CONTENT OF ADVANCED CALCULUS:

Series: definition, algebra operation, convergence, series with positive terms, convergence tests, the radius of convergence, absolute convergence, conditional convergence, alternating series, rearrangement of series terms. Riemann integral: partition, length of partition, upper and lower Riemann integral, Riemann integral and its properties, Darboux integral, primitive of Riemann integrable function and its properties, integral as upper bound function. Gamma and Beta functions.

After completing the course of Advanced Calculus, students are expected to have:

CO 1. the ability to investigate the divergence or convergence of real number series.

CO 2. the ability to determine the convergence interval of power series. 

CO 3. the ability to identify the Riemann integrability of a function according to the definition and its properties, and to have the ability to identify the Darboux integrability of a function according to the definition and its properties.

CO 4. the ability to determine the primitive of Riemann/Darboux integrable function and its properties. 

CO 5. the ability to prove some basic properties of the gamma and beta functions.