Lectures related to Piecewise Continuous Functions

Covers the integration of limit expansions and continuous functions by pieces.

Explores Fubini's Theorem for multiple integrals, emphasizing the n=2 case.

Introduces Riemann sums as approximations of the area under a function's graph.

Explores Taylor series for function approximation and properties of definite integrals, including linearity and symmetry.

Covers the definition and properties of multiple integrals, including double and triple integrals.

Covers techniques for computing double integrals using Fubini's Theorem and examples.

Covers the definition of double integrals for functions of two variables over a domain in the plane R^2.

Explores integral calculus fundamentals, including antiderivatives, Riemann sums, and integrability criteria.

Covers Taylor polynomials, function properties, double integrals, partial derivatives, and function boundaries.

Introduces the Dirac delta function and discusses its properties and applications in signal processing and physics.

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

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

Explores double integrals over unbounded domains and convergence of sequences.

Covers integration techniques for series and functions, including power series and piecewise functions.

Explores the integral part of the Fundamental Theorem of Analysis with examples like y = cos(x).

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Explores changing variables in multiple integrals, with a focus on polar transformations and their applications in calculating areas.

Explores the integral change of variable formula and its applications in calculus.

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

Explores the concept of Lebesgue integrability and the criteria for Lebesgue integrability, emphasizing the importance of upper and lower integrals.