What Is Numerical Analysis?

An introduction to numerical analysis, explaining numerical methods, their importance, and applications across various fields.

Key Takeaways

Numerical methods allow approximate but practical solutions to complex math problems.
Computational power makes numerical methods increasingly accessible and useful.
There is often a balance between solution accuracy and computational effort.
Numerical analysis is applicable across many scientific, engineering, and financial domains.
Learning numerical methods involves both theory and practical software implementation.

What the video covers

Numerical analysis is a branch of math focused on studying and developing numerical methods.
Numerical methods provide approximate solutions to math problems when exact solutions are difficult or impossible.
Analytical methods use exact steps like addition and multiplication, but numerical methods accept approximations.
Numerical methods are powerful especially with the rise of cheaper computational power.
These methods are computation-heavy and well-suited for programming.
There is a trade-off between accuracy and computational time in numerical methods.
Numerical analysis applies to many fields including finance, engineering, and science.
Topics covered in the course include solving linear systems, root-finding, interpolation, numerical differentiation, and integration.
The course includes examples and software implementations to demonstrate the power of numerical analysis.
Viewers are encouraged to engage by liking, subscribing, and commenting with questions or concerns.

Chapters

What is numerical analysis?

Numerical analysis is a branch of mathematics focused on developing numerical methods to find approximate solutions to mathematical problems when exact solutions are difficult or impossible.

Why are numerical methods important?

Numerical methods allow us to solve complex problems approximately and efficiently, especially when analytical solutions are not feasible or would take too long to compute.

What topics are covered in this numerical analysis course?

The course covers solving linear systems, root-finding methods, interpolation, numerical differentiation, integration, and includes practical software implementations of these algorithms.

Full Transcript — Download SRT & Markdown

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Let's talk about what numerical analysis is. Numerical analysis is a branch of math that focuses on studying and developing numerical methods. Well, that still might be confusing for you if you're new to the topic, so let's break down this concept a bit further.

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And begin talking about what numerical methods are. Numerical methods, at their core, are just a mathematical tool where we are going to have to solve certain problems. But how do they do that? Well, put simply, they allow us to find

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and accept approximate answers to math problems rather than needing to find the exact one. Previously, in your math classes, you have been solving problems analytically, meaning you take some certain steps: addition, subtraction, multiplication, division, to achieve the exact solution.

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However, sometimes finding the solution to a math problem analytically is impossible or will just take us a very long time. As a quick example, let's say you're asked to find the integral of the following discrete data set. Well, we first need a function to

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integrate, which we can use interpolation to find the function for a future topic in this course, and then even calculate the integral numerically, which is also something that we will cover in a future video. Numerical methods are incredibly

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powerful, especially as computation power is becoming much cheaper globally. As many numerical methods are computation-heavy by nature, they are suitable for programming, which will also be extensively covered throughout this course. In summary, we use numerical methods to

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compute approximate answers to math problems, and although our answers are approximate, we want them to be accurate and as computationally easy as possible to ensure our solution is as close to the exact answer and can be found quickly. Often, these two are a trade-off, as

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numerical methods are often iterative, and we exchange an accurate solution with more computation time. The methods that will be taught throughout this numerical analysis course can aid anyone from the financial sector, every engineering and science field, and really about just any field

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where computations can be applied. Throughout this numerical analysis course, we will cover many topics such as solving linear systems of equations, root-finding methods, interpolation, numerical differentiation, integration, and more. Additionally, as I've stated previously, throughout this course we will also go

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through many examples of each algorithm and implement the various methods into different computer software to demonstrate the true power of numerical analysis and the subsequent numerical methods humans have developed and optimized. I hope this helped you have a

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brief understanding of what numerical analysis is and why you should learn more about it. If you enjoyed, please like, subscribe, and consider checking out our YouTube memberships by clicking the join button down below. However, if you have any

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comments, questions, or concerns about the information I provided in this video, please leave a comment down below, and I will do my best to address your concerns.

Topics:numerical analysisnumerical methodsapproximate solutionscomputational mathinterpolationroot-findinglinear systemsnumerical differentiationnumerical integrationmath programming

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