Chemical - Advanced Numerical Analysis (English)

   Friday, May 02, 2025   

Starting a new Lecture Notes Series on Chemical - Advanced Numerical Analysis

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Lecture 1: Mod-01 Lec-01 Introduction and Overview

Lecture 2: Mod-01 Lec-02 Fundamentals of Vector Spaces

Lecture 3: Mod-01 Lec-03 Basic Dimension and Sub-space of a Vector Space

Lecture 4: Mod-01 Lec-04 Introduction to Normed Vector Spaces

Lecture 5: Mod-01 Lec-05 Examples of Norms,Cauchy Sequence and Convergence, Introduction to Banach Spaces

Lecture 6: Mod-01 Lec-06 Introduction to Inner Product Spaces

Lecture 7: Mod-01 Lec-07 Cauchy Schwaz Inequality and Orthogonal Sets

Lecture 8: Mod-01 Lec-08 Gram-Schmidt Process and Generation of Orthogonal Sets

Lecture 9: Mod-01 Lec-09 Problem Discretization Using Appropriation Theory

Lecture 10: Mod-01 Lec-10 Weierstrass Theorem and Polynomial Approximation

Lecture 11: Mod-01 Lec-11 Taylor Series Approximation and Newton's Method

Lecture 12: Mod-01 Lec-12 Solving ODE - BVPs Using Firute Difference Method

Lecture 13: Mod-01 Lec-13 Solving ODE - BVPs and PDEs Using Finite Difference Method

Lecture 14: Mod-01 Lec-14 Finite Difference Method (contd.) and Polynomial Interpolations

Lecture 15: Mod-01 Lec-15 Polynomial and Function Interpolations,Orthogonal Collocations Method for Solving

Lecture 16: Mod-01 Lec-16 Orthogonal Collocations Method for Solving ODE - BVPs and PDEs

Lecture 17: Mod-01 Lec-17 Least Square Approximations, Necessary and Sufficient Conditions

Lecture 18: Mod-01 Lec-18 Least Square Approximations :Necessary and Sufficient Conditions

Lecture 19: Mod-01 Lec-19 Linear Least Square Estimation and Geometric Interpretation

Lecture 20: Mod-01 Lec-20 Geometric Interpretation of the Least Square Solution (Contd.) and Projection

Lecture 21: Mod-01 Lec-21 Projection Theorem in a Hilbert Spaces (Contd.) and Approximation

Lecture 22: Mod-01 Lec-22 Discretization of ODE-BVP using Least Square Approximation

Lecture 23: Mod-01 Lec-23 Discretization of ODE-BVP using Least Square Approximation and Gelarkin Method

Lecture 24: Mod-01 Lec-24 Model Parameter Estimation using Gauss-Newton Method

Lecture 25: Mod-01 Lec-25 Solving Linear Algebraic Equations and Methods of Sparse Linear Systems

Lecture 26: Mod-01 Lec-26 Methods of Sparse Linear Systems (Contd.) and Iterative Methods for Solving

Lecture 27: Mod-01 Lec-27 Iterative Methods for Solving Linear Algebraic Equations

Lecture 28: Mod-01 Lec-28 Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis

Lecture 29: Mod-01 Lec-29 Iterative Methods for Solving Linear Algebraic Equations:

Lecture 30: Mod-01 Lec-30 Iterative Methods for Solving Linear Algebraic Equations: Convergence

Lecture 31: Mod-01 Lec-31 Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis

Lecture 32: Mod-01 Lec-32 Optimization Based Methods for Solving Linear Algebraic Equations: Gradient Method

Lecture 33: Mod-01 Lec-46 Solving ODE-IVPs: Convergence Analysis of Solution Schemes (contd.)

Lecture 34: Mod-01 Lec-47 Solving ODE-IVPs: Convergence Analysis of Solution Schemes (contd.)

Lecture 35: Mod-01 Lec-48 Methods for Solving System of Differential Algebraic Equations

Lecture 36: Mod-01 Lec-49 Methods for Solving System of Differential Algebraic Equations

Lecture 37: Mod-01 Lec-33 Conjugate Gradient Method, Matrix Conditioning and Solutions

Lecture 38: Mod-01 Lec-34 Matrix Conditioning and Solutions and Linear Algebraic Equations (Contd.)

Lecture 39: Mod-01 Lec-35 Matrix Conditioning (Contd.) and Solving Nonlinear Algebraic Equations

Lecture 40: Mod-01 Lec-36 Solving Nonlinear Algebraic Equations: Wegstein Method and Variants of Newton's Method

Lecture 41: Mod-01 Lec-37 Solving Nonlinear Algebraic Equations: Optimization Based Methods

Lecture 42: Mod-01 Lec-38 Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis

Lecture 43: Mod-01 Lec-39 Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis (Contd.)

Lecture 44: Mod-01 Lec-40 Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs)

Lecture 45: Mod-01 Lec-41 Solving Ordinary Differential Equations - Initial Value Problems

Lecture 46: Mod-01 Lec-42 Solving ODE-IVPs : Runge Kutta Methods (contd.) and Multi-step Methods

Lecture 47: Mod-01 Lec-43 Solving ODE-IVPs : Generalized Formulation of Multi-step Methods

Lecture 48: Mod-01 Lec-44 Solving ODE-IVPs : Multi-step Methods (contd.) and Orthogonal Collocations Method

Lecture 49: Mod-01 Lec-45 Solving ODE-IVPs: Selection of Integration Interval and Convergence Analysis