Tutorials > Precalculus Algebra, Functions, And Trigonometry

Precalculus Algebra, Functions, And Trigonometry


Date: 31 August 2022 | Posted by: voska89
Precalculus Algebra, Functions, And Trigonometry
Published 8/2022
MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz
Language: English | Size: 630.91 MB | Duration: 2h 36m


Get prepared for Calculus by bridging the gaps between high school and university.
What you'll learn
The origin and history of Calculus
The definition of a set, and different notations involving relationships between sets and elements.
The set of Real Numbers, along with the definition Natural Numbers, Integers, and Rational vs Irrational numbers.
The definition of the absolute value, including inequalities and order properties
Bounded functions and sets in the set of real numbers
Algebra, including the quadratic equation, powers and roots
Geometry, including volume, area, and circumference for both 2D and 3D solids
Inequalities, including solving for a solution set around large polynomials
The coordinate plane, including distance, midpoints, slopes, and parallel vs perpendicular lines
Functions, including the domain, range, vertical line test, and odd vs even symmetry
Restrictions on domains for functions, involving vertical and horizontal asymptotes
Elementary functions such as rational functions, polynomials and trigonometric functions
Trigonometry, including the difference between degree and radian measure
Combinations of functions, including linear combinations and function composition
Requirements
Grade 12 Math
Description
Precalculus:В Algebra, Functions and Trigonometry1. Introduction to the courseA little about myself, and an overview of the course.2. What is Calculus?In this section, you will have a brief overview on the history of calculus and how it has come to its current state. (Optional Section)3. Elementary MathematicsIn this section you will learn about sets, real numbers, boundedness, absolute value, algebra and geometry.4. Inequalities and Solution SetsIn this section you will learn how to find a solution set to an inequality that may involve absolute values.5. The Coordinate Plane; Analytic GeometryIn this section you will learn about the coordinate plane. Students will be exposed to finding the distance between two points on a plane, along with find the midpoint and slope of a line. Examples will include finding a line that is parallel or perpendicular as well as solve for the point of intersection.6. FunctionsIn this section students will learn about the domain and range of a function. Moreover, students will learn about the vertical line test and how to graph a function. Lastly, we will apply some domain restrictions on a function and solve for the domain and range.7. Polynomials and Trigonometric FunctionsIn this section students will learn about polynomials and their degrees. Additionally, we will be introduced to sine and cosine in a new way, along with understanding the difference between radian and degree measure.8. Combinations of FunctionsIn this section students will learn about function composition and linear combinations.
Overview
Section 1: Introduction
Lecture 1 Welcome to Precalculus
Lecture 2 Course Overview
Section 2: Chapter 1: What is Calculus?
Lecture 3 History of Calculus
Section 3: Chapter 2: Elementary Mathematics
Lecture 4 Introduction to elementary mathematics and sets
Lecture 5 Sets Example
Lecture 6 Real Numbers
Lecture 7 Decimal Representation
Lecture 8 Number Line
Lecture 9 Order Properties
Lecture 10 Absolute Value
Lecture 11 Triangle Inequality
Lecture 12 Intervals
Lecture 13 Boundedness
Lecture 14 Factorials
Lecture 15 Algebra
Lecture 16 Polynomials
Lecture 17 Polynomial Example
Lecture 18 Geometry
Section 4: Inequalities
Lecture 19 Introduction to inequalities
Lecture 20 Example 2 - Inequalities
Lecture 21 Example 3 - Inequalities
Lecture 22 Inequalities and Absolute Value
Lecture 23 Example 4 - Inequalities
Lecture 24 Example 4 - On your own
Section 5: Coordinate Plane; Analytic Geometry
Lecture 25 Introduction to the Coordinate Plane
Lecture 26 Distance
Lecture 27 Midpoint
Lecture 28 Example - Distance and Midpoint
Lecture 29 Lines and Slopes
Lecture 30 Intermission
Lecture 31 Example - Parallel Lines
Lecture 32 Example - Perpendicular line (on your own)
Lecture 33 Example - Line Intersection
Section 6: Functions
Lecture 34 Domain and Range
Lecture 35 Graph of a Function
Lecture 36 Example - Graphing a function
Lecture 37 Vertical Line Test
Lecture 38 Even and Odd Functions; Symmetry
Lecture 39 Conventions on Domain
Lecture 40 Example - Conventions on Domains
Section 7: Elementary Functions
Lecture 41 Polynomial of Degree 1 and 2
Lecture 42 Polynomial of Degree 3
Lecture 43 Rational Functions and Asymptotes
Lecture 44 Example - Rational Functions
Lecture 45 Trigonometry Introduction
Lecture 46 Degrees vs Radians
Lecture 47 Sine and Cosine
Lecture 48 Trigonometry Continued and Example
Section 8: Combinations of Functions
Lecture 49 Introduction to combination of functions
Lecture 50 Linear Combinations
Lecture 51 Function Composition
Lecture 52 Example - Function Composition
Section 9: Thank you!
Lecture 53 Thank you!
This course is for students looking to begin their journey in Calculus.,This course is for students looking for a refresher in higher level math


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