What are Numerical Root Finding Methods?
Numerical Root Finding Methods are essential techniques in mathematics and science for locating solutions to equations, particularly when finding exact solutions isn’t straightforward. These methods are like mathematical detectives, helping us discover where a function crosses the zero line. This has numerous applications, from solving complex equations in physics and engineering to optimizing algorithms in computer science.
When you want to find the root of an equation, think of it as finding the “x” value that makes the equation equal to zero. But this can be tricky, especially with complicated functions. That’s where numerical methods come to the rescue. These methods include strategies like the Bisection method, Secant method, and Newton-Raphson method, each with its own strengths and use cases.
The Bisection method is like narrowing down a search area until you find the answer, like guessing a number between two bounds. The Secant method is more flexible, estimating the root without needing a specific range. Finally, the Newton-Raphson method is like a powerful magnifying glass, zooming in on the root with great precision.
In essence, Numerical Root Finding Methods are your tools for solving equations when the solutions aren’t apparent. They help you uncover the hidden answers to mathematical mysteries, making complex problems in various fields more manageable.
Why do we use Numerical Root Finding Methods and why is it important to learn it?
Numerical Root Finding Methods are like mathematical tools that help us solve complex equations when traditional methods fall short. They’re important because they allow us to find solutions to equations that might not have straightforward answers. Imagine trying to pinpoint the exact location where a function crosses the zero line – that’s what these methods help us do.
In the real world, equations can represent everything from engineering problems to scientific mysteries. These methods are like problem-solving superpowers, making it possible to optimize designs, predict physical behaviors, and analyze data more effectively.
Learning Numerical Root Finding Methods is essential because it equips us with problem-solving skills that are valuable in various fields. Whether you’re an engineer, scientist, or programmer, these methods provide you with tools to tackle complex equations and find solutions that might otherwise remain hidden. So, learning them opens up a world of possibilities for solving real-world problems.
About this Free Numerical Root Finding Methods Course
Welcome to our Free Numerical Root Finding Methods Course! In this course, we’ll dive into the fascinating world of numerical methods designed to find the roots of equations, a crucial skill for solving real-world problems. Whether you’re an aspiring engineer, scientist, or programmer, understanding these methods can significantly enhance your problem-solving abilities.
This course covers the numerical methods for Root Finding (Solving Algebraic Equations) from theory to implementation. In this course, three methods are reviewed and implemented using Python and MATLAB from scratch.
This course is structured to take you on a journey through three essential root-finding techniques: Bisection, Secant, and Newton-Raphson. You’ll start with the basics, learning the theories and concepts behind each method. Then, we’ll roll up our sleeves and get hands-on by implementing the code in both Python and MATLAB, giving you practical experience that you can apply in various domains.
At first, two interval-based methods, namely Bisection method and Secant method, are reviewed and implemented. Then, a point-based method which is knowns as Newton’s method for root finding, a.k.a. Newton–Raphson method, is reviewed and implemented. This course is instructed by Dr. Mostapha Kalami Heris, who has years of practical work and active teaching in the field of programming, mathematics, control engineering and computational intelligence
By the end of this course, you’ll be equipped with a toolkit of numerical methods, ready to tackle equations, optimize designs, and make data-driven decisions. Join us on this exciting learning adventure and take the first step towards becoming a proficient problem solver with Numerical Root Finding Methods!
What you will gain
By enrolling in this Free Numerical Root Finding Methods Course, you’ll gain invaluable problem-solving skills that are essential across various fields and industries. Starting with a strong foundation in the fundamental concepts, you’ll progress to practical implementation, enabling you to confidently tackle real-world equations and optimize solutions. After completing this course, you’ll have the ability to employ three powerful root-finding methods: Bisection, Secant, and Newton-Raphson, and you’ll master their implementation in both Python and MATLAB.
Imagine the impact on your career or academic pursuits when you can efficiently find roots of complex equations, make data-driven decisions, and optimize designs. With these skills, you’ll be better equipped to excel in engineering, scientific research, data analysis, and more. Don’t miss this opportunity to enhance your problem-solving abilities and take your skills to the next level. Join us on this learning journey, and you’ll emerge with the confidence to tackle challenging problems and make a significant impact in your chosen field.
All source codes implemented within course and hand-written notes of the lectures, are available to download, in the downloads section of this very page.
Course Outline and Content
Our Free Numerical Root Finding Methods Course is structured to provide you with a comprehensive understanding of three essential root-finding techniques: Bisection, Secant, and Newton-Raphson. The part for each of the 3 methods begin with a solid theoretical foundation, explaining the core concepts of that method of root finding and the underlying mathematics. You’ll then dive into practical implementation, learning how to apply these methods to real-world problems step by step.
