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Eddie W.
High school mathematics and technology teacher.
13K karma · Sydney, Australia
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How do you graph parametric equations?
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Are there different kinds of rate of change?
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Half-Angle Identities
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Proving Identities
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Graphing Inverse Trigonometric Functions
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Basic Inverse Trigonometric Functions
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Fractional Exponents
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Graphs of Absolute Value Equations
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Applications of Exponential Functions
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Calculus
1
Introduction to Calculus
Prologue and Historical Context
Prologue to Calculus
Understanding the Gradient function
First Principles for the Gradient Function
2
Derivatives
Normal Line to a Tangent
Finding the Equation of a Normal
First Principles Example 1: x²
First Principles Example: x²
First Principles Example 2: x³
First Principles Example: x³
First Principles Example 3: square root of x
First Principles Example: Square Root of x
Standard Notation and Terminology
Calculus Notation & Terminology
Differentiable vs. Non-differentiable Functions
Differentiability (includes counter-examples)
3
Basic Differentiation Rules
Power Rule
Calculus - Important Results (2 of 2)
Calculus - Important Results (1 of 2)
Product Rule
Why We Need The Product Rule
Product Rule - example question
Proof of the Product Rule
Proving Product Rule
Chain Rule
Chain Rule
Summary of Differentiation Rules
Review - Basic Differentiation Rules
4
Differentiating Trigonometric Functions
Limits Involving Trigonometric Functions
Tricky Trig Limit Question
Intuitive Approach to the derivative of y=sin(x)
Intuitive Approach to Gradient Function of sin(x)
Derivative Rules for y=cos(x) and y=tan(x)
Determining Derivatives for cos(x) & tan(x)
Differentiating sin(x) from First Principles
Differentiating sin(x) from First Principles
Special Limits Involving sin(x), x, and tan(x)
Convergence of sin(x), x, and tan(x)
Evaluating Simple Limits Involving sin x, x & tan x
Graphical Relationship Between sin(x), x, and tan(x), using Radian Measure
Radian Measure result for sin(x), x and tan(x)
Differentiating Inverse Trigonometric Functions
Differentiating sin inverse x & cos inverse x
Differentiating tan inverse x
5
Differentiating Exponential Functions
From First Principles
Differentiating Exponential Functions (First Principles)
Differentiating Exponential Functions with Calculators
Differentiating Exponential Functions (Computer Aided)
Differentiating Exponential Functions with Base e
Differentiating Exponential Functions: e
6
Differentiating Logarithmic Functions
Differentiating Logarithmic Functions with Base e
Differentiating Logarithmic Functions
Differentiating Logarithmic Functions without Base e
Differentiating Logarithmic Functions Without Base e
Overview of Different Functions
Overview of Differentiation Rules
7
Graphing with the First Derivative
Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)
Sign of the First Derivative
Curve Sketching: Locating Stationary Points
Curve Sketching: Determining Nature of SPs
Curve Sketching: Drawing the Graph
Graph Behaviour Chart
Identifying Stationary Points (Critical Points) for a Function
Stationary Points
Non-Turning Stationary Points
Finding Stationary Points
Overview of Critical Points (1 of 2)
Overview of Critical Points (2 of 2)
Overview of Critical Points: Examples (1 of 2)
Overview of Critical Points: Examples (2 of 2)
Identifying Turning Points (Local Extrema) for a Function
Turning Points
Non-Stationary Turning Points (2 of 2)
Finding and Confirming Turning Points
8
Graphing with the Second Derivative
Relationship between First and Second Derivatives of a Function
Second Derivative: Relationship w/ First Derivative
Analyzing Concavity of a Function
Second Derivative: Concavity
Notation for the Second Derivative
Second Derivative: Notation
First Derivative Test vs Second Derivative Test for Local Extrema
Choosing First or Second Derivative
The special case of x⁴
The Special Case of x^4
Critical Points of Inflection
Horizontal Points of Inflexion
Examples of Curve Sketching
Curve Sketching w/ Calculus (Basic Example)
9
Applications of Derivatives
Introduction
Introduction to Max/Min Problems (1 of 2)
Introduction to Max/Min Problems (2 of 2)
Solving Optimization Problems
Max/Min: Squares of Two Numbers (1 of 3)
Max/Min: Squares of Two Numbers (3 of 3)
Max/Min: The A4 Box (1 of 2)
Max/Min: The A4 Box (2 of 2)
Max/Min Problem Solving Steps: The 3 Cs
Max/Min: Rowing/Walking Problem (1 of 2)
Max/Min: Rowing/Walking Problem (2 of 2)
Max/Min: Rectangle Inscribed in Scalene Triangle (1 of 2)
Max/Min: Rectangle Inscribed in Scalene Triangle (2 of 2)
Max/Min: Two Cars Approaching An Intersection (1 of 2)
Max/Min: Two Cars Approaching An Intersection (2 of 2)
Tricky Max/Min Question: Finding the Derivative
Tricky Max/Min Question: Solving for Stationary Points
Max/Min Question w/ Inverse Trig
10
Introduction to Integration
Sigma Notation
Sigma Notation
Integration: the Area Problem
The Story of Integration (1 of 4): Areas Under Curves
The Story of Integration (3 of 4): The Relation to Derivatives
Formal Definition of the Definite Integral
The Story of Integration (4 of 4): Forming & Evaluating an Integral
Definite and indefinite integrals
Definite & Indefinite Integrals
Integrals of Polynomial functions
Reverse Chain Rule for Polynomials: Basic Examples
Reverse Chain Rule for Polynomials: Be Careful!
