Lectures in course MATH-105(b): Advanced analysis II

Advanced Analysis II: Differential Equations and Timers

Discusses advanced analysis concepts, focusing on differential equations and timers in microcontrollers.

Advanced Analysis II: Functions and Equations

Covers the definition and properties of non-constant functions and equations of order 4.

Covers the general solution of Cauchy problems in first-order differential equations.

Explores maximum solutions and their applications in modeling population growth, economic scenarios, and climate, with a focus on exponential growth interpretation and tropical days prediction.

Linear First Order Differential Equations

Covers linear first order differential equations, separation of variables, particular solutions, uniqueness, and coefficients application.

Advanced Analysis II: Resonant Functions

Covers resonant functions such as the Riccati, Bernoulli, and Clairaut equations.

Linear Differential Equations: Second Order with Constant Coefficients

Covers the definitions and solutions of linear differential equations of the second order with constant coefficients.

Advanced Analysis II: Resonant Cases and Variable Coefficients

Covers resonant cases, variable coefficients, and methods for solving differential equations.

Linear Differential Equations of Higher Order

Revises linear differential equations with constant coefficients of higher order and their geometric interpretation.

Advanced Analysis II: Isoclines Method

Explores the Isoclines Method and solutions of differential equations with tangents.

Advanced Analysis II: Recap and Open Sets

Covers a recap of Analysis I and delves into the concept of open sets in R^n, emphasizing their importance in mathematical analysis.

Interior and Closure in Topology

Covers the concepts of interior and closure of a set in a topological space, as well as isolated points and accumulation points.

Continuity of Functions: Definitions and Notations

Explores the continuity of functions in R² and R³, emphasizing accumulation points and limits.

Norm Estimation and Continuity

Covers the estimation of norms and continuity in mathematical functions.

Functions Reciprocal and Monotone: Advanced Analysis II

Explores reciprocal functions, strict monotonicity, and continuity in advanced analysis.

Parametric Curves and Derivatives

Explores parametric curves, derivatives, equivalence of paths, and local behavior of functions.

Advanced Analysis II: Length of Continuously Differentiable Paths

Explores the length of continuously differentiable paths using integrals and parametrizations.

Advanced Analysis II: Functions in R²

Explores functions in R² with sets where x² + y² ≤ 1.

Level Sets and Continuity

Covers level sets and continuity in advanced analysis, emphasizing the importance of understanding level sets for various functions.

Advanced Analysis II: Level Sets and Limits

Explores level sets, limits, and approaches to evaluating limits in advanced analysis.