This course on Numerical Analysis aims to teach students the following learning outcomes and goals: understanding interpolation, integration, and differentiation; mastering various interpolation formulas such as Newton's, Lagrange's, and Bessel's; learning numerical integration techniques like the Trapezoidal and Simpsons rules; becoming proficient in numerical methods for solving differential equations including Picard, Euler, Runge Kutta, and Milne methods; and acquiring skills in curve fitting using the method of least squares. The course utilizes a combination of theoretical explanations, examples, and problem-solving sessions to impart these skills. The intended audience for this course includes students and professionals seeking to enhance their knowledge and skills in numerical analysis and related fields.
Overview
Syllabus
Overview of Numerical Analysis | Interpolation | Integration | Differentiation.
Interpolation Formula -Newton Forward & Backward | Example and Solution.
Interpolation Formula - Stirling, Gauss Forward & Backward, Bessel's | Example & Solution.
Lagrange Interpolation | Unequal Interval |Newton divided difference.
Numerical Integration - Trapezoidal Rule, Simpsons 1/3 & 3/8 Rule.
Picard method of successive approximations Example for solving ODE.
Euler Modified Method - Solution Of ODE By Numerical Method | Example.
Runge Kutta Method of 4th Order - Solution of ODE By Numerical Method.
Milne Predictor & Corrector Method - Solution Of ODE Numerical Method.
Adam Bashforth Predictor And Corrector Method - Solution Of ODE By NA.
Curve Fitting Straight Line & Second Degree Parabola By Least Square.
Curve Fitting Of Exponential Curve By Least Square Method Examples.
Bisection Method | Numerical Methods | Solution of Algebraic & Transcendental Equation.
Regula Falsi Method | False Position Method | Numerical Methods.
Iteration Method | Fixed Point Iteration Method | Numerical Methods.
Secant Method | Chord Method | Numerical Methods , Formula & Examples.
Newton Raphson Method | Numerical Methods | Formula & Example.
Gauss Elimination Method | Numerical Methods | solution of Linear Equations.
Gauss Jordan Method | Numerical Methods | solution of Linear Equations.
LU Decomposition Method | Numerical Methods | Solution of Linear Equation.
Jacobi method | Iterative method | Solution of Linear System Equation.
Gauss Seidel Method | Iterative Method | Numerical Methods | Problems.
Coronavirus | How To Protect Your Self | Advice For Students & Community Members.
Taught by
Gajendra Purohit
