bound of Lagrange interpolation)
Numerical differentiation
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Numerical integration, Trapezoidal and Simpson’s rules
Numerical Integration 1 (Formula for the trapezoidal rule)
Numerical Integration 2 (Error in trapezoidal rule)
Numerical Integration 3 (Simpsons 1/3 rule of integration)
Numerical Integration 4 (Degree of precision or accuracy)
Numerical solution of a system of linear equations: direct methods (Gauss elimination, LU decomposition), iterative methods (Jacobi and Gauss-Seidel)
Numerical solution of initial value problems of ODEs: Euler’s method, Runge-Kutta methods of order 2
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