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Mathematical modeling notes
Mathematics has many facets. Though it has a wealth of applications, Mathematics is also a science, and an art, in its own right. Like other sciences, Mathematics is useful, but, just like other forms of art, Mathematics is beautiful, in its own unique way.!

Calculus
1. numerator & denominator 分子和分母

2. Factorization 因式分解: In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original.

Trigonometry
Different types of Triangles:

1. Right angled triangle: 直角三角形

2. Scalene triangle: 斜三角形

3. Isosceles triangle: 等腰三角形

4. Equilateral triangle: 等边三角形

Hyperbolic functions 双曲函数

双曲函数与三角函数有如下的关係:
 * $$\sinh x = {{e^x - e^{ - x} } \over 2}$$
 * $$\cosh x = {{e^x + e^{ - x} } \over 2}$$
 * $$\tanh x = {{\sinh x} \over {\cosh x}}$$
 * $$\coth x = {1 \over {\tanh x}}$$
 * $${\mathop{\rm sech}} x = {1 \over {\cosh x}}$$
 * $${\mathop{\rm csch}} x = {1 \over {\sinh x}}$$


 * $$\sinh x = -i \sin ix \!$$


 * $$\cosh x = \cos ix \!$$


 * $$\tanh x = -i \tan ix \!$$


 * $$\coth x = i \cot ix \!$$


 * $$\operatorname{sech} x = \sec ix \!$$


 * $$\operatorname{csch} x = i\,\csc\,ix \!$$

Differential Equation
1.Ordinary differential equation常微分方程

2.Partial differential equation偏微分方程

3.Difference equation差分方程[]

4.Eular's equation欧拉方程

Ansatz A solution method(educated guess) for differential equations. Seperates space and time.

Derivatives
$$f'(x0)=\lim_{\delta x to 0}{\delta y \over \delta x}$$

Learning Materials
Wikiversity, School of Mathematics:[]