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MTL122 - Coggle Diagram
MTL122
Complex Analysis
Differentiability
Analogous to R and almost the same idea
implies R^2 Differentiability
Any linear transformation is Differentiable
Necessary condition for differentiability and the CR Equation
Partial derivatives same as in R^2
Sufficient condition for differentiability Continuity of PD and CR Equation
Connectedness
Open and Connected
Path Connected+Extra
Extra Special kind of paths line segments parallel to x and y axis
Domains in Complex
Path Connectedness
Limit of functions
Same as in R2
Important idea relating to different paths and many possibilities
Can be used to define continuity
Sequential defination essential idea that the point is not part of the sequence
Functions from C to C
Can write identify the real and imaginary parts as separate fucntions
One point compactification
Extended real and complex system which is compact