Overview

This course is designed to emphasize the core concepts, key computational methods, and essential techniques of Calculus I. We will streamline our focus by skipping trivial details, overly elementary topics, and non-essential theorem proofs.By the end of this course, you will have a solid grasp of all the fundamental topics in Calculus I, establishing a strong foundation for future studies and ensuring you are well-prepared for the final exam.Practice exercises are assigned at the end of each lesson as an essential part of the course. They are designed to help you better understand and master the material. The exercises are concise and won't take much time to complete, so please make an effort to work through them.The course content is organized as follows:1. Methods to evaluate limits: limit laws; l'Hospital's rule; factoring; compare the order of infinity; rationalization;squeeze theorem; limits with trigonometric functions; one-sided limits.2. Continuity and discontinuous points: definition of continuity; removable discontinuous points; step discontinuous points; infinity discontinuous points; oscillating discontinuous point; intermediate value theorem; horizongtal , vertical and slant asymptotes.3. Derivative and defferential rules: definition of derivative; basic differential formulas; summation and subtraction rule; product and quotient rule; chain rule; implicit differentiation; logarithm differentiation; derivative for inverse functions; tangent and normal line; higher order derivatives; linear approximation and differential.4. Applications of derivative: increasing and decreasing; concave up and concave down; local and global maximum and minimum; inflection points; curve sketching; related rates; optimization; Newton's method; mean value theorem.

Skills

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