Numerical Analysis & Methods with Python: Theory & Practice – Radhe Global

Learn Numerical Methods: Linear-algebra, Eigenvalues, Differential Equations, Interpolation, Numerical Analysis & more

Instructor Names: Mohamed Essadki

link: https://www.udemy.com/course/numerical-methods-with-python/

Objective

Foundations of Numerical Methods: Understand the fundamental concepts, principles, and techniques used in numerical analysis. Mathematical Background: Review essential mathematical foundations required for numerical computations, including calculus and linear algebra. Root-Finding Methods: Learn various algorithms for finding roots of equations, such as the Bisection method, Newton-Raphson method, and Secant method.

Curriculum

Introduction to Numerical Methods, Introduction to Numerical Methods, Number representation, Introduction to Number Representation, Positional Integer Number Systems, Exercise: Integer Number System Base, Python Exercise: Positional Integer Number Systems, Positional Real Number Systems, Python Exercise: Positional Real Number Systems, Fix Point Representation, Floating Point Representation, IEEE Standard 754 for Floating Point, Linear Algebra, Vector Space Introduction, Vector Subspace, Python Exercise: vectors using Numpy array, Linear Span Set, Linearly Independent Vector Set, Basis and Dimension of Vector Space, Inner Product, Linear Transformations and Matrices, Matrix-Matrix and Matrix-vector multiplication, Python Exercise: Matrix operations, Python Exercise: Rank and Null Space of a Matrix, Matrices and System of Linear Equations: Direct and Iterative Solvers, Linear System introduction, Matricial Formulation of Linear Systems, Determinant and Inverse of a Matrix, EigenValues and EingenVectors, Matrix diagonalization, Exercise Diagonalization, Gaussian Elimination Method, Gaussian Elimination: Augmented Matrix, Python Exercise: Gaussian Elimination, QR decomposition, Python Exercise: Gram Schmidt QR-Decomposition, Root finding, Root Finding Introduction, Bisection Method, Python Exercise: Bisection Method, Newton Method, Python Exercise: Newton Method, Secant Method, Python Exercise: Secant Method, Convergence Rate, Interpolation, Introduction, Polynomial Interpolation Problem, Existence and Uniqueness of Polynomial Interpolation, Vandermond Matrix method, Python Exercise: Vandermond Matrix Method, Lagrange Method, Python Exercise: Lagrange Method, Newton Method, Python Exercise: Newton Method, Divided Difference Formula, Python Exercise: Runge Phenomenon, Intro to Piecewise polynomial Interpolation, Cubic Spline Interpolation part 1, Cubic spline interpolation part 2, Python Exercise: Cubic Spline, Curve fitting and Optimization, Curve fitting Introduction, Linear Regression, Python Exercise: Linear Regression, Multi Linear Regression, Python Exercise: Multi-Linear Regression, Numerical Integration, Introduction to Numerical Integration, Newton Cotes Formulation, Python Exercise: Newton Cotes Part 1, Python Exercice: Newton Cotes Scipy Part 2, Trapezoidal Rule, Simpson’s Rule, Error Analysis: Error Upper Bound of Newton Cotes methods, Python Exercise: Error Analysis of Newton Cotes methods, Ordinary Differential Equations: Analytical solutions, Introuction, ODE Definition, Linear Homogeneous ODEs, Linear Non Homegeneous ODEs, Variation of Parameters method, Exercise: Variation of Parameters, Variable Separation Method, Initial Value Problem, Cauchy Lipshitz Global Theorem 1, Cauchy Lipshitz Local Theorem 2, Exercise: Cauchy Lipshitz, Ordinary Differential Equations: Numerical Solutions, Introduction to Numerical ODEs, Forward Euler Method, Backward Euler Method, Python Exercise: Euler Methods, Leapforg Method, Introduction to Runge Kutta 2, Python Exercise: RK2, Derivation of Runge Kutta 2, Appendix: Python, Python Basics

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No. Of Subscribers: 543

Rating: 3.9301033

No. Of Reviews:  43

Instructional Level: All Levels