MATH-105(b): Advanced analysis II

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Lectures in this course (47)

Partial Derivatives: Definitions and Applications

Explores the definitions and applications of partial derivatives in functions of several variables, emphasizing the importance of specifying the choice of variables.

Partial Derivatives: Definitions and Examples

Covers the concept of partial derivatives and their applications in mathematical analysis.

Differentiability and Derivatives

Revisits the definition of differentiability and the existence of derivatives for functions in open intervals.

Advanced Analysis II: Differentiability and Continuity

Explores differentiability and continuity in advanced analysis, emphasizing the importance of continuity and demonstrating key concepts.

Differential Functions and Tangent Plan

Covers differentiable functions, derivatives, and tangent planes in mathematics.

Advanced Analysis II: Tangent Plan and Differentiability

Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.

Derivatives of Functions: Differentiability and Matrices

Explores differentiability, matrices, and composite functions through examples and mathematical notations.

Advanced Analysis II: Derivatives and Functions

Covers the review of derivatives and functions, including the concept of chain rule and graphical representation.

Differentiable Functions in R²

Covers the representation of differentiable functions in R² and the concept of changes of coordinates through bijections.

Advanced Analysis II: Laplacian and Coordinates

Covers the Laplacian operator in different coordinate systems and its applications in differential equations.

Advanced Analysis II: Gradient Generalizations

Explores gradient generalizations and applications in advanced analysis.

Generalized Integrals and Convergence

Explores generalized integrals, convergence, implicit functions, and higher-order derivatives.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Advanced Analysis II: Demonstration of Functions and Tangent Planes

Covers the demonstration of functions and the application of tangent planes.

Directional Derivative: Definitions and Examples

Covers the definition of directional derivative and provides illustrative examples.

Advanced Analysis II: Differentiable Functions

Explores differentiable functions, Taylor approximations, and directional derivatives in open sets.

Advanced Analysis II: Methods of Calculus Composition

Covers the second method of calculus composition and the application of the binomial formula.

Local Extrema of Multivariable Functions

Revisits local and absolute extrema of multivariable functions, discussing their properties and identification conditions.

Advanced Analysis II: Taylor Expansion

Covers the Taylor expansion and properties of the Hessian matrix for stationary points.

Advanced Analysis II: Eigenvalues and Compact Sets

Covers the reconstruction of a table using diagonal matrices and explores extreme values and set definitions.

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