数值分析笔记

Numerical Analysis, different from Data Analysis, is a subject of mathematics. The main purpose of this course is using numerical methods such as fitting methods, approaching methods and interpolation methods to approach the results of PDE, ODE, integrations, and solutions of linear equations.

These methods are widely used in many aspects, include physics, computer science, biology technology, etc. As long as people need to solve these equations or calculate some functions, they will need the methods in Numerical Analysis. So, it is no doubt that this subject is one of the most important subjects and it is also really hard to master (in my mind).

At that semester, this subject took up 6 credits and 100+ hours. During this time, we completed 5 or more experiments and a project with a presentation. This experience made me comprehend this subject better and during the final exam period, I completed these three notes.

One is the outline of Numerical Analysis, include the main methods and theories behind them in different chapters and their applications. This note can help me master the whole frame of this subject and get to learn how we gradually learned it.

It was not an easy time for me to summary this frame because there were really too many parts of methods and also hard to figure out the relationships between them. Fortunately, I finished it anyway. I always think remembering and mastering the frame of a subject is really important, not only for understanding the details better but remembering them better.

The second note is about the definitions in Numerical Analysis. Just like Topology, remembering and understanding basic definitions is crucial for further study. In Numerical Analysis, it is not “better to do”, but “have to do”. If you do not master these definitions, it will be really tough to understand the methods because you have to check each step and learn what this character means and why it can be concluded by other things.

There are many formulas and it seems not easy to remember them, but actually, there are many regular patterns of them and if you can master them, it will be easy to remember these formulas.

And the final note is the most painstaking one. It includes the details of the different methods and some theories we should master. Of course, it is better to read the textbook seriously and then try to reference this note, because there are no explanations in detail in this note.

So, just “enjoy” this subject for its sophisticated methods and amazing theories.


The overall structure of Numerical Analysis.pdf


The definitions in Numerical Analysis.pdf


The summary of methods in Numerical Analysis.pdf


You can also find notes in detail from chapter 0 to chapter 7.