2016년 5월 24일 화요일

Express Functions from Taylor Series





Before read this post,

read

Taylor Series





Taylor Series and Maclaurin Series



We can express some functions by the series.







Fourier Transform from Fourier Series





Before you see this post,

see


Definite Integral of Multiplied 2 Trigonometric Functions



Express Functions from Taylor Series









We can think f(t) is sum of wave functions and a constant.

if t=0, f(0) = a_0.




Then, let's find a_0.


We can find a_0 like process above.






Through

Definite Integral of Multiplied 2 Trigonometric Functions,


we can find a_n ( except n = 0 ) and b_n.







Use

Express Functions from Taylor Series,


we can develop the formula.




In the process, we can derive Fourier Transform from Fourier Series.



2016년 5월 23일 월요일

2016년 4월 25일 월요일

Exact Differential Equation





Before you see this post,

see

Relationship between Integral and Differential


Total differential








Definition of exact differential equation






Solutions of exact differential equation








Matrix Operation


pic. 1

Let's think about possible conditions of matrix operation
by reading pic. 1.



Example

pic. 2





pic. 3

There are n x n matrices, A and B.
Every matrix has rows and columns like pic. 3.


Let's operate matrices.

pic. 4

We can operate like pic. 4.





Example

pic. 5
Examples of Matrix Operation