   ## Calculus I (0301101)

Welcome to Calculus I

Course Description:

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.

Textbook:

James Stewart (2015) Calculus (Early Transcendentals), 8th Edition, Thomson, Metric international version.

References:

- Saturnino Salas, Einar Hille, Garrett Etgen. Calculus: One and Several Variables, 10th Edition.

Howard Anton. Calculus: Early Transcendentals, Single Variable. 10th Edition.​​

Course Syllabus

Lecture notes:

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:​

 Semester Exam Key​ Highest score​ Lowest score Fall 2016 First Exam Solutions 20/20 0/20 Second Exam​ Solutions 30/30 0/30