Course

MATH-106(f): Analysis II

Lectures in this course (84)

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

Covers the theorem of implicit functions for n>2, with examples demonstrating the application of the theorem.

Covers the derivation of an integral dependent on a parameter, focusing on the analysis of functions and their properties.

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.

Explains extrema of functions in several variables, stationary points, saddle points, and the role of the Hessian matrix.

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

Explores Lagrange multipliers for optimizing functions in 2 variables, emphasizing global and local extrema.

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

Explores continuity and limits, emphasizing their relationship and practical applications in function analysis.

Covers the nature of extremum points and their classification as stationary or saddle points.

Explores the Fubini theorem on closed rectangles in R², discussing integrability, iterated integrals, and compact sets.

Explores curve length, function definition, continuity, derivatives, integrals, and graphical representations of functions in two variables.

Explores differentiability in R², discussing key properties and the theorem of the two genderines.

Explores optimization with inequality constraints, emphasizing finding extreme values and stationary points.

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

Explores domains defined by level leagues and double integrals over such domains.

Covers the variable change theorem in polar coordinates and its applications.

Covers differentiability, composition of functions, partial derivatives, Jacobian matrix, and polar coordinates.

Explores the geometric interpretation of derivatives and properties of derivable functions.