Numerical Analysis Full Course | Part 1

In this Numerical Analysis full course, you'll learn everything you need to know to understand and solve problems with numerical analysis. If you're interested in learning more about numerical analysis, then this course is for you! By the end of this course, you'll have a good understanding of the basics of numerical analysis, Numerical analysis is a type of mathematics that we can use to solve problems through numerical approximations (numerical methods)!

This timeline is meant to help you better navigate this numerical analysis full course:
0:00 Numerical vs Analytical Methods
2:25 Systems Of Linear Equations
5:59 Understanding Singular Matrices
8:15 What Are Special Matrices? (Identity, Diagonal, Lower and Upper Triangular Matrices)
11:10 Introduction To Gauss Elimination
15:10 Gauss Elimination 2x2 Example
18:37 Gauss Elimination Example 2 | 2x2 Matrix With Row Switching
21:14 Partial Pivoting Purpose
24:09 Gauss Elimination With Partial Pivoting Example
29:24 Gauss Elimination Example 3 | 3x3 Matrix
32:53 LU Factorization/Decomposition
38:22 LU Decomposition Example
42:43 Direct Vs Iterative Numerical Methods
45:08 Iterative Methods For Solving Linear Systems
49:41 Diagonally Dominant Matrices
52:04 Jacobi Iteration
55:29 Jacobi Iteration Example
59:54 Jacobi Iteration In Excel
1:04:39 Jacobi Iteration Method In Google Sheets
1:10:28 Gauss-Seidel Method
1:14:50 Gauss-Seidel Method Example
1:19:48 Gauss-Seidel Method In Excel
1:24:36 Gauss-Seidel Method In Google Sheets
1:32:18 Introduction To Non-Linear Numerical Methods
1:35:31 Open Vs Closed Numerical Methods
1:39:13 Bisection Method
1:42:39 Bisection Method Example
1:47:14 Bisection Method In Excel
1:51:49 Gauss-Seidel Method In Google Sheets
1:58:33 Bisection Method In Python
2:03:11 False Position Method
2:06:53 False Position Method In Excel
2:11:36 False Position Method In Google Sheets
2:16:56 False Position Method In Python
2:22:18 False Position Method Example
2:26:05 Newton’s Method
2:29:45 Newton’s Method Example
2:33:02 Newton’s Method In Excel
2:36:20 Newton’s Method In Google Sheets
2:39:34 Newton’s Method In Python
2:45:00 Secant Method
2:47:38 Secant Method Example
2:51:18 Secant Method In Excel
2:54:05 Secant Method In Sheets
2:56:35 Secant Method In Python
2:59:34 Fixed Point Method Intuition
3:02:39 Fixed Point Method Convergence
3:05:43 Fixed Point Method Example 2
3:09:34 Fixed Point Iteration Method In Excel
3:13:30 Fixed Point Iteration Method In Google Sheets
3:17:25 Introduction To Interpolation
3:19:18 Lagrange Polynomial Interpolation Introduction
3:24:00 First-Order Lagrange polynomial example
3:27:39 Second-Order Lagrange polynomial example
3:32:33 Third Order Lagrange Polynomial Example
3:37:51 Divided Difference Interpolation & Newton Polynomials
3:42:31 First Order Divided Difference Interpolation Example
3:45:46 Second Order Divided Difference Interpolation Example

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This video is part of our Numerical Methods / Numerical Analysis course. Numerical methods is about solving math problems through approximating the solution of problems that would be difficult or impossible to solve analytically. In this playlist we will cover topics such as solving systems of linear equations, solving systems of non-linear equations, numerical integration, numerical derivatives, etc..
#studysession #numericalanalysis #numericalmethods

[ProfessorNoobster]

I'm taking this course at my uni in the fall, this is going to be VERY useful in the future. Thank you very much for this video.

[ZachArchibald]

Yo how is this free? Thank you so much for all of this content. You teach very concisely.

[koungoulover]

Hi, you made an error at 3:22:43, where j = 2 and k = 3. In the expression, you initially wrote ((x - x1) * (x - x2)) / ((x2 - x1) * (x2 - x3)). The accurate part should be ((x - x1) * (x - x3)) / ((x2 - x1) * (x2 - x3)). Nevertheless, your overall performance was superb.

[LaxmanNarrates]

Hai sir, I have watched the part1 covered all topics, Great work, and am interested in part 2 also, is part 2 coming?

[mohammedfathi]

59:09
Just for feeback, there are many errors in these calculations starting with the very beginning values.

[justinhepburn]

is it possible that you can do videos on the aitkens method, the steffensens method and the modified newtons method; the code and how to perform them by hand?

[delightfulant]

Does part 1 cover everything or will there be more parts?

[justinhepburn]

how did you install python so that it can run all of your codes

[youssefabsi]

what is the difference between numerical methods and numerical analysis?