In the first part, you’ll explore the Bisection method, starting with the theory and concepts behind it. You’ll learn to implement this technique in both Python and MATLAB, gaining hands-on experience and insight into its strengths and limitations. Moving forward, the second part delves into the Secant method, equipping you with the knowledge and skills needed to apply this powerful approach. The course concludes with the third part, where you’ll master the Newton-Raphson method, understanding its advantages and best practices.
Upon completion of this course, you’ll have a solid grasp of numerical root finding methods, bolstered by the ability to implement them in Python and MATLAB. Whether you’re a student, a professional seeking career advancement, or someone looking to enhance their problem-solving skills, this course offers a structured and accessible path to mastery in this essential domain. Join us on this journey to unlock your potential and achieve greater success in your field.
Topics covered in this part are listed below:
- Introduction to Bisection Method
- Implementation of Bisection Method in Python
- Implementation of Bisection Method in MATLAB
- Introduction to Secant Method
- Implementation of Secant Method in Python
- Implementation of Secant Method in MATLAB
- Introduction to Newton–Raphson Method
- Implementation of Newton–Raphson Method in Python
- Implementation of Newton–Raphson Method in MATLAB
All source codes implemented within course and hand-written notes of the lectures, are available to download, in the downloads section of this very page.
This course includes:
- More than one hour on-demand video
- Access on PC, mobile, tablet and TV on different platforms such as Yarpiz website, Youtube, Udemy and Alison
- Downloadable resources
- Certificate available on Alison
Requirements
To embark on this Free Numerical Root Finding Methods Course, there are minimal prerequisites. You’ll need a basic understanding of mathematics, including concepts such as functions, derivatives, and mathematical notation. Familiarity with programming languages like Python and MATLAB is advantageous, although not mandatory, as we provide step-by-step instructions for implementation. Having access to a computer or laptop with the necessary software installed is essential to practice the code examples shared throughout the course.
While this course is designed to be beginner-friendly, a strong desire to learn and an enthusiasm for problem-solving are invaluable. If you possess these qualities and meet the basic requirements mentioned, you’re well-prepared to embark on a rewarding journey through the world of numerical root finding methods. So, whether you’re a student eager to enhance your mathematical skills, a professional seeking to bolster your problem-solving toolkit, or someone passionate about expanding your knowledge, this course is accessible to a wide range of learners. Join us today and take the first step toward mastering numerical root finding methods.
Who can benefit from this course?
This Free Numerical Root Finding Methods Course is tailored for a diverse audience seeking to harness the power of numerical techniques for solving mathematical problems and real-world challenges. Whether you’re a student, a working professional, or an enthusiast eager to expand your skill set, this course offers valuable insights and practical skills.
Students pursuing degrees in mathematics, engineering, computer science, or related fields will find this course to be an invaluable supplement to their academic journey. It provides a solid foundation in numerical methods and equips students with problem-solving skills applicable in various domains.
Professionals working in engineering, data analysis, finance, and scientific research can benefit significantly from this course. It offers a practical understanding of numerical root finding methods and demonstrates their relevance in optimizing processes, making data-driven decisions, and solving complex equations.
Enthusiasts and self-learners looking to explore the world of numerical mathematics will discover a welcoming entry point in this course. With its accessible approach and real-world applications, it’s designed to empower learners from diverse backgrounds to embark on a rewarding journey into numerical root finding methods.
About the Instructor
Dr. Mostapha Kalami Heris, your instructor for the “Practical Genetic Algorithm in Python and MATLAB” course, is a renowned expert in Control and Systems Engineering. Born in Heris, Iran, in 1983, he earned his B.S. from Tabriz University in 2006, his M.S. from Ferdowsi University of Mashhad in 2008, and his PhD from Khaje Nasir Toosi University of Technology in 2013, all in Control and Systems Engineering.
Dr. Kalami is more than just an instructor; he is also a key member of the Yarpiz Team, which provides valuable academic resources and tutorials. His interests span a wide range of topics, including computer programming, machine learning, artificial intelligence, meta-heuristics, and control engineering. With his vast knowledge and expertise, Dr. Kalami is the ideal mentor to guide you through the exciting world of genetic algorithms, making complex concepts understandable and engaging for learners of all levels.
Watch Online
The video tutorial is available to watch online, via Yarpiz YouTube Channel. The YouTube playlist, containing all parts of this series, follows.
One Response
How can I use Newton’s Method for an array of elements of x?