Precalculus: Algebra, Functions, And Trigonometry

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: 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