• views: 113
• date: 16 January 2025
• posted by: voska89

What you'll learn

Methods for finding limits: limit laws, l'Hospital's rule, factoring, rationalization,order o infinity
Continuity and types of discontinuous points: removable,jump,infinity and oscillating discontinuous points
Derivatives: product, quotient, chain rule, implicit differentiation, logarithm differentiation,tangent and normal line
Derivatives and the shape of a curve: increasing, decreasing,maximum, minimum, concave up, concave down, inflection points, asymptotes
Applicatin of derivatives: optimization, related rates,Newton's method

Requirements

You should have completed high school mathematics course.
You should familiar with power functions, exponential functions, logarithm functions, trigonometric functions

Description

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.

Overview

Section 1: Introduction
Lecture 1 Limit laws
Lecture 2 L'Hospital's Rule I
Lecture 3 L'Hospital's Rule II
Lecture 4 L'Hospital's Rule III
Lecture 5 Factoring
Lecture 6 Compare the Order of Infinity
Lecture 7 Rationalization
Lecture 8 Squeeze Theorem
Lecture 9 Limits Involve Trigonometric Functions
Lecture 10 Left and Ritht Limits
Section 2: Continuity and Discontinuous Points
Lecture 11 Continuity
Lecture 12 Removable Discontinuous Points
Lecture 13 Jump Discontinuous Points
Lecture 14 Infinity Discontinuous Points
Lecture 15 Oscillating Discontinuous Points
Lecture 16 Intermediate Value Theorem
Section 3: Asymptotes
Lecture 17 Horizontal and Vertical Asymptotes
Lecture 18 Slant Asymptotes
Section 4: Derivative and Derivative Rules
Lecture 19 Definition of Derivative
Lecture 20 Basic Formulas of Derivative and Summation & Subtraction Rule
Lecture 21 Product Rule
Lecture 22 Quotient Rule
Lecture 23 Tangent and Normal Line
Lecture 24 Chain Rule
Lecture 25 Chain Rule Mixed with Product and Quotient Rule
Lecture 26 Chain Rule Mixed with Summation and Subtraction Rule
Lecture 27 Implicit Differentiation
Lecture 28 Logarithm Differentiation
Lecture 29 Derivative of Inverse Functions
Lecture 30 Higher Order Dirivatives
Lecture 31 Linear Approximation
Section 5: Derivative and Shape of Function
Lecture 32 Increasing and Decreasing
Lecture 33 Concave Up and Concave Down
Lecture 34 Local Maximum and Minimum
Lecture 35 Global Maximum and Minimum
Lecture 36 Inflection Points
Lecture 37 Curve Sketching
Lecture 38 More Examples on Curve Sketching
Section 6: Other Applications of Derivatives
Lecture 39 Related Rates
Lecture 40 Optimization
Lecture 41 Newton's Method
Lecture 42 Mean Value Theorem
For undergraduate students who want to prepare for final exam. For people who want to quick review the key material of calculus I. For people who want to study Calculus I in a concise form.

Homepage:

https://www.udemy.com/course/calculus1-keypoints/

   
   
   

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