IB Math HL Math IA (7점)

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본 문서는 2021년 작성한 Euler Method를 활용한 IB MATH IA 입니다.
7점 받았기에, 도움 많이 되시리라 생각합니다.

 

[본문내용]

Introduction

Back when I learned integration during mathematics classes, I learned that there are several ways to integrate functions: generally known integration for polynomial expressions, integration of some particular function, integration by substitution, integration by parts, and integration using trigonometric identities. Most integration problems were solvable with formulae given on the data booklet. Integration using trigonometric identities was no exception. I remember one day, I wondered ‘What if trigonometric identities were not given? If so, how would I integrate trigonometric functions without them?’. Now that I learned all core concepts for IBDP Mathematics HL, I tried to think of everything that I learned related to trigonometry. I looked through the IB mathematics HL formula booklet to quickly remind myself what I learned during last two years and found the way of writing a

complex number in an Euler’s form ( = { () + ()} = ) (Edukraft., 2012).

…(중간생략)…

Eventually, this investigation will answer the main question of this IA, ‘To what extent is Euler’s identities effective in integrating trigonometric functions?’. The investigation is worthy of notice as it allows me to explore a unique integration method. I look forward to seeing myself developing acquired knowledge.

 

Main Body

There are various ways to prove Euler’s formula: Euler’s formula can be proved by a differential equation, by using the Taylor Series, by visualising Euler’s formula and so on (Tralie, n.d). I specifically wanted to try proving Euler’s formula by using the Taylor Series. This is because, from the IB mathematics HL core part, I learned how to solve a differential equation and how to plot a complex number in rectangular form, meaning there are fewer concepts for me to explore if I choose to prove Euler’s formula by a differential equation or by visualising Euler’s formula. However, in the case of the Taylor Series, it is included on the option topic that I did not get to deal with. Plus, my favourite mathematical concept from the core part is integration. Since I can learn the new mathematical concept related to integration, I chose to prove Euler’s formula via Taylor Series…

 

  • 총 페이지수: 23 pages
  • 과목명: Mathematics
  • 주제: To what extent is Euler’s identities effective in integrating trigonometric functions?
  • The file is in PDF format.
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IB Math HL Math IA (7점)

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