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Vector Calculus Series 1 - Differentiation Basics

This course will provide students with a solid foundation in the fundamentals of differentiation in vector calculus (Calculus 2).

(4.5) 24 reviews

874 learners

  • tkn
Integral Differential

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What you will learn!

  • Properties and operations of vectors and matrices in Euclidean space

  • How to use various coordinate systems

  • Differentiation concepts and rules for multivariable functions

  • Applying vector calculus to solve real-world problems

Introducing the 'Vector Calculus' Series

Vector calculus is essential knowledge in countless fields, including physics, engineering, AI, deep learning, computer graphics, and economics. However , the vast amount of content makes it difficult to study on your own. That's why I created this series, which focuses on the essentials and provides a thorough overview.

If you slowly conquer each series one by one, you too will be able to conquer vector calculus.
Vector calculus, once considered boring and difficult, becomes easier with this course! 👊

The series is structured like this:

Series 1 - Fundamentals of Differentiation Current Course

  • Chapter 1 The Geometry of Euclidean Space
  • Chapter 2 Differentiation

Series 2 - Advanced Differentiation

  • Chapter 3 Higher-Order Derivatives; Maxima and Minima
  • Chapter 4 Vector-Valued Functions

Series 3 - Fundamentals of Integration

  • Chapter 5 Double and Triple Integrals
  • Chapter 6 The Change of Variables Formula

Series 4 - Integral Advanced

  • Chapter 7 Integral Over Paths and Surfaces
  • Chapter 8 The Integral Theorems of Vector Analysis

[Basic Differentiation] The first series of vector calculus lectures!

Curious about differentiation and integration of multivariable functions?🙄
Are you finding Calculus 2 or Vector Calculus at your university too difficult?😭

In this course, you will learn the fundamentals of differentiation in vector calculus.

Let's take a look at some of the things you might be curious about about the course. 🙋‍♂️

Q. What will I learn in Vector Calculus Series 1?
A. In this course, you will learn how to define the differentiation of general functions, such as n-variable functions or vector-valued functions.
* You can get more detailed information by watching the course introduction videos for Units 1 and 2.

Q. I find Calculus 2, a subject I'm learning in college, difficult..😂 Will this course help me?
A. It will be very helpful. Because the lecture time is limited compared to the difficulty of the course at school, it's understandable that students might find it difficult. This course includes detailed explanations, numerous illustrations, and animations to facilitate thorough understanding.

Q. Are any prerequisite subjects required?
A. The prerequisite for taking Series 1 is differentiation of single-variable functions, which is covered in Calculus 1. The course assumes a basic understanding of differentiation of polynomials, logarithmic functions, and trigonometric functions.
As the class progresses, we will cover the basic necessary parts, so even if you don't remember the contents of Calculus 1, you can look them up again and study them.

Q. Why did you split the series into four parts?
A. If I were to open it as a single course, the lecture volume would be enormous, and I was concerned that students would be able to fully understand it. I thought it would be better to divide the course into four series, allowing students to master each section one by one. From a course creator's perspective, I also felt that properly creating and uploading each series would result in a higher level of completion.

Q. The lecture materials are in English. Isn't that difficult?
A. I believe it's ultimately more helpful to learn mathematical terms in their original form rather than through translation, so I've created lecture materials in English. However, classes are conducted in Korean, and the English proficiency required for the lectures is not high, so don't worry. Even if you find Calculus 2 at school difficult because it's taught in English, I believe this course will be helpful.

Please note before taking the class!

  • 😲 It takes at least 30 hours of effort to complete each course. I hate doing things half-heartedly.
  • 😪 If you feel like the lecture is speaking slowly, I recommend watching it at 1.25~1.5x speed.
  • 🙋‍♂️ Please feel free to let me know if you have any questions or suggestions for improvement.
  • 😫 We do not accept questions about personal homework, exam solutions, or genealogy solutions outside of the course content.
  • 🌱 The Calculus 1 course may be produced in the future upon request.

People like this will love hearing this!

  • college students (especially engineering students)
  • postgraduate student
  • People who want to learn math as a hobby
  • For those who want to know about differentiation of multivariable functions

Would you like to take this course too?

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Differentiation in Detail: Foundations of Optimization Theory and Vector Functions
Integration Basics
Integral Advanced

Recommended for
these people

Who is this course right for?

  • For those who want to build a solid foundation in mathematics

  • For those who are new to vector calculus

  • Students preparing for advanced mathematics

  • Anyone who wants to use mathematical tools in engineering and science

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Answers

4.7

Rating

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Courses

새로운것을 배우고 가르치는걸 좋아합니다.
인프런을 통해 많은 분들에게 도움이 되면 좋겠습니다.

