Section numbers are from the textbook Calculus Adams & Essex Edition 9.
Lecture 1 (13.07.2026 - Mon): Introduction to the course, Syllabus, Sequences (9.1), Terminology: bounded above/below, positive/negative, increasing/decreasing, monotonic, alternating sequences, ultimate versions, Convergence of sequences
Lecture 2 (20.07.2026 - Mon): Series (9.2), Geometric series, Harmonic series, Convergence and divergence of series, Convergence tests for positive series (9.3), Integral test, p-series, Direct comparison test, Limit comparison test, Ratio test, Root test, Absolute and conditional convergence (9.4), Alternating series test
Lecture 3 (22.07.2026 - Wed): Power series (9.5), Radius of convergence via ratio test, Interval of convergence, Derivatives and integrals of power series, Power series representation of functions, Taylor and Maclaurin series (9.6), Analytic and non-analytic functions, Taylor theorem, Taylor polynomials, Applications of Taylor and Maclaurin series (9.7), Approximations, Indeterminate forms