Video Lecture Numerical Method of Optimization (NMO)

Faculty: Anup Goel, Video Duration: 76 Hrs, Size:64 GB.
Faculty: Anup Goel
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₹ 4,999
₹ 4,499

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Numerical Method of Optimization (NMO) Video Lectures Syllabus

Unit - I

Roots of Equation and Error Approximations Roots of Equation Bisection Method, Newton Raphson method and Successive approximation method. Error Approximations Types of Errors: Absolute, Relative, Algorithmic, Truncation, Round off Error, Error Propagation, Concept of convergence-relevance to numerical methods. (Chapters-2, 3)

Unit - II

Simultaneous Equations Gauss Elimination Method with Partial pivoting, Gauss-Seidel method and Thomas algorithm for Tri diagonal Matrix, Jacobi iteration method. (Chapter-4)

Unit - III

Optimization Introduction to optimization, Classification, Constrained optimization (maximum two constrains): Graphical and Simplex method, One Dimensional unconstrained optimization: Newton’s Method. Modern Optimization Techniques: Genetic Algorithm (GA), Simulated Annealing (SA). (Chapter-5)

Unit - IV

Numerical Solutions of Differential Equations Ordinary Differential Equations [ODE] Taylor series method, Euler Method, Runge-Kutta fourth order, Simultaneous equations using Runge Kutta order method. Partial Differential Equations [PDE] : Finite Difference methods Introduction to finite difference method, Simple Laplace method, PDEs- Parabolic explicit solution, Elliptic explicit solution. (Chapters-6, 7)

Unit - V

Curve Fitting and Regression Analysis Curve Fitting Least square technique- Straight line, Power equation, Exponential equation and Quadratic equation. Regression Analysis Introduction to multi regression analysis, Lagrange’s Interpolation, Newton’s Forward interpolation, Inverse interpolation (Lagrange’s method only). (Chapters-8, 9)

Unit - VI

: Numerical Integration Numerical Integration (1D only) Trapezoidal rule, Simpson’s 1/ Rule, Simpson’s 3/ Rule, Gauss Quadrature 2 point and 3 point method. Double Integration Trapezoidal rule, Simpson’s 1/ Rule (Chapter-10)

Demo Lecture

 

Numerical Method of Optimization (NMO) Video Lectures Syllabus

Unit - I

Roots of Equation and Error Approximations Roots of Equation Bisection Method, Newton Raphson method and Successive approximation method. Error Approximations Types of Errors: Absolute, Relative, Algorithmic, Truncation, Round off Error, Error Propagation, Concept of convergence-relevance to numerical methods. (Chapters-2, 3)

Unit - II

Simultaneous Equations Gauss Elimination Method with Partial pivoting, Gauss-Seidel method and Thomas algorithm for Tri diagonal Matrix, Jacobi iteration method. (Chapter-4)

Unit - III

Optimization Introduction to optimization, Classification, Constrained optimization (maximum two constrains): Graphical and Simplex method, One Dimensional unconstrained optimization: Newton’s Method. Modern Optimization Techniques: Genetic Algorithm (GA), Simulated Annealing (SA). (Chapter-5)

Unit - IV

Numerical Solutions of Differential Equations Ordinary Differential Equations [ODE] Taylor series method, Euler Method, Runge-Kutta fourth order, Simultaneous equations using Runge Kutta order method. Partial Differential Equations [PDE] : Finite Difference methods Introduction to finite difference method, Simple Laplace method, PDEs- Parabolic explicit solution, Elliptic explicit solution. (Chapters-6, 7)

Unit - V

Curve Fitting and Regression Analysis Curve Fitting Least square technique- Straight line, Power equation, Exponential equation and Quadratic equation. Regression Analysis Introduction to multi regression analysis, Lagrange’s Interpolation, Newton’s Forward interpolation, Inverse interpolation (Lagrange’s method only). (Chapters-8, 9)

Unit - VI

: Numerical Integration Numerical Integration (1D only) Trapezoidal rule, Simpson’s 1/ Rule, Simpson’s 3/ Rule, Gauss Quadrature 2 point and 3 point method. Double Integration Trapezoidal rule, Simpson’s 1/ Rule (Chapter-10)

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