Reverse Chain Rule for Polynomials: General Rules
Determining Basic Rates of Change Using Integrals
Primitives and Rates of Change (Example 2)
Integrals of Trigonometric Functions
Primitives of Trigonometric Functions
Integrating Basic & Reciprocal Trigonometric Functions
Integrating Squared Trigonometric Functions
Integrals of Exponential Functions
Primitives of Exponential Functions
Integrals of Rational Functions
Reverse Chain Rule for Rational Functions
Basic Properties of Definite Integrals
Properties of Definite Integrals: Constant Co-efficients
Properties of Definite Integrals: Even Functions
11
Techniques of Integration
Evaluating the Constant of Integration
Primitive Functions: Evaluating the Constant
12
Using Integrals to Find Areas and Volumes
Symmetrical Areas
Symmetrical Areas
Calculating Areas using Integrals
Relating Integrals & Areas
Calculating Volume using Integrals
Volumes: Examples around x-axis & y-axis
Compound Volumes (2 of 2)
Deriving Formulae Related to Circles using Integration
Integration & Circle Formulas
13
Methods of Approximating Integrals
Integration Using Simpson's Rule
Simpson's Rule: Deriving the Basic Form (1 of 2)
Simpson's Rule: Deriving the Basic Form (2 of 2)
Simpson's Rule: Multiple Sub-Intervals
Simpson's Rule Example (1 of 2)
Simpson's Rule Example (2 of 2)
14
Applications of Definite Integrals
Net Change: Motion on a Line
Definite Integrals & Total Displacement/Velocity
Determining the Volume of a Solid of Revolution
Introduction to Solids of Revolution
Verifying Formulae for Cylinder, Cone & Sphere
Volumes: Examples around x-axis & y-axis
Compound Volumes (1 of 2)
Compound Volumes (2 of 2)
Volume Involving Trigonometric Functions & Identities
Subtraction of Volumes: Class Discussion
Subtraction of Volumes
15
Tests of Convergence / Divergence
Harmonic Series
Counter-Intuitive Mathematics: The Harmonic Series, e, and Different Infinities
Precalculus
1
Functions Defined and Notation
Domain
Domain & Range
Symmetry
Odd & Even Functions
Odd & Even Polynomials
2
Real Zeros of Polynomials
Synthetic Division
Synthetic Division
Synthetic Division: Longer Example
3
Exponential and Logistic Functions
Exponential and Logistic Graphs
Understanding Exponential Functions and their Gradients: First Principles Approach
Understanding Exponential Functions and their Gradients: Intuitive Approach
4
Exponential and Logistic Modeling
Exponential Growth and Decay
Introduction to Exponential Growth & Decay
Exponential Growth Example (1 of 2)
Exponential Growth Example (2 of 2)
Introducing Exponential Growth Through Compound Interest
Anatomy of an Exponential Growth Question
5
Geometry of a Parabola
Identify Critical Points
Introduction to Conics: Revising the Parabola
6
Geometry of an Ellipse
General Form of the Equation
Introduction to Conics: Meeting the Ellipse
Identify Critical Points
Determining Focus from Equation of Ellipse
Determining Directrix from Equation of Ellipse
7
Geometry of a Hyperbola
General Form of the Equation
Introduction to the Hyperbola
Identify Critical Points
Foci & Directrices of the Hyperbola
Eccentricity, Transverse Axis & Conjugate Axis of the Hyperbola
Asymptotes of the Hyperbola
8
The Binomial Theorem
Powers of the Binomial
Basic Binomial Expansions
Pascal's Triangle and Binomial Expansion
Binomial Theorem & Pascal's Triangle
Pascal's Identity (1 of 2)
Pascal's Identity (2 of 2)
Binomial Identities: Pascal Example
The Binomial Theorem
Binomial Theorem: Introductory Exercises
Factorial Identities
