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

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Lectures in this course (50)

Generalized Integrals: Definition and Applications Log in to Mediaspace to watch this video

Covers the definition and applications of generalized integrals in advanced analysis, including real functions, differential equations, and multiple integrals.

Limits and Convergence Log in to Mediaspace to watch this video

Covers the concept of limits and convergence, including the definition of limits and absolute convergence.

Taylor and Lagrange Formulas Log in to Mediaspace to watch this video

Explores limited and Taylor formulas for derivatives around specific points.

Integral Functions: Parameters and Uniform Convergence Log in to Mediaspace to watch this video

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

Inverse Function Theorem Log in to Mediaspace to watch this video

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

Inverse Functions: Properties and Continuity Log in to Mediaspace to watch this video

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

Deficiency in Cupliere Sulposous Log in to Mediaspace to watch this video

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

Vectorial Calculus Log in to Mediaspace to watch this video

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

Extreme Points of Functions Log in to Mediaspace to watch this video

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

Optimization Problems: Lagrange Multiplier Equations Log in to Mediaspace to watch this video

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

Extreme Values and Optimization Log in to Mediaspace to watch this video

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

Integral Definition Log in to Mediaspace to watch this video

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

Vector Spaces: Operations and Properties Log in to Mediaspace to watch this video

Explores vector spaces, scalar products, standards, and symmetric matrices in the context of operations and properties.

Riemann Integral: Properties and Characterization Log in to Mediaspace to watch this video

Explores the properties and characterization of the Riemann integral on different sets and measurable sets.

Riemann Integral: Properties and Generalization Log in to Mediaspace to watch this video

Explores characterizations and generalizations of the Riemann integral, showcasing its properties and applications.

Integration and Transformations Log in to Mediaspace to watch this video

Covers the calculation of definite integrals and different coordinate systems.

Ordinary Differential Equations Log in to Mediaspace to watch this video

Introduces first-order scalar differential equations, higher-order equations, global solutions, and the selection process for equations.

First-Order Linear Equations: Existence Theorems and Solutions Log in to Mediaspace to watch this video

Explores first-order linear equations, existence theorems, and integral solutions in differential equations.

Homogeneous Equations: Advanced Analysis II Log in to Mediaspace to watch this video

Explores second-order linear scalar homogeneous equations in advanced analysis II.

Characteristic Polynomial: Selections and Equations Log in to Mediaspace to watch this video

Discusses characteristic polynomials, real roots selections, and tick equations.

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