Real Analysis: Exam 2018 Review

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Covers the Continuity Theorem for functions dependent on a parameter, proving the continuity of a function g.

Complex Integration and Cauchy's Theorem

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Uniqueness of Solutions: Cauchy-Lipschitz Theorem

Covers the uniqueness of solutions in differential equations, focusing on the Cauchy-Lipschitz theorem and its implications for local and global solutions.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.