Calculus Ii

AY2022/2023 Semester 2

This course aims to develop fundamental mathematical concepts such as definite integrals and their applications to find areas and volumes, Fundamental Theorem of Calculus, integration techniques, tests for convergence and divergence of sequences and series, interval and radius of convergence of power series, differentiation and integration of power series, and Taylor series. Techniques learned in this course will prepare students for more advanced quantitative courses in mathematics, science and engineering. Antiderivatives and definite integral, Fundamental Theorem of Calculus, improper integrals, substitution rule, area between curves, volume using the disk/washer method, volume using the cylindrical shell method, integration by parts, trigonometric substitution, integration using partial fractions, limit of sequences, integral test, comparison test, absolute/conditional convergence, the ratio test, the root test, power series, radius and interval of convergence, Taylor and Maclaurin series, the binomial series.