Lectures in course MATH-106(e): Analysis II

Analyse II 2021: Course Organization

Covers the organization of the Analyse II course for 2021, including webinars, exercises, and the final exam.

Differential Equations: Solutions and Derivatives

Explores differential equations solutions, derivatives, differentiability, composite functions, and continuous functions.

Ordinary Differential Equations

Explores ordinary differential equations, including general solutions, separate variables, order, linearity, and proof methods.

Differential Equations: Existence and Uniqueness

Covers differential equations with separated variables, existence and uniqueness of a solution with a given initial condition.

Linear Differential Equations: General Solutions

Covers linear differential equations of the first order and methods of demonstration.

Linear Differential Equations: Solutions and Wronskian

Covers linear differential equations, focusing on solutions, the Wronskian, and methods for solving non-homogeneous equations.

Linear Differential Equations

Explores linear differential equations of the second order and the construction of linearly independent solutions.

Differential Equations: Coefficients and Methods

Discusses methods for solving differential equations, focusing on undetermined coefficients and variation of constants.

Linear Differential Equations

Covers second-order linear differential equations and their solutions, including the method of variation of constants.

Linear Differential Equations

Explores solving second-order linear differential equations with constant coefficients and various demonstration methods, including demonstration by absurdity.

Vector Spaces and Topology

Covers normed vector spaces, topology in R^n, and the principle of drawers as a demonstration method.

Convergence in R^n

Explores open and closed subsets, convergence in R^n, and bounded sequences.

Compact Subsets of R^n

Explores compact subsets of R^n, convergence theorems, and set properties.

Real Functions of Several Variables: Definitions and Examples

Covers definitions and examples of real functions of several real variables, including limits and visualization techniques.

Limits of Functions: Characterization and Operations

Explores limit characterization using sequences and algebraic operations on limits.

Limits of Functions: Calculus Methods

Explores the concept of limits of functions of several variables and methods for calculation, including criteria based on convergent sequences and the 'two gendarmes' theorem.

Maximum and Minimum of Functions

Explores limits, minimum and maximum values of functions, and continuity criteria in a compact set.

Recurrence Method: Generalization and Differential Calculus

Explores the fundamental principle of the recurrence method and differential calculus of functions of several variables.

Partial Derivatives and Gradient

Explores partial derivatives, gradient, directional derivatives, and differentiability in determining slopes.

Differential Functions: Derivability and Gradient

Explores differentiability in functions and the role of gradients in directional derivatives.