Section numbers are from the textbook Calculus Adams & Essex Edition 9.
Lecture 1 (08.07.2024 - Mon): Introduction to the course, Syllabus, History of calculus, Preliminaries, Real numbers (P1), Cartesian coordinates (P2), Quadratic equations (P3)
Lecture 2 (10.07.2024 - Wed): Preliminaries, Functions and graphs (P4), Scaling and shifting of graphs (P3), Operations on functions (P5), Polynomials (P6), Trigonometry (P7)
No class for 15.07.2024 - Mon due to the national holiday
Lecture 3 (17.07.2024 - Wed): 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), Continuity (1.4), One-sided continuity, Continuous extension, Maximum-minimum theorem, Intermediate value theorem
Lecture 4 (22.07.2024 - Mon): The notion of derivative (2.2), One-sided derivatives, Derivatives of fundamental functions, Differentials, Tangent lines, Differentiation rules (2.3), Leibniz rule, Chain rule (2.4), Derivatives of trigonometric functions (2.5), Higher order derivatives (2.6)
Lecture 5 (24.07.2024 - Wed): Mean value theorem and its proof (2.8), Rolle's theorem, Fermat's theorem, Increasing and decreasing functions, Implicit differentiation (2.9), Folium of Descartes
Lecture 6 (29.07.2024 - Mon): Transcendental numbers and functions, Inverse notion for functions (3.1), Exponential and logarithm (3.2), Natural logarithm and exponential (3.3), Logarithmic differentiation
Lecture 7 (31.07.2024 - Wed): Inverses of trigonometric functions (3.5), Review for the midterm
Lecture 8 (05.08.2024 - Mon): Indeterminate forms, L’Hospital’s rule (4.3), Review for the midterm, MIDTERM in the afternoon session
Lecture 9 (07.08.2024 - Wed): Extreme values (4.4), Critical, singular, end, inflection points, Concavity (4.5), First and second derivative tests, Sketching graphs of functions (4.6), Applications of extreme values (4.8)
Lecture 10 (12.08.2024 - Mon): Sigma notation for sums (5.1), Areas as limits of sums (5.2), Riemann sums (upper and lower), Partitions, Integrability, Definite integral (5.3), Properties of definite integrals (5.4), Fundamental theorem of calculus (5.5)
Lecture 11 (14.08.2024 - Wed): Techniques of integration, Substitution method (5.6), Integration by parts (6.1), Integration of rational functions (6.2), Inverse substitution method (6.3)
Lecture 12 (19.08.2024 - Mon): Techniques of integration recall, Improper integrals (6.5)
Lecture 13 (21.08.2024 - Wed): Applications of integration, velocity and acceleration (2.11), Areas of plane regions (5.7), Solids of revolution (7.1), Review for the final, Closing remarks