Programming Numerical Methods in Python

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Murad Elarbi

12:18:24

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1 - Introduction

1 - 1-Introduction.pdf

1 - Introduction.mp4

04:50

2 - Roots of HighDegree Equations

2 - 2-roots-of-high-degree-equations.pdf

2 - Introduction and Simple Iterations Method.mp4

05:41

3 - Simple Iterations Method Code I for Loop.mp4

26:25

4 - Simple Iterations Method Code II while Loop.mp4

14:22

5 - Convergence vs Divergence.mp4

05:54

6 - NewtonRaphson Method.mp4

15:28

7 - Bisection Method Algorithm.mp4

11:45

8 - Bisection Method Code.mp4

17:29

9 - False Position Regula Falsi Mehtod.mp4

13:55

9 - Regula-Falsi-Method.pdf

10 - Secant Method.mp4

15:49

10 - secant-method.pdf

11 - UserDefined Functions RunTime Input.mp4

11:02

12 - Root Finding in SciPy Summary.mp4

10:46

3 - Interpolation and Curve Fitting

13 - 3-interpolation-and-curve-fitting.pdf

13 - Introduction and Linear Interpolation Method.mp4

15:26

14 - Lagranges Method Algorithm.mp4

07:31

15 - Lagranges Method Code.mp4

17:33

16 - Newtons Method Algorithm.mp4

10:58

17 - Newtons Method Code.mp4

16:06

18 - Linear Regression Algorithm.mp4

04:09

19 - Linear Regression Code I for Loop.mp4

08:17

20 - Linear Regression Code II NumPy Arrays.mp4

08:28

21 - Polynomial Fit Algorithm.mp4

04:43

22 - Polynomial Fit Code.mp4

24:00

23 - Interpolation Functions of SciPy.mp4

08:58

24 - Curve Fitting Functions of SciPy Summary.mp4

14:53

4 - Numerical Differentiation

25 - 4-numerical-differentiation.pdf

25 - Introduction and Finite Differences Method.mp4

12:05

26 - Finite Differences Method Code I.mp4

11:30

27 - Finite Differences Method Code II.mp4

11:26

28 - Plotting Derivative Curves.mp4

17:40

29 - Numerical Differentiation Function in SciPy Summary.mp4

10:00

5 - Numerical Integration

30 - 5-numerical-integration.pdf

30 - Introduction Trapezoidal Rule Algorithm.mp4

07:38

31 - Trapezoidal Rule Code.mp4

11:58

32 - Simpsons 13 Rule Algorithm.mp4

07:22

33 - Simpsons 13 Rule Code.mp4

08:17

34 - Simpsons 38 Rule Algorithm.mp4

05:27

35 - Simpsons 38 Rule Code.mp4

09:41

36 - Double Integration Algorithm.mp4

07:54

37 - Double Integration Code.mp4

16:01

38 - Quadrature in SciPy Summary.mp4

14:20

6 - Systems of Linear Equations

39 - 6-systems-of-linear-equations.pdf

39 - Introduction Gauss Elimination Method Algorithm.mp4

26:00

39 - gauss-elimination-example.pdf

40 - Gauss Elimination Method Code I Elimination.mp4

21:09

41 - Gauss Elimination Method Code II BackSubstitution.mp4

21:40

42 - Gauss Elimination Method Code III Modifications.mp4

16:38

43 - Jacobis Method Algorithm.mp4

07:14

44 - Jacobis Method Code.mp4

32:07

45 - GaussSeidels Method.mp4

10:48

45 - pnmp-6-05.zip

46 - Diagonal Dominance.mp4

05:06

47 - Linear System Solution in NumPy and SciPy Summary.mp4

08:36

48 - GaussJordan Method Procedure.mp4

13:56

48 - Gauss-Jordan-Method.pdf

49 - GaussJordan Method Algorithm Code.mp4

12:54

49 - pnmp-6-07.zip

7 - Ordinary Differential Equations

50 - 7-ordinary-differential-equations.pdf

50 - Introduction Eulers Method.mp4

16:22

51 - Second Order RungeKuttas Method.mp4

07:15

52 - Fourth Order RungeKuttas Method.mp4

08:37

53 - Fourth Order RungeKuttas Method Plot Numerical and Exact Solutions.mp4

15:57

54 - HigherOrder ODEs Algorithm.mp4

08:27

55 - HigherOrder ODEs Code.mp4

22:52

56 - HigherOrder ODEs Plotting Solutions.mp4

20:12

57 - ODE Solution in SciPy Summary.mp4

16:47

Description

A Practical Approach to Understand the Numerical Methods

What You'll Learn?

Program the numerical methods to create simple and efficient Python codes that output the numerical solutions at the required degree of accuracy.
Create and manipulate arrays (vectors and matrices) by using NumPy.
Use the plotting functions of matplotlib to present your results graphically.
Apply SciPy numerical analysis functions related to the topics of this course.

Who is this for?

The students who currently study their first course in numerical methods and need to understand how the methods are coded in detail.

The students who need to create their own numerical analysis codes or use Python numerical libraries for their course, project or thesis works.

What You Need to Know?

You should have a good background in algebra and calculus, in addition to the basic knowledge about computers

A Python IDE and its libraries NumPy, matplotlib and SciPy should be installed on your computer.

No previous experience in programming in Python is required.

More details

Description
Many of the Numerical Analysis courses focus on the theory and derivations of the numerical methods more than the programming techniques. Students get the codes of the numerical methods in different languages from textbooks and lab notes and use them in working their assignments instead of programming them by themselves.

For this reason, the course of Programming Numerical Methods in Python focuses on how to program the numerical methods step by step to create the most basic lines of code that run on the computer efficiently and output the solution at the required degree of accuracy.

This course is a practical tutorial for the students of Numerical Analysis to cover the part of the programming skills of their course.

In addition to its simplicity and versatility, Python is a great educational computer language as well as a powerful tool in scientific and engineering computations. For the last years, Python and its data and numerical analysis and plotting libraries, such as NumPy, SciPy and matplotlib, have become very popular programming language and tool in industry and academia.

Thatâ€™s why this course is based on Python as programming language and NumPy and matplotlib for array manipulation and graphical representation, respectively. At the end of each section, a number of SciPy numerical analysis functions are introduced by examples. In this way, the student will be able to program his codes from scratch and in the same time use the advanced library functions in his work.

This course covers the following topics:

Roots of High-Degree Equations
Interpolation and Curve Fitting
Numerical Differentiation
Numerical Integration
Systems of Linear Equations
Ordinary Differential Equations
Who this course is for:
The students who currently study their first course in numerical methods and need to understand how the methods are coded in detail.
The students who need to create their own numerical analysis codes or use Python numerical libraries for their course, project or thesis works.

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Python

Murad Elarbi

Instructor's Courses

I am a Mechanical Engineering Lecturer in the University of Benghazi, Libya since 2005. I taught courses of Strength of Materials, Theory of Machines, Machine Design Projects and Engineering Drawing. My research interest is the computational mechanics where numerical methods and computer programming are the main tools of solution in addition to theories of mechanics. I instructed several computer language training courses of BASIC, Fortran, C++ and MATLAB. Currently, I am in the USA for the Ph.D. degree.

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