Proving Binomial Identities
9
Sequences
Limits of Infinite Sequences
Limiting Sum of a GP
Arithmetic Sequences
Intro to Arithmetic Progressions (1 of 3)
Intro to Arithmetic Progressions (2 of 3)
Intro to Arithmetic Progressions (3 of 3)
Geometric Sequences
Intro to Geometric Progressions (1 of 2)
Intro to Geometric Progressions (2 of 2)
10
Series
Summation Notation
Sigma Notation
Sums of Arithmetic Sequences
Intro to Arithmetic Progressions (1 of 3)
Intro to Arithmetic Progressions (2 of 3)
Intro to Arithmetic Progressions (3 of 3)
Sums of Geometric Sequences
Intro to Geometric Progressions (1 of 2)
Intro to Geometric Progressions (2 of 2)
Convergence of Geometric Series
Limiting Sum of a GP
Limiting Sum (2013 explanation)
Visualising the Limiting Sum
Limiting Sum: Tricky Questions (1 of 2)
Limiting Sum: Tricky Questions (2 of 2)
11
Limits, Motion, and Areas
Connection to Areas
Relating Integrals & Areas
The Definite Integral
The Story of Integration (1 of 4): Areas Under Curves
The Story of Integration (2 of 4): Riemann's Integral
The Story of Integration (3 of 4): The Relation to Derivatives
The Story of Integration (4 of 4): Forming & Evaluating an Integral
Trigonometry
1
Trigonometric Identities and Equations
Proving Identities
Proving Trig Identities with t-results
Proving Simple Trigonometric Identities
Half-Angle Identities
Half-Angle Results
Questions Involving "Half-Angle" Results
2
Inverse Trigonometric Functions
Basic Inverse Trigonometric Functions
Introduction to Inverse Trig Functions (1 of 2): Why a whole new topic?
Introduction to Inverse Trig Functions (2 of 2): Reviewing Functions & Relations
Inverse Trigonometric Functions: sin x & cos x
Inverse Trigonometric Functions: tan x
Graphing Inverse Trigonometric Functions
Graphing Inverse Trig Functions (1 of 2)
Graphing Inverse Trig Functions (2 of 2)
Graphing y = sin (sin inverse x)
Graphing y = sin inverse (sin x)
Graphing y = cos inverse (cos x)
Graphing y = tan inverse (tan x)
Algebra
1
Linear Inequalities and Absolute Value
Graphs of Absolute Value Equations
Graphing Composite Absolute Value Functions
2
Exponents and Exponential Functions
Exponential Properties Involving Products
How to Use Basic Index Laws
Overview of the Multiplication/Division Index Laws
Negative Exponents
Negative Indices
Rewriting Expressions w/ Negative Indices (Basic Examples)
Fractional Exponents
What happens when the power isn't a whole number? (Fractional Indices)
Working w/ Fractional Indices: Basic Example Questions
Scientific Notation
Scientific Notation (1 of 3): Review of Index Notation
Scientific Notation (2 of 3): Review of Significant Figures
Scientific Notation (3 of 3): Why it exists, and how to write it
Review: Converting Numbers to Scientific Notation
Scientific Notation with a Calculator
Entering & Interpreting Scientific Notation on Calculators
Exponential Growth
Exponential Growth Example: Insect Population
Introduction to Exponential Growth & Decay
Exponential Growth Example (1 of 2)
Exponential Growth Example (2 of 2)
Exponential Decay
Exponential Decay Example 1: The Fridge
Considering the Nature of Exponential Decay
Applications of Exponential Functions
A more sophisticated model for Exponential Growth & Decay with constraints
Introduction to Growth & Decay with Constraints
Modified Growth & Decay: Introductory Thoughts
Modified Growth & Decay: Example Problem (1 of 2)
Modified Growth & Decay: Example Problem (2 of 2)
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