MATH-106(f): Analysis II

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Lectures in this course (101)

Partial Derivatives: Functions and Definitions Log in to Mediaspace to watch this video

Explores partial derivatives of functions with multiple variables, emphasizing their definitions and properties.

Implicit Functions: Theory and Examples Log in to Mediaspace to watch this video

Explores the theory of implicit functions, their properties, and illustrative examples.

Nature of Extremum Points Log in to Mediaspace to watch this video

Explores the nature of extremum points in functions of class e² around the point (0,0), emphasizing the importance of understanding their behavior in the vicinity.

Taylor Series: Development and Applications Log in to Mediaspace to watch this video

Explores Taylor series development up to order 2 and its applications.

Lagrange Multipliers Theorem Log in to Mediaspace to watch this video

Explores the Lagrange multipliers theorem for n>2, demonstrating its application in optimization problems with constraints.

Extrema Absolutes Log in to Mediaspace to watch this video

Explores absolute extrema, continuity, compactness, and interval properties on compact sets.

Theorem of the Average Log in to Mediaspace to watch this video

Explores the Theorem of the Average, integrability criteria, properties of the integral, and volume concepts.

Integral Calculus: Riemann Integration Log in to Mediaspace to watch this video

Explores Riemann integration for functions of several variables, Darboux sums, and the criteria for integrability.

Center of Gravity and Variable Change Log in to Mediaspace to watch this video

Discusses center of gravity, variable change, spherical coordinates, and bijectivity in mathematical analysis.

Change of Variables: Integrability and Fubini's Theorem Log in to Mediaspace to watch this video

Explores changing variables in double integrals and applying Fubini's theorem in R² for simplifying calculations.

Sphere, Cone, and Paraboloid Log in to Mediaspace to watch this video

Explores the intersection of a sphere, cone, and paraboloid in 3D space.

Change of Coordinates: Notation and Examples Log in to Mediaspace to watch this video

Covers the notation and examples of change of coordinates in various scenarios and systems.

Volume Calculation of Revolution Bodies Log in to Mediaspace to watch this video

Explores volume calculation of revolution bodies using mathematical formulas and inequalities.

Tangent Plane to Implicit Function Log in to Mediaspace to watch this video

Explores the tangent plane to implicit functions, emphasizing equations and graphical representations.

Extreme Absolute Points: Examples Log in to Mediaspace to watch this video

Covers examples of absolute extrema and how to find extreme points.

Intersection between Sphere and Cone Log in to Mediaspace to watch this video

Explores the intersection between a sphere and a cone using spherical and cylindrical coordinates.

Functions of Class C^p Log in to Mediaspace to watch this video

Explores functions of class C^p, emphasizing continuity and differentiability properties.

Implicit Functions Theorem Log in to Mediaspace to watch this video

Covers the theorem of implicit functions for n>2, with examples demonstrating the application of the theorem.

Derivation of an Integral: Parameter Dependency Log in to Mediaspace to watch this video

Covers the derivation of an integral dependent on a parameter, focusing on the analysis of functions and their properties.

Extrema of Functions in Several Variables Log in to Mediaspace to watch this video

Explains extrema of functions in several variables, stationary points, saddle points, and the role of the Hessian matrix.

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