This covers the epsilon-delta definitions of limits, continuity, and differentiability for complex-valued functions, each defined using the complex modulus in place of the real absolute value, together with foundational point-set topology of the complex plane (epsilon-neighborhoods, open sets, boundary points, path-connectedness, and convexity). It belongs to complex analysis and largely mirrors real analysis, with standard limit laws (sum, product, quotient) carrying over unchanged, while highlighting that seemingly natural operations (complex conjugation, real part, imaginary part, modulus) can fail to be differentiable even though they are continuous.
This covers the epsilon-delta definitions of limits, continuity, and differentiability for complex-valued functions, each defined using the complex modulus in place of the real absolute value, togeth…