PreCalculus

Lines and Planes Videos

Parallel Lines, Skew Lines and Planes

Proving Parallel Lines

Functions and Transformation of Graphs Videos

Difference Quotient of Function I
Difference Quotient of Function II

Domain of a Function

Greatest Integer Function I
Greatest Integer Function II

Piece-Wise Functions I
Piece-Wise Functions II
Piece-Wise Functions III

Even and Odd Functions I
Even and Odd Functions II

Parent Functions and their Graphs

Transformation of Linear Functions

Transformation of Quadratic Functions

Horizontal and Vertical Graph Transformations

Horizontal And Vertical Graph Stretches and Compressions.

Reflective Transformations

Examples of Graph Transformations

Composite Functions I
Composite Functions II
Composite Functions III

One-to-one Functions

Inverse of a Function I
Inverse of a Function II

Polynomials Videos

Power Functionns

Polynomial Functions

Graphing Polynomial Functions I
Graphing Polynomial Functions II

Families of Polynomials

Graphing Polynomials with Repeated Factors

Finding the Equation of a Polynomial Function

Finding Maximum and Minimum Values of Polynomial Functions

Finding the Zeros of a Polynomial Function I
Finding the Zeros of a Polynomial Function II

Conjugate Zeros Theorem

Reciprocal of a Function

Rational Functions Videos

Introduction to Rational Functions

Limits of Rational Functions

Graphing Rational Functions I
Graphing Rational Functions II

Horizontal Asymptotes I
Horizontal Asymptotes II

Vertical Asymptotes

Vertical and Horizontal Asymptotes

Oblique or Slant Asymptotes

Graphing Rational Functions with Holes

Rational Function Problems

Limits of a Function

Introduction to Limits of Functions

Limits of Rational Functions

Examples to Learn about Limits

Calculating Limits using Different Techniques I
Calculating Limits using Different Techniques II

Limit Laws to Evaluate a Limit

One Sided Limits
Squeeze Theorem for Limits

The Limit defimition of Continuity

Complex Numbers Videos

Introduction to Complex Numbers I
Introduction to Complex Numbers II

Adding and Subtracting Complex Numbers
Multiplying Complex Numbers
Dividing Complex Numbers

Trigonometric or Polar Form of Complex Numbers

Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form

Roots of a Complex Number 

Complex Quadratic Equations I
Complex Quadratic Equations II

Simplify Complex Rational Expressions

Basic Complex Analysis
Exponential form to find complex roots
Complex Conjugates
Complex Determinant Example

Exponential Function Videos

Introduction to Exponential Functions

Graphing Exponential Functions I
Graphing Exponential Functions II

Applying Exponential Functions I
Applying Exponential Functions II

Solving Exponential Equations with the Same Base

Solving Exponential Equations with Different Bases I
Solving Exponential Equations with Different Bases II
Solving Exponential Equations with Different Bases III

Logarithmic Function Videos

Introduction to Logarithmic Functions

Exponential and Logarithmic Functions

Logarithm Review - Product Rule
Logarithm Review - Product & Quotient Rules
Logarithm Review - Power Rule
Logarithm Review - Change of Base Rule

Properties of Logarithms (or Rules of Logarithms)
Proof of Logarithm Properties

Expanding Logarithmic Expressions
Simplifying (or Condensing) Logarithmic Expressions
Simplifying and Expanding Logarithmic Expressions

Solving Logarithmic Equations I
Solving Logarithmic Equations II

Graphs of Logarithmic Functions

Conic Sections Videos

Introduction to Conic Sections

Conic Sections - Circles I
Conic Sections - Circles II

Conic Sections - Ellipses I
Conic Sections - Ellipses II

Conic Sections - Parabolas

Conic Sections - Hyperbolas I
Conic Sections - Hyperbolas II
Conic Sections - Hyperbolas III

Conic Sections Summary

Identify and Graph Conic Sections

Matrices Videos

Introduction to Matrices

Matrix Addition and Subtraction I
Matrix Addition and Subtraction II

Matrix Scalar Multiplication

Matrix Multiplication I
Matrix Multiplication II
Matrix Multiplication III

Identity Matrix

Determinant of a 2x2 Matrix

Determinant of a 3x3 Matrix I
Determinant of a 3x3 Matrix II

Simplifying Determinant

Inverse of 2x2 Matrix I
Inverse of 2x2 Matrix II

Inverse of 3x3 Matrix

Singular Matrix - A Matrix with no Inverse

Solving a 2x2 System of Equations Using a Matrix Inverse I
Solving a 2x2 System of Equations Using a Matrix Inverse II

