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 `d^(-1.5)/dx^(-1.5)` sin(x) = ? `d^1.5/dx^1.5` cos(x) = ? `d^0.5/dx^0.5` |cos(x)| = ? `d^1.2/dx^1.2 e^(x)` = ? `d^0.5/dx^0.5 x^2` = ? `d^1.5/dx^1.5` log(x) = ? `d/dx int _0^(x^2) ln(t^2+1) dt` = ? expand( `Gamma(3,x)` ) = ? `sum x` = ? solve( `x^2+3*x+2>0` ) ? solve(log(x+1)-log(1-x)=1) ? solve(y'=x*y+x) ? `d ^ -1.5 / dx ^ -1.5` sin (x) ? = `d ^ 1.5 / dx ^ 1.5` cos (x) ? = `d ^ 0.5 / dx ^ 0.5` | cos (x) | =? ` d ^ 1.2 / dx ^1.2 e ^ (x) ` =? `d ^ 0.5 / dx ^0.5 x ^ 2` =? `d ^ 1.5 / dx ^ 1.5` log (x) =? `d / dx int _0 ^ (x ^ 2) ln(t ^ 2 + 1) dt` =? expand (`Gamma (3, x)`) =? `sum` x =? Solve (`x ^ 2 + 3 * x + 2> 0`) ? Solve (log (x + 1) -log (1-x) = 1) ? Solve (y '= x * y + x) ?

数学 Mathematics

最早是研究量、结构、变化以及空间模型的科学 。 The earliest research quantity, structure, space model change and science . 在现代，数学又是利用逻辑形式研究现实世界的空间形式和数量关系的学科，尽管对某一特定结构的研究往往属于自然科学，特别是物理学的范畴。 In modern times, mathematics is the study of form and discipline but also the relationship between the number of real-world use of space logical form, although the study of a particular structure is often part of the natural sciences, especially in areas of physics. 同时由于数学自身的发展，数学家也要研究纯粹属于数学内部的结构。 At the same time due to the development of mathematics itself, mathematicians have to study the internal structure of a purely mathematical.

数学内容: 包括初等数学 、初等数论、微积分、解析几何与微分几何、高等代数、微分方程与积分方程、函数论、概率论、傅立叶分析、矢量与张量、特殊函数等。 Math Content: Includes elementary mathematics , elementary number theory, calculus, analytic geometry and differential geometry, advanced algebra, differential equations and integral equations, function theory, probability theory, Fourier analysis, vector and tensor, special functions and so on.

数学方法: 如最优化方法、有限元法、数理统计、实验数据处理等。 Mathematical Methods: as optimization method, finite element method, mathematical statistics, experimental data processing.

数学理论: 如抽象代数、线性空间、一般拓扑学、泛函分析等。 Mathematical theory: as abstract algebra, linear space, general topology, functional analysis and so on.

数学分初等数学和高等数学 。 Mathematics in elementary mathematics and higher mathematics .

数学分支学科： Branches of mathematics:
1. 初等数学 : 1 Elementary Mathematics :
代数 Algebra
初等函数初等几何平面三角与三角函数球面三角代数方程 Elementary function elementary geometric plane triangle spherical trigonometry and trigonometric algebraic equations

2. 高等数学 : 2. Higher Mathematics :
矩阵行列式线性代数微分学积分学解析几何微分几何场论黎曼几何抽象代数线性空间泛函分析复变函数傅立叶级数与积分变换特殊函数常微分方程偏微分方程积分方程概率统计与随机过程误差理论与实验数据处理最优化方法有限元法数论集论拓扑学 Matrix determinant linear algebra Differential calculus analytic geometry Riemannian differential geometry field theory of abstract algebraic linear space functional analysis of complex function and integral transform Fourier series of special functions of ordinary differential equations partial differential equations integral equations statistical probability and stochastic process error Theoretical and experimental data processing methods to optimize the number of FEM Essays on Topology

改变世界面貌的十个数学公式 Changing the World Ten mathematical formulas

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