Functions: domain, operations on functions, graphs of functions; trigonometric functions; limits: meaning of a limit, computational techniques, limits at infinity, infinite limits; continuity; limits and continuity of trigonometric functions; the derivative: techniques of differentiation, derivatives of trigonometric functions; the chain rule; implicit differentiation; differentials; Roll’s Theorem; the mean value theorem; the extended mean value theorem; L’Hopital’s rule; increasing and decreasing functions; concavity; maximum and minimum values of a function; graphs of functions including rational functions (asymptotes) and functions with vertical tangents (cusps); antiderivatives; the indefinite integral; the definite integral; the fundamental theorem of calculus ; area under a curve; area between two curves; transcendental functions: inverse functions, logarithmic and exponential functions and their derivatives and integrals; limits (the indeterminate forms); hyperbolic functions and their inverses; inverse trigonometric functions; some techniques of integration.
James Stewart (2015) Calculus (Early Transcendentals), 8th Edition, Thomson, Metric international version.
- Saturnino Salas, Einar Hille, Garrett Etgen. Calculus: One and Several Variables, 10th Edition.
- Howard Anton. Calculus: Early Transcendentals, Single Variable. 10th Edition.
Course Syllabus: Click here!
The following lecture-by-lecture notes were handwritten by Dr. Baha Alzalg.
These materials might not be used for commercial purposes without my consent.
- Functions (PDF).
- Limits (PDF).
- Continuity (PDF).
- Vertical and horizontal asymptotes (PDF).
- Differentiantion (PDF).
- Chain rule, more on differentiantion (PDF).
- Rate of change, velocity, acceleration (PDF).
- Implicit differentiantion (PDF).
- Derivatives of inverse and hyperbolic functions (PDF).
- Differentials and linearization (PDF).
- Indeterminate forms and l'Hospital's rule (PDF).
- The mean value theorem (PDF).
- Increasing/decreasing functions and extrema (PDF).
- Concavity (PDF).
- Curve sketching (PDF).
- The definite integral (PDF).
- The fundamental theorem of calculus (PDF).
- The indefinite integral (PDF).
- Integration by substitution (PDF).
Exams & Keys: