Brief Introduction
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Brief Summaries of Topics
0.1 Linear Algebra
0.2 Real Analysis
0.3 Differential Vector-Valued Functions
0.4 Point Set Topology
0.5 Classical Stokes\' Theorems
0.6 Differential Forms and Strokes\' Theorem
0.7 Curvature for Curves and Surfaces
0.8 Geometry
0.9 Countability and the Axiom of Choice
0.10 Elementary Number Theory
0.11 Algebra
0.12 Algebraic Number Theory
0.13 Complex Analysis
0.14 Analytic Number Theory
0.15 Lebesgue Integration
0.16 Fourier Analysis
0.17 Differential Equations
0.18 Combinatorics and Probability Theory
0.19 Algorithms
0.20 Category Theory
A brief introduction to complex analysis
(underline{Def:})A func (U(subset mathbb{C}) stackrel{f}longrightarrow mathbb{C})is (complex) differentiable at a point (z_0 in intU)(int:内部)
If f is cpx diff at (z_0),we call the limit the (cpx) derivative of f at (z_0) and devote it by (f^{prime}(z_0))or (frac{df(z_0)}{dz})
if (U stackrel{f}longrightarrow mathbb{C})is (cpx)diff at every z
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