Implicit Functions: Local Existence Theorem

Covers the advanced analysis of implicit functions, focusing on the application of the theorem of implicit functions.

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Explores divergence of vector fields, rotational definitions, and integral derivation applications.

Covers derivability on an interval, including Rolle's Theorem and practical applications in function analysis.

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.