 

전문분야 (+좋아하는 분야) 👨‍🎓

  • 전공: 원자력
  • 수학: 선형대수학개론, 대학미적분, 벡터미적분학, 응용미분방정식, 응용해석방정식, 확률과 통계, 수치해석
  • 컴퓨터 언어: 포트란(MPI, OpenMP 포함), Javascript (nodeJS), C#, C++, Python, Solidity, …

출신학교 

  • 박사: 카이스트, 원자력 및 양자공학과, 2011 ~ 2016
  • 석사: 카이스트, 원자력 및 양자공학과, 2009 ~ 2011
  • 학부: 카이스트, 원자력 및 양자공학과, 2005 ~ 2009
  • 고등학교: 경기과학고, 2003 ~ 2005

경력 

  • 2019 ~: 인프런강사
  • 2017 ~ 2018: 스탠다드에너지, 연구소장 
  • 2016 ~ 2017: 스탠다드에너지, 특수연구 총괄

링크

Curriculum

All

16 lectures ∙ (11hr 3min)

Published: 
Last updated: 

Reviews

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24 reviews

4.5

24 reviews

  • athran234169님의 프로필 이미지
    athran234169

    Reviews 1

    Average Rating 5.0

    5

    100% enrolled

    高校時代に文科だったのに、どうして工隊を交差支援したから… 微積分がいつも大変だったのでおかげでとても役に立ちました。以前は数学が好きだったのに、年をとるほど嫌になったんですけど(仕事になってそうか嫌いになりましたよ) 聞きながら理解できたので中が後悔した感じです!あまりにもよく合う講義でした。すべての講義をすべて理解したわけではありません。しばしば再度聞く必要があるようですが、一生所有だからとても心強いですね!講義本当にありがとうございます!

    • tkn
      Instructor

      一生役立つ講座でありますように!ありがとうございます!

  • zemssung4873님의 프로필 이미지
    zemssung4873

    Reviews 2

    Average Rating 5.0

    5

    100% enrolled

    基礎からじっくりと詳しく説明していただき、簡単に理解できるようです。

    • tkn
      Instructor

      大切な受講評 ありがとうございます。

  • generalcode님의 프로필 이미지
    generalcode

    Reviews 20

    Average Rating 4.6

    5

    100% enrolled

    ㅎㅎㅎ 線形代数学もいいと思っていましたが、この授業はもっと面白いですね。

    • tkn
      Instructor

      大切な受講評 ありがとうございます。 これからも面白い講座を作るように努力します。 良い一日を過ごしてください:)

  • engineering123님의 프로필 이미지
    engineering123

    Reviews 1

    Average Rating 5.0

    5

    100% enrolled

    電気電子工学科を志望する高校生です。普段も大学数学に関心が高かったのですが、この講座を頑張ることで最初のボタンを挟むようになりました。本に記載されているすべての内容を本当に細心の注意を払って親切に説明していただき、おかげで概念を一つも欠かさずに跳ねて行きました。連続や微分可能性のように、高校微積分(一変微積分)と重なる部分も多いのですが、このようなことを見ながら、私が見逃していた概念を復習できました。また、説明するときに行列の概念をよく使用していましたが、おかげで不慣れな行列の概念にも慣れることができてよかったです。次のシリーズも引き続き受講する予定です。

    • tkn
      Instructor

      ありがとうございます。 高校生の方がすでにこんな講座を…!情熱に拍手します。 私の講座が少しでも役に立ったようで気持ちいいですね。 大切な受講評ありがとうございました。 これからも便利な講座を作ります!ありがとう:)

  • eugene님의 프로필 이미지
    eugene

    Reviews 3

    Average Rating 3.7

    5

    6% enrolled

    高校数学も長すぎてこの講座を聞くことになってみると、一度見て理解がすぐにはできませんが、それでも丁寧によく説明してみると、一人で数学に挑戦するよりももっと楽しくすることができていいですね。現在シリーズ3まであったのですが、数ヶ月間は楽しく勉強しそうですね。そして、このシリーズが完成した後、次の講座も楽しみにしています。

    • tkn
      Instructor

      本当にありがとうございます! どうすれば内容をうまく伝えることができるのか、たくさん悩んで作りました。だからこういう受講評を見ると、とても嬉しくてもっと一生懸命作りたい気がします。 今はシリーズ4を一生懸命作っていますが、最後のシリーズまで良い講座作るように努力します。 おそらく、次の講座は本物になる可能性が高いです。 それでは、おやすみ、質問、改善点、いつでもお問い合わせください。 大切な受講評もう一度ありがとうございました!

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