Systems of linear equations: Direct methods (Gaussian elimination, LU decomposition, Cholesky factorization), Iterative methods (Gauss-Seidel and Jacobi) and their convergence for diagonally dominant coefficient matrices; Numerical solutions of nonlinear equations: bisection method, secant method, Newton-Raphson method, fixed point iteration; Interpolation: Lagrange and Newton forms of interpolating polynomial, Error in polynomial interpolation of a function; Numerical differentiation and error, Numerical integration: Trapezoidal and Simpson rules, Newton-Cotes integration formulas, composite rules, Mathematical errors involved in numerical integration formulae; Numerical solution of initial value problems for ordinary differential equations: Methods of Euler, Runge-Kutta method of order 2

### Course Curriculum

 Numerical Analysis NA Lec-1 || Bisection Method – NA – Numerical Analysis – Descartes Rule of Signs – Iteration Method 01:53:00 NA Lec-2 || NA – Secant Method, Ragula Falsi Method, Newton Raphson Method – Numerical Analysis 01:25:00 NA Lec-3 || NA – Questions & Solutions – Root Finding Methods – Complete Course 00:56:00 NA Lec-4 || NA – Questions and Solutions – Bisection Method, Newton Rapson Method, Order of Convergence 01:38:00 NA Lec-5 || Gauss Eliminations Method – LU Decomposition – Cholesky Method – System of Linear Equations 01:24:00 NA Lec-6 || NA – Iterative methods – Gauss-Seidel and Gauss Jacobi – Complete Course Course 01:46:00 NA Lec-7 || NA – Eigen Values – Gerschgorin Theorem – Brauer’s Therorem – Complete Course 01:03:00 NA Lec-8 || NA – Interpolation and Approximation – Complete Course Numerical Analysis 01:16:00 NA Lec-9 || Gate Questions and Solutions – Error in Interpolation – Complete Course Numerical Analysis 01:35:00 NA Lec-10 || Finite Difference Operators – Forward & Backward Difference Operators – Numerical Analysis 01:33:00 NA Lec-11 || Trapezoidal Rule – Simpson’s one-third & three Eight Rule – Numerical Integration 01:38:00 NA Lec-12 || Error in Trapezoidal Rule & Simpson’s one-third rule – Gate Questions Numerical Analysis 01:33:00 NA Lec-13 || Questions and Solutions – Real Analysis – IIT-JAM Mathematics 01:28:00

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