MATH AA HL IA – Laplace Transform

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M22 Math AA HL 과목의 IA입니다. 총점 18/20를 받아 7점을 프리딕과 파이널에서 모두 받았습니다. 주제는 Laplace transform입니다. 현재 실라버스와 더 advanced 컨셉이 적당히 잘 섞여 좋은 피드백과 점수를 받았습니다.

 

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PERSONAL ENGAGEMENT AND AIM

In a school test for the differential equation unit, I was given a question on kinematics that required multiple steps of integration techniques:


      Figure 1: Question of the test (Taken by author)

The first aim of the paper is to explain the differential equation of skydiving by discussing the relation between acceleration and velocity with Physics. Then, using the derived acceleration, we will attempt to apply various mathematical understanding to derive the velocity and displacement functions.

DERIVATION OF THE INITIAL ACCELERATION EQUATION

Firstly, it is important to discuss why the acceleration of skydiving was given in terms of velocity in the question. To understand the modelling, we need to consider the existence of gravity and air resistance that divers face during diving. we will apply the Newton’s second law of motion; Newton’s second law states that the force is a product of mass and acceleration:

F = ma

F: force in N
m: mass in
a: acceleration in /²

 

  • 총 페이지수: 23 pages
  • 과목명: Mathematics
  • 주제: Laplace transform
  • The file is in PDF format. 
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MATH AA HL IA – Laplace Transform

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