Section numbers are from the textbook Calculus Adams & Essex Edition 9.
Lecture 1 (16.02.2026 - Mon): Introduction to the course, Syllabus
Lecture 2 (18.02.2026 - Wed): Sequences (9.1), Terminology: bounded above/below, positive/negative, increasing/decreasing, monotonic, alternating sequences, ultimate versions
Lecture 3 (23.02.2026 - Mon): Convergence of sequences, Series (9.2), Geometric series, Harmonic series, Convergence and divergence of series
Lecture 4 (25.02.2026 - Wed): Convergence tests for positive series (9.3), Integral test, p-series, Direct comparison test
Lecture 5 (02.03.2026 - Mon): Limit comparison test, Ratio test, Root test, Absolute and conditional convergence (9.4), Alternating series test
Lecture 6 (04.03.2026 - 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
Lecture 7 (09.03.2026 - Mon): Abel's theorem, Taylor and Maclaurin series (9.6), Analytic and non-analytic functions, Taylor theorem, Taylor polynomials, Lagrange remainder error terms
Lecture 8 (11.03.2026 - Wed): Applications of Taylor and Maclaurin series (9.7), Approximations, Integral calculations, Indeterminate forms
Lecture 9 (16.03.2026 - Mon): Analytic geometry in 3-dimension (10.1), Distance, Regions corresponding to equations and inequalities, n-dimensional Euclidean space
Lecture 10 (18.03.2026 - Wed): Vectors (10.2), Addition, Scalar multiplication, Basis vectors, Linear combination, Scalar (dot) product, Scalar and vector projections
Lecture 11 (23.03.2026 - Mon): Cross product (10.3), Determinants, Properties of cross product, Right-hand rule
Lecture 12 (25.03.2026 - Wed): 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
Lecture 13 (30.03.2024 - Mon): Functions of several variables (12.1), Domain and range, Graphs, Level curves, Level surfaces
Lecture 14 (01.04.2026 - Wed): Limits and continuity (12.2), Limit properties, Non-existence of limits via different approaching paths
Lecture 15 (06.04.2026 - Mon): Partial derivatives, Tangent planes, Normal lines (12.3)
Lecture 16 (08.04.2026 - Wed): Higher order derivatives, Equality of mixed partial derivatives, Laplace and wave equations (12.4)
Lecture 17 (15.04.2026 - Wed): Chain rule (12.5), Linear approximations (12.6)
Lecture 18 (20.04.2026 - Mon): Differentiability, 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 19 (22.04.2026 - Wed): Implicit functions, Systems of equations, Jacobian, Implicit function theorem (12.8)
Lecture 20 (29.04.2026 - Wed): Applications of partial derivatives (13.1), Extreme values, Classification of critical points, Second derivative test, Extreme values of functions defined on restricted domains (13.2)
Lecture 21 (04.05.2026 - Mon): Lagrange multipliers (13.3)
Lecture 22 (11.05.2026 - Mon): Multiple integration, Properties of multiple integrals, Double integrals (14.1), Iteration of double integrals in Cartesian coordinates (14.2), Order of integration
Lecture 23 (18.05.2026 - Mon): Change of coordinates, Jacobian, Polar coordinates, Double integral in polar coordinates (14.4), Cylindrical coordinates, Triple integral in cylindrical coordinates (14.6)
Lecture 24 (20.05.2026 - Wed): Triple integration, Iteration of triple integrals in Cartesian coordinates (14.5), Spherical coordinates, Triple integral in spherical coordinates (14.6)