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
Lecture 4 (27.07.2026 - Mon): Analytic geometry in 3-dimension (10.1), Distance, Regions corresponding to equations and inequalities, n-dimensional Euclidean space , Vectors (10.2), Addition, Scalar multiplication, Basis vectors, Unit vectors, Linear combination, Scalar (dot) product, Scalar and vector projections
Lecture 5 (29.07.2026 - Wed): Cross product (10.3), Determinants, Properties of cross product, Right-hand rule, 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, Distances from a point to a plane or a line
Lecture 6 (03.08.2026 - Mon): Functions of several variables (12.1), Domain and range, Graphs, Level curves, Level surfaces, Limits and continuity (12.2), Limit properties, Non-existence of limits via different approaching paths
Lecture 7 (05.08.2026 - Wed): Partial derivatives, Tangent planes, Normal lines (12.3), Higher order derivatives, Equality of mixed partial derivatives, Laplace and wave equations (12.4), Chain rule (12.5)
Lecture 8 (10.08.2026 - Mon): Review lecture for the midterm (by Oğuzhan Selçuk)
Lecture 9 (12.08.2026 - Wed): Linear approximations, Differentiability (12.6), 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 10 (17.08.2026 - Mon): 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), Lagrange multipliers (13.3)
Lecture 11 (19.08.2026 - Wed): Multiple integration, Properties of multiple integrals, Double integrals (14.1), Iteration of double integrals in Cartesian coordinates (14.2), Order of integration