Programming Numerical Methods in Python from Udemy

What's inside

Learning objectives

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.

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.

Syllabus

Introduction

An introduction to numerical methods, advantages of Python, course goals, course audience, course requirements, how to get the Python IDE and course contents. At the end of this lecture the student will know the knowledge and skills that he will learn in this course. He will know how to install the Python IDE and required modules on his computer.

Program simple iterations, Newton-Raphson and bisection methods. He will know the related SciPy functions.

Introduction and Simple Iterations Method

Simple Iterations Method: Code I (for Loop)

Simple Iterations Method: Code II (while Loop)

Convergence vs Divergence

Newton-Raphson Method

Bisection Method: Algorithm

Bisection Method: Code

False Position (Regula Falsi) Mehtod

This lecture is includes the graphical illustration about how secant method works in addition to the numerical coding by using a Python function.

User-Defined Functions & Run-Time Input

Root Finding in SciPy & Summary

Program linear, Lagrange and Newton interpolation, and linear regression and polynomial curve fitting methods in addition to use related SciPy functions.

Introduction and Linear Interpolation Method

Lagrange's Method: Algorithm

Lagrange's Method: Code

Newton's Method: Algorithm

Newton's Method: Code

Linear Regression: Algorithm

Linear Regression: Code I (for Loop)

Linear Regression: Code II (NumPy Arrays)

Polynomial Fit: Algorithm

Polynomial Fit: Code

Interpolation Functions of SciPy

Curve Fitting Functions of SciPy & Summary

Program finite differences method and represents the results graphically by using matplotlib in addition to use numerical differentiation function of SciPy.

Introduction and Finite Differences Method

Finite Differences Method: Code I

Finite Differences Method: Code II

Plotting Derivative Curves

Numerical Differentiation Function in SciPy & Summary

Program trapezoidal, simpson's 1/3 and 3/8 rules and double integration methods in addition to use the SciPy Quadrature functions.

Introduction & Trapezoidal Rule: Algorithm

Trapezoidal Rule: Code

Simpson's 1/3 Rule: Algorithm

Simpson's 1/3 Rule: Code

Simpson's 3/8 Rule: Algorithm

Simpson's 3/8 Rule: Code

Double Integration: Algorithm

Double Integration: Code

Quadrature in SciPy & Summary

Program Gauss-Elimination, Jacobi and Gauss-Seidel methods in addition to use the NumPy and SciPy linear equations solvers.

Introduction & Gauss Elimination Method: Algorithm

Gauss Elimination Method: Code I (Elimination)

Gauss Elimination Method: Code II (Back-Substitution)

Gauss Elimination Method: Code III (Modifications)

Jacobi's Method: Algorithm

Jacobi's Method: Code

Gauss-Seidel's Method

Diagonal Dominance

Linear System Solution in NumPy and SciPy & Summary

In this lecture, the steps of Gauss-Jordan method are explained by using a symbolic 4-equation system as well as a hand-solved numeric example. The outcome is to help the student comprehend the theoretical basis of the method.

In this lecture, the algorithm of Gauss-Jordan method is explained in the light of the general formulas written in the previous lecture. A Python code is also developed to solve the numeric problem. Finally, some modifications are made on the code to utilized the internal Numpy loops instead of explicit Python for loop.

Program Euler, second order Runge_Kutta, fourth order Runge_Kutta and higher order solution methods in addition to SciPy ODE solver.

Introduction & Euler's Method

Second Order Runge-Kutta's Method

Fourth Order Runge-Kutta's Method

Fourth Order Runge-Kutta's Method: Plot Numerical and Exact Solutions

Higher-Order ODE's: Algorithm

Higher-Order ODE's: Code

Higher-Order ODE's: Plotting Solutions

ODE Solution in SciPy & Summary

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Develops skills and knowledge essential to computational scientific programming in industry and academia

Meets a gap in the industry by offering a course that focuses on programming techniques

Provides a strong foundation by covering essential topics in numerical analysis

May require students to have existing programming knowledge

Reviews summary

Python intro to numerical methods

According to students, this course is a good introductory course on numerical methods. Students note that the course uses Python programming language to solve initial and boundary problems.

Uses Python to solve problems.

"The course uses Python programming language to solve initial and boundary problems,"

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Programming Numerical Methods in Python with these activities:

Python refresher

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Brush up on your Python programming skills before starting the course to ensure a solid foundation.

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Review the basics of Python syntax and data types.
Practice writing simple Python scripts.
Use online resources or tutorials to refresh your memory.
Complete a few coding challenges to test your understanding.

Numerical Analysis refresher

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Review the fundamental concepts of numerical analysis to enhance your comprehension of the course material.

Browse courses on Numerical Analysis

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Go over your previous notes or textbooks on numerical analysis.
Focus on key concepts such as error analysis, interpolation, and integration.
Solve practice problems to test your understanding.
Consult online resources or videos for additional clarification.

Connect with a mentor

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Seek guidance and support from experienced professionals in the field of numerical methods.

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Identify potential mentors who have expertise in numerical methods.
Reach out to them and express your interest in mentorship.
Establish regular communication channels.
Seek advice, feedback, and support on your projects and learning journey.

Six other activities

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SciPy library tutorial

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Familiarize yourself with the SciPy library for scientific and engineering computations.

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Find an online tutorial or documentation for SciPy.
Follow the tutorial and explore the different functions and modules.
Try out some examples and experiment with the library.
Identify how SciPy can complement your programming skills.

Python coding drills

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Reinforce your understanding of Python programming and numerical methods by solving coding problems.

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Find online Python coding challenges.
Choose a problem that aligns with the topics covered in the course.
Code the solution in Python.
Test your code and debug any errors.
Review the solution and identify areas for improvement.

Peer programming group

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Enhance your learning by collaborating with peers and solving problems together.

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Find a group of peers with similar interests.
Meet regularly to work on assignments or projects.
Discuss different approaches and share ideas.
Provide feedback and support to each other.

Attend a numerical analysis workshop

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Engage in hands-on learning and gain practical insights by attending a numerical analysis workshop.

Browse courses on Numerical Analysis

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Find a relevant numerical analysis workshop in your area or online.
Register and attend the workshop.
Actively participate in the discussions and exercises.
Network with other attendees.

Python notebook with coded examples

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Solidify your understanding by creating a Python notebook that demonstrates the numerical methods covered in the course.

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Start a new Python notebook.
Implement the numerical methods using Python code.
Include clear and concise explanations for each step.
Test your code and ensure it produces the correct results.
Share your notebook with others or use it for future reference.

Numerical Recipes: The Art of Scientific Computing

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Deepen your understanding of numerical methods and algorithms by reading a classic reference book.

View Numerical Recipes in C++ on Amazon

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Read and understand the relevant chapters.
Work through the exercises and examples.
Apply the concepts to your own programming projects.
Discuss the book with classmates or mentors.

Career center

Learners who complete Programming Numerical Methods in Python will develop knowledge and skills that may be useful to these careers:

Data Scientist

Data Scientists blend skills in programming, statistics, and business to mine and analyze large datasets. A background in Python, numerical analysis, and linear equations is highly relevant to Data Science. This course in Programming Numerical Methods in Python can help you build a foundation in these key areas, preparing you for entry into the field.

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Financial Analyst

Financial Analysts use historical data to model future financial performance of companies, industries, and economies. Programming Numerical Methods in Python can help you develop the quantitative skills necessary for building financial models and analyzing financial data.

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Software Developer

Software Developers write and maintain applications for a range of industries. This course will teach you how to program numerical methods in Python and use libraries such as NumPy for data manipulation and matplotlib for data visualization. These skills translate directly to Software Development.

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Data Engineer

Data Engineers design and build systems for storing, managing, and processing big data. The Python, numerical methods, and data manipulation skills taught in this course are essential for Data Engineers.

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Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to analyze financial data, risks, and trends. This course can teach you the Python programming, numerical analysis, and linear algebra skills required in this role.

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Machine Learning Engineer

Machine Learning Engineers design and implement machine learning models for a variety of applications. This course can help you build a foundation in Python programming, numerical analysis, and data visualization, which are essential for this role.

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Business Analyst

Business Analysts help businesses understand and optimize their performance. This course can help you develop the quantitative and analytical skills necessary for evaluating business processes and making data-driven recommendations.

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Operations Research Analyst

Operations Research Analysts use mathematical models to analyze and solve complex business problems. This course can help you develop the Python programming and numerical analysis skills needed for this role.

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Physicist

Physicists study the fundamental laws of nature. This course can help you develop the Python programming and numerical analysis skills that are essential for modeling and simulating physical systems.

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Mathematician

Mathematicians study the properties of numbers, quantities, and structures. This course can help you develop the Python programming and numerical analysis skills that are increasingly important in mathematical research and applications.

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Computational Scientist

Computational Scientists use computers to solve scientific problems. This course can help you develop the programming and numerical analysis skills needed to work with complex scientific data and models.

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Financial Risk Manager

Financial Risk Managers identify, assess, and manage financial risks. This course can help you develop the Python programming, numerical analysis, and data visualization skills that are essential for this role.

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Statistician

Statisticians collect, analyze, interpret, and present data. This course can help you develop the Python programming, numerical analysis, and data visualization skills that are essential for this role.

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Actuary

Actuaries use mathematical and statistical models to assess and manage risks. This course can help you develop the Python programming, numerical analysis, and data visualization skills that are essential for this role.

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Economist

Economists study the production, distribution, and consumption of goods and services. This course can help you develop the Python programming and numerical analysis skills that are increasingly important in economic research and forecasting.

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