Course

MATH-105(a): Advanced analysis II - vector analysis

Lectures in this course (50)

Covers the existence and uniqueness theorem for Cauchy problems and explores global solutions of differential equations.

Explores limited and Taylor formulas for derivatives around specific points.

Covers the definition of multiple integrals, volume calculation, tensorial partitions, and integrable functions.

Explores the challenges of integrating functions with parameters and the importance of uniform convergence.

Discusses inverse functions and local invertibility based on the determinant of the Jacobian matrix.

Explores the uniqueness of solutions to differential equations, emphasizing global solutions and the linearity of second-order scalar equations.

Covers the definition and properties of multiple integrals, including partitions and the theorem of Fubini.

Explores properties of inverse functions, continuity, and hyper surfaces.

Explores the Cauchy-Lipschitz theorem for ODE solutions and linear transformations.

Explores deficiency in cupliere sulposous through mathematical functions and variable relationships.

Explores vectorial calculus, divergence, curl, gradient, implicit functions, and local inversion theorems.

Explores diffeomorphisms, implicit functions, and coordinate transformations in advanced analysis.

Covers the definition of extremum of a function and necessary conditions for local extrema.

Explores the local inversion theorem, demonstrating uniqueness of solutions and continuity of functions.

Explores linear second-order ODEs with constant coefficients and methods for finding particular solutions.

Introduces the Lagrange multiplier method for solving optimization problems with constraints.

Covers extreme values, optimization conditions, feasible sets, and partition formation for optimization.

Covers the solution of linear second order ODEs with constant coefficients and explores the method of variation of parameters.

Covers the local inversion theorem and uniqueness of solutions in a ball around a point.

Covers the definition of the integral, Riemann integral, upper and lower Riemann integrals, and the integrability of functions.