differentiation

현은영, Jan 4, 2016

1. differentiation principle 2. integral calculus 3. differential and integral calculus

Table of Contents

  1. differentiation
    1. Differentiation from First Principles
    2. Differentiation from First Principles
    3. parabola-gradient and secant
    4. Differentiation Introduction
  2. applied differentiation
    1. differential of a function
    2. Example of Implicit Differentiation
    3. Implicit function with vertical tangent
    4. Implicit Differentiation
    5. Derivative of f(x)=sinx
  3. Integral
    1. Integral
    2. Area of fence Example 1
    3. Fundamental Theorem of Calculus
  4. differential and integral calculus
    1. Differentiation vs integration - ex1
    2. Differentiation vs integration

1.

differentiation

[color=#c51414]미분[/color]이란 한 점에서의 기울기, 즉 순간 가속도를 의미한다. 점 하나를 움직일때마다 2차함수에서 점 하나가 갖는 기울기가 1차함수로 나타나게 되는데 이때 이 1차함수는 2차함수의 순간가속도이며 [color=#c51414]미분함수[/color]로 불리게 된다.

  • 1. Differentiation from First Principles
  • 2. Differentiation from First Principles
  • 3. parabola-gradient and secant
  • 4. Differentiation Introduction

1.1.

Differentiation from First Principles

Differentiation from First Principles
– Lindsay McLanachan

1.2.

–

1.3.

–

1.4.

–

2.

applied differentiation

미분함수는 2차함수 뿐 아니라 2차함수 이상의 다항함수 (3차함수 4차함수 등) 와 원에서도 가질 수 있다. 이때 다항 함수들은 음함수의 미분법 (implicit function)으로 구할 수 있다.

  • 1. differential of a function
  • 2. Example of Implicit Differentiation
  • 3. Implicit function with vertical tangent
  • 4. Implicit Differentiation
  • 5. Derivative of f(x)=sinx

2.1.

differential of a function

differential of a function
differential of a function
differential of a function
– Tom Owsiak

2.2.

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2.3.

–

2.4.

–

2.5.

–

3.

Integral

적분은 미분과 많이 연관이 되어있는데 적분은 미분의 반대라고 보면 된다. 미분함수보다 1차 높은 함수로 쓰이는데 대부분 미분함수의 어떤 구간에서 넓이를 구할 때 쓰인다.

  • 1. Integral
  • 2. Area of fence Example 1
  • 3. Fundamental Theorem of Calculus

3.1.

Integral

Integral
Integral
Integral
– matte Lena, mtamim1

3.2.

–

3.3.

–

4.

differential and integral calculus

  • 1. Differentiation vs integration - ex1
  • 2. Differentiation vs integration

4.1.

Differentiation vs integration - ex1

Differentiation vs integration [br]Example 1
Differentiation vs integration - ex1
– Chow Kong Fai

4.2.

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