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

Explains convergent sequences, bounded sequences, subsequences, and compact sets with illustrations and proofs.

Explores the Cauchy problem, emphasizing solution finding and verification processes.

Discusses methods for solving first-order linear differential equations, focusing on separation of variables and the integrating factor method.

Introduces the Analysis 2 course, covering course structure, language support, and exercise sessions.

Explores dynamic systems, focusing on control mechanisms and stability analysis through practical examples and mathematical modeling.

Explores general solutions of Cauchy problems and differential equations with integrating factors.

Explores solving EDOs in the form y'(x) = h(y(x)/x) with practical examples and calculation processes.

Explores continuity in analysis through limits of functions and characterization of continuous functions.

Explores Ordinary Differential Equations definitions, solutions, polynomial degrees, autonomous solutions, maximal solutions, and Cauchy's problem.

Explores functions from R^n to R, focusing on graph correspondence and deficiency analysis.

Covers curve length calculations and graphing functions over intervals.

Explores general solutions of differential equations, emphasizing homogeneous and inhomogeneous equations and the process of finding solutions.

Discusses norms, distances, and the classification of open and closed sets in mathematical analysis.

Covers mathematical modeling in chemistry and biology, including chemical reactions, enzymatic kinetics, and population dynamics.

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

Covers the general solution of EOLI in homogeneous and explores linear applications and identity functions.

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

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

Covers the method of plates with coefficients to find solutions of differential equations.

Covers the principles of static equilibrium and the balance of forces in mechanical systems.