MATH-106(f): Analysis II

Lectures in this course (101)

Covers the correction of an exam from 2018, focusing on Taylor polynomials and Jacobian matrices.

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Covers solutions of differential equations with initial conditions and boundedness concepts.

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

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

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

Explores the Euclidean norm, triangular inequality, and distance calculations in R².

Explores finding particular solutions in differential equations using indeterminate coefficients and solving associated homogeneous equations.

Reviews open sets, denseness, real numbers, convergence, curves, continuity, and derivatives in analysis.

Covers the definition of open balls, important subsets, interior points, open sets, closed sets, adhesion points, and border points.

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

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

Covers curve length calculations and graphing functions over intervals.

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

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

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

Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.

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