Section numbers are from the textbook Calculus Adams & Essex Edition 7.
Lecture 1 (25.09.2024 - Wed): Introduction to the course, Syllabus, Preliminaries, Real numbers (P1), Cartesian coordinates (P2), Functions and graphs (P4), Operations on functions (P5), Polynomials (P6)
Lecture 2 (30.09.2024 - Mon): Preliminaries recall and exercises
Lecture 3 (02.10.2024 - Wed): Polynomials in detail, Euclidean division, Quadratic equations (P3), Conic sections, Circles, Ellipses, Parabolas, Hyperbolas, Trigonometric functions (P7)
Lecture 4 (07.10.2024 - Mon): The notion of limit (1.2), One-sided limits, Informal and formal definitions of limit, Examples and properties of limit, Squeeze theorem, Limits at infinity and infinite limits (1.3)
Lecture 5 (09.10.2024 - Wed): Continuity (1.4), One-sided continuity, Continuous extension, Maximum-minimum theorem, Intermediate value theorem, Tangent and normal lines (2.1), The notion of derivative (2.2), One-sided derivatives, Derivatives of fundamental functions
Lecture 6 (14.10.2024 - Mon): Derivative recall, Differentiation rules (2.3), Leibniz rule, Chain rule (2.4)
Lecture 7 (16.10.2024 - Wed): Differentiation and chain rules recall, Derivatives of trigonometric functions (2.5), Proof of the fact that the derivative of sine function is the cosine, Higher order derivatives (2.6)
Lecture 8 (21.10.2024 - Mon): Trigonometry and higher order derivatives recall, Implicit differentiation (2.9), Folium of Descartes, Anti-derivatives and indefinite integrals (2.10 partially)
Lecture 9 (23.10.2024 - Wed): Mean value theorem (2.8), Increasing and decreasing functions
Lecture 10 (28.10.2024 - Mon): Proof of mean value theorem, Rolle's theorem, Fermat's theorem, Inverse functions (3.1)
Lecture 11 (30.10.2024 - Wed): Inverse functions recall, Derivative of a function's inverse, Algebraic and transcendental numbers, Transcendental functions, Exponential and logarithm (3.2)
Lecture 12 (04.11.2024 - Mon): Natural logarithm and exponential (3.3), Logarithmic differentiation, Inverses of trigonometric functions and their derivatives (3.5)
Lecture 13 (06.11.2024 - Wed): Inverses of trigonometric functions recall, Indeterminate forms, L’Hospital’s rule (4.3)
Lecture 14 (11.11.2024 - Mon): Extreme values (4.4), Local and absolute maximum and minimum, Singular and critical points, endpoints, First derivative test
Lecture 15 (14.11.2024 - Thu): Concavity (4.5), Inflection points, Second derivative tests, Sketching graphs of functions (4.6), Vertical, horizontal, oblique asymptotes
Lecture 16 (18.11.2024 - Mon): Applications and problems of extreme values (4.8), Sigma notation for sums (5.1), Areas as limits of sums (5.2), Riemann sums (upper and lower), Partitions, Integrability, Definite integral (5.3)
Lecture 17 (20.11.2024 - Wed): Riemann sums recall, Properties of definite integrals (5.4), Mean value theorem for integrals, Average value or mean of a function, Fundamental theorem of calculus (5.5)
Lecture 18 (25.11.2024 - Mon): Method of substitution (5.6)
Lecture 19 (02.12.2024 - Mon): Areas of plane regions (5.7), Integrals with respect to x and y variables, Area and volume elements
Lecture 20 (04.12.2024 - Wed): Integration by parts (6.1)
Lecture 21 (09.12.2024 - Mon): Partial fraction decomposition of rational functions, Integration of rational functions (6.2)
Lecture 22 (16.12.2024 - Mon): Method of inverse substitution (6.3)
Lecture 23 (23.12.2024 - Mon): Improper integrals of type I and type II (6.5), Convergence and divergence of integrals
Lecture 24 (25.12.2024 - Wed): Volume calculations (7.1), Solids of revolution, Slicing to disks, Cylindrical shells, Closing remarks