Akademik Dersler - İçerik

Will be able to explain the concept of the Riemann integral and its fundamental properties.
Defines Riemann–Darboux lower and upper sums.
Explains the definite integral of a function and its properties.
States the fundamental theorem of differential and integral calculus.
Explains the concept of the indefinite integral.
Will be able to analyze Riemann integrability and related criteria.
Explains the concept of sets of measure zero.
Determines whether a function is Riemann integrable.
Explains the relationship between integrability and continuity.
Will be able to classify improper integrals and examine their convergence.
Classifies improper integrals according to their types.
Applies convergence tests for improper integrals.
Defines the Gamma function and explains its fundamental properties.
States and applies the Wallis formula.
Will be able to use the concept of the integral in theoretical and applied problems.
States the mean value theorem for integrals.
Explains and applies Taylor theorem with integral remainder.
Will be able to analyze some special integrals and related problems.
States the Basel problem and explains its solution approach.
Defines the real Riemann zeta function.
Will be able to explain the concept of transcendental functions and properties of certain numbers.
Explains the concept of transcendental functions.
Explains the transcendence of some elementary functions.
Explains the irrationality of the number e.
Explains the irrationality of the number pi.
Will be able to analyze the concept of Fourier series and their fundamental properties.
Defines Fourier series.
Obtains the Fourier series of a function.
Explains the convergence properties of Fourier series.
Applies Fourier series to practical problems.