Solving a 3x3 System of Equations Using a Matrix Inverse
Using Gauss-Jordan to Solve a System of Three Linear Equations

Row Reducing a Matrix to solve a System of Equations
Solving a System of Equations using Matrix Row Transformations

Cramer's Rule

Using Determinant to find the Area of a Parallelogram

Cross Product of Vectors and Determinants

Sequences and Series Videos

Introduction to Sequences

Arithmetic Sequences I
Arithmetic Sequences II

Arithmetic Sequences - Finding the nth Term

Geometric Sequences I
Geometric Sequences II

Geometric Sequences - Finding the nth Term

Recursion Sequences

Series and Summation

Arithmetic Series I
Arithmetic Series II

Geometric Series I
Geometric Series II

Infinite Geometric Series

Mathematical Induction

Examples of Mathematical Induction I
Examples of Mathematical Induction II

Probabilty and Combinatorics Videos

Introduction to Probability I
Introduction to Probability II

Fundamental Counting Principles

Permutations I
Permutations II
Permutations III

Combinations I
Combinations II

Permutations and Combinations

Probability of Multiple Events

Probability of Independent Events

Probability of Dependent Events

Probabilty of Complementary Events

Conditional Probability I
Conditional Probability II
Conditional Probability III

Pascal's Triangle and the Binomial Theorem
Binomial Theorem I
Binomial Theorem II

Advanced Trigonometry Videos

Inverse Trigonometric Functions I
Inverse Trigonometric Functions II

Factoring Trigonometric Equations

Trig Identities - cofunctions, reciprocal, quotient, ratio, Pythagorean, and even/odd

Sum and Difference Identities I
Sum and Difference Identities II

Sine and Cosine Addition Formulas

Double Angle Identities I
Double Angle Identities II

Power Reducing Identities

Half Angle Identities

Half Angle and Double Angle Examples

Vectors and Parametric Equations Videos

Geometric Representation of Vectors
Algebraic Representation of Vectors

Components of a Vector I
Components of a Vector II

Adding Vectors Graphically or Head-to-Tail Method

Adding Vectors using Components I
Adding Vectors using Components II

Vector Addition and Scalar Multiplication

Vector Magnitude and Direction

The Resultant of Two Forces
Components of a Force

Solve Navigation Problems using Vectors

Unit Vectors I
Unit Vectors II

Vector Equation of a Line

Parametric Equations and Motion
Parameterize a Line Segment and a Circle
Parametric Equations

Dot Product of Vectors
Angle between Two Vectors

Vectors in Three Dimensions
Lines in 3D Coordinate Systems

Vectors and Planes I
Vectors and Planes II

Polar Coordinates Videos

Introduction to Polar Coordinates

Conversion between Polar Coordinates & Rectangular Coordinates

Polar Coordinates Distance Formula

Equations of Lines in Polar Coordinates 

Symmetry of Polar Graphs

Graphing Polar Equations

Families of Polar Curves: Circles, Cardiods, Limaçon, Roses & Conic Sections

IIT JEE Questions

IIT JEE Trigonometry Problem
IIT JEE Perpendicular Planes
IIT JEE Complex Root Probability
IIT JEE Position Vectors
ITT JEE Matrix Equations
IIT JEE Integral Limit
IIT JEE Algebraic Manipulation
IIT JEE Function Maxima
IIT JEE Diameter Slope
IIT JEE Hairy Trig and Algebra
IIT JEE Complex Numbers
IIT JEE Differentiability and Boundedness
IIT JEE Integral with Binomial Expansion
IIT JEE Symmetric and Skew-Symmetric Matrices
IIT JEE Trace and Determinant
IIT JEE Divisible Determinants
IIT JEE Circle Hyperbola Intersection
IIT JEE Circle Hyperbola Common Tangent
IIT JEE Trigonometric Constraints
IIT JEE Trigonometric Maximum
Vector Triple Product Expansion (very optional)
IIT JEE Lagrange's Formula
Tangent Line Hyperbola Relationship (very optional)
2010 IIT JEE Paper 1 Problem 50 Hyperbola Eccentricity
Normal vector from plane equation
Point distance to plane
Distance Between Planes
Periodic Definite Integral
Complex Determinant Example
Series Sum Example
Trigonometric System Example
Simple Differential Equation Example

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