Section numbers are from the textbook Calculus Adams & Essex Edition 9.
Lecture 1 (22.09.2025 - Mon): Introduction to the course, Syllabus
Lecture 2 (24.09.2025 - Wed): Sequences (9.1), Terminology: bounded above/below, positive/negative, increasing/decreasing, monotonic, alternating sequences, ultimate versions, Convergence and limit of sequences
Lecture 3 (29.09.2025 - Mon): Series (9.2), Geometric series, Harmonic series, Convergence and divergence of series, nth term test for divergence
Lecture 4 (01.10.2025 - Wed): Convergence tests for positive series (9.3), Integral test, p-series, Direct comparison test, Limit comparison test, Ratio test
Lecture 5 (06.10.2025 - Mon): Root test for positive series, Absolute and conditional convergence (9.4), Alternating series test
Lecture 6 (08.10.2025 - Wed): Power series (9.5), Radius of convergence via ratio test, Interval of convergence, Cauchy product of series, Derivatives and integrals of power series, Power series representation of functions, Abel theorem
Lecture 7 (13.10.2025 - Mon): Taylor and Maclaurin series (9.6), Analytic and non-analytic functions, Taylor theorem, Taylor polynomials, Lagrange remainder error terms
Lecture 8 (15.10.2025 - Wed): Applications of Taylor and Maclaurin series (9.7), Approximations, Integral calculations, Indeterminate forms
Lecture 9 (20.10.2025 - Mon): Analytic geometry in 3-dimension (10.1), Distance, Regions corresponding to equations and inequalities, n-dimensional Euclidean space, Terminology: neighborhood, open and closed sets, complement, boundary, interior and exterior
Lecture 10 (22.10.2025 - Wed): Vectors (10.2), Addition, Scalar multiplication, Basis vectors, Linear combination, Scalar (dot) product, Projections, Cross product (10.3), Determinants
Lecture 11 (27.10.2025 - Mon): Planes and lines (10.4), Plane equation via a point and a normal vector, Pencil of planes, Line equation via a point and a direction vector, Distance from a point to a plane and to a line
Lecture 12 (03.11.2025 - Mon): Functions of several variables (12.1), Domain and range, Graphs, Level curves
Lecture 13 (05.11.2025 - Wed): Limits and continuity (12.2), Limit properties, Non-existence of limits via different approaching paths
Lecture 14 (17.11.2025 - Mon): Partial derivatives, Tangent planes, Normal lines (12.3), Higher order derivatives, Equality of mixed partial derivatives (12.4), Chain rule (12.5)
Lecture 15 (19.11.2025 - Wed): Linear approximations, Differentiability (12.6)
Lecture 16 (24.11.2025 - Mon): Gradient of a function, Gradient as a normal vector, Directional derivatives, Relation between the gradient and directional derivative, Maximum rates of increase or decrease (12.7)
Lecture 17 (01.12.2025 - Mon): Implicit functions, Systems of equations, Jacobian, Implicit function theorem